Category Archives: Semantics in Medical Science Literature

Causation in Medical Scientific Statements

The concept of causation is a very difficult philosophical topic and doesn’t. The causation implied by the Research Analysis model has been of interest to me for some time, but the inspiration for this article came from Handbook of Analytic Philosophy of Medicine by Kazem Sadegh-Zadeh [1]. Sadegh-Zadeh provides a great overview of the philosophy of causation and, in particular, Etiology the science of clinical causation. “Etiology, from the Greek term αιτια (aitia) meaning “the culprit” and “cause”, is the inquiry into clinical causation or causality including the causes of pathological processes and maladies” [1].

In this article, I will explore some of the tools provided in the handbook (You should refer to section 7.5 of the handbook for a more thorough introduction and overview) and discuss how they can be applied to the Research Analysis model. I will explore the probabilistic interpretations of claims, the concept of causation in relation to claims and the causal relevance of competing claims.

Probabilistic dependence

Let’s take an example claim from Research Analysis:

(1)         Statins decrease coronary events in normal humans

This claim can be found in Research Analysis here and its semantics are analysed in this previous article here. The semantic analysis resulted in the following logical description of the claim:

(2)         ꓯe (DECREASE(statin, myocardial infarction, e) & IN(e, normal human))

Where e represents an event. In my previous article, I discussed that the word case may be more natural than event for this model, where “the concept of a case suggests that the time period and medical process will be appropriate to the specific disease treatment paradigm”.

A lot of the logical formalisation relates to the event or case. If one specific case is considered then we have the simpler claim:

(3)         DECREASE(statin, myocardial infarction)

This claim suggests that there is a decreasing relationship between:

  • The administration of statins, and
  • Myocardial infarction.

At this point probability theory can be introduced. Sadegh-Zadeh [1, p253] shows using probability theory that an event B is probabilistically independent of another event A if and only if (iff):

(4)         P(B|A) = p(B)

Where P(B|A) is the probability of the event B conditional on the fact that the event A has occurred. If events A and B are independent then the fact that event A has occurred will have no impact on the probability of event B occurring and thus the conditional probability will simply equal the probability of B occurring independently of A.

Dependence of two events is then simply represented by the opposite probability relationship:

(5)         P(B|A) ≠ p(B)

That is, two events are dependent if the conditional probability of B given A is not equal to the probability of even B occurring independently – the fact that A occurred effects the probability that B will occur.

Coming back to the simple example, the claim “The administration of statins decreases myocardial infarction” implies that there is a conditional dependence between the two events and that:

(6)         p(Myocardial infarction | The administration of statins) ≠ p(Myocardial infarction)

That is, the probability of myocardial infarction given that statins have been administered to the patient is not equal to the probability of myocardial infarction in general. There is a probabilistic dependence between the event of statin administration and myocardial infarction.

Note that this probabilistic “dependence” does not imply that there is any causal interaction between the two events A and B or myocardial infarction and statins, only that there is a probabilistic correlation between the events. Correlation may exhibit one of two directions in particular cases giving:

(7)         Positive correlation:       p(B|A) > p(B)

(8)         Negative correlation:     p(B|A) < p(B)

In our example, “decrease” is intended to mean that there is a negative correlation between the events and using the probabilistic terminology we have:

(9)         p(Myocardial infarction | The administration of statins) < p(Myocardial infarction)

This statement says that the administration of statins decreases the probability of myocardial infarction when compared to the general unconditional population or that there is a negative correlation between myocardial infarction and the administration of statins. As discussed in our article relating to Popper’s philosophy of science (find it here), the declarative statements like (1,2) found in Research Analysis are scientific statements in a form that can be logically falsified, but in the real world there is never certainty and thus experience only ever supports probabilistic correlations like that in (9) (actually even probabilities are technically not available according to Popper, but probability has use beyond its risks in many fields of science).

Does the statement (9) imply that there is a causal link between statins and myocardial infarction? To answer this question it is necessary to introduce some further concepts.

Probabilistic relevance or irrelevance

The Research Analysis model has always highlighted the importance of the reference population or model for each claim by requiring the specification of the reference species, disease model and whether it is a whole animal or organ model. Most medical research begins in cell culture or animal models, but has the goal of moving into human applications. It is important to clearly separate claims that relate to mice from those that relate to humans. For this reason, the concept of probabilistic relevance conditional on a reference population or background context is introduced below (refer [1, p255-257] for a more detailed introduction):

(10)       p(B|X∩A) > p(B|X)          Positive probabilistic relevance or conditional correlation

(11)       p(B|X∩A) < p(B|X)          Negative probabilistic relevance or conditional correlation

(12)       p(B|X∩A) = p(B|X)          Probabilistic irrelevance or no conditional correlation

Positive probabilistic relevance (10) says that the probability of event B conditional on both events X and A occurring (X ∩ A) is greater than the probability of event B conditional on X alone. In this presentation of probabilistic relevance, X represents the reference population and A and B are the events for which cause and effect are being evaluated. The following example using (1) can be provided:

(13)       p(Myocardial infarction | normal humans ∩ the administration of statins) < p(Myocardial infarction | normal humans)

This sentence says that the probability of myocardial infarction is lower in normal humans that have been administered statins than it is in normal humans in general. As noted, Research Analysis has always included the reference population or background context because research is conducted in many different species, genetic types and disease models. Sadegh-Zadeh in his work notes that the notion of background context is of great importance when analyzing issues of causality and that “There are no such things as ‘causes’ isolated from the context where they are effective or not. The background context will therefore constitute an essential element of our concept of causality.” [1, p 256]

Spurious correlations & Screening Off

To this point in the discussion, it has not been possible to introduce the concept of causation and instead the weaker concepts of relevance and correlation have been used. Where there is a non-zero relevance or correlation between two events A and B as in (10,11), then B could be a potential cause of A, but “Correlation does not imply causation”. To define the concept of causation it is necessary first do define spurious correlation and the concept of screening off.

(14)       Screening off: X screens A off from B iff p(B|X∩A) = p(B|X)

This says that X screens off A if and only if A is, in relation to the reference population X (or some other event or set of events), probabilistically irrelevant to B [1, p257]. We can take this concept a step further and define a spurious cause by incorporating it into the sentences (10-12) to assess whether there is an alternative event C that explains the probabilistic relevance of A on B.

(15)       Spurious cause: A is a spurious cause of B if there is a C such that p(B |X ∩ A ∩ C) = p(B |X ∩ C).

We can rephrase this and introduce the concept of time order as follows: in a reference population X, an event A is a spurious cause of an event B iff:

  1. A is a potential cause of B in X,
  2. There is an event C that precedes A
  3. C screens A off from B.

An example of a spurious cause can be provided as follows:

p(Death | Humans ∩ AIDS ∩ HIV) = p(Death |Humans ∩ HIV)

In this example, AIDS is screened off by HIV. AIDS is the spurious cause that is screened off by HIV infection. The time order of events is discussed further in the next section.

Dominant cause

In the previous example, AIDS could certainly be a cause of Death in untreated individuals. However, AIDS is screened off by HIV. Both AIDS and HIV can be considered as causes of death. Here the concept of Dominant cause can be introduced to provide a ranking between causes.

(16) Dominant Cause:  At1 is a dominant cause of Bt2 in X iff there is no t such that for all events Ct in X:

  1. t1 ≤ t < t2,
  2. p(Bt2|X ∩ At1 ∩ Ct) = p(Bt2|X ∩ Ct).

This definition says that a cause is dominant if no simultaneous or later event is able to screen it off from the effect [1, p275]. This can be demonstrated with the AIDS example:

  • A person contracts HIV in 2001
  • They present with AIDS in 2003
  • They Die in 2010

In this example there would exist the following probability relationship:

p(Death2010 | Humans ∩ HIV2001 ∩ AIDS2003) = p(Death2010 | Humans ∩ AIDS2003)

This relationship says that the combination of HIV with a Human and AIDS provides the same probability of death as the combination of AIDS with a Human. It can also be seen that 2001 ≤ 2003 < 2010, which says that the HIV occurred prior to the AIDS. This result confirms that AIDS is not the dominant cause of death in this case as there does exist an earlier event HIV2001 that screens of AIDS2003 from Death2010. The following shows the causes reordered:

p(Death2010 | Humans ∩ AIDS2003 ∩ HIV2001) = p(Death2010 | Humans ∩ HIV2001)

This relationship in a similar way says that the combination of AIDS with a Human and HIV provides the same probability of death as the combination of HIV with a Human. However, in this case the Ct  event (AIDS) does not occur in time between the At1 (HIV) and Bt2 (Death) terms. So AIDS cannot be the dominant cause.

The concept of dominant cause provides a means for ruling out spurious causes and for keeping track of the cause that has not been ruled out to date. But in reality we will never be able to test all possible events as causes. Knowledge of the dominant cause of a disease will always be subject to future falsification. This is further complicated by the fact that causal chains run off into the infinite past. Taking the example, it may be that the HIV infection was caused by unprotected sex. At the time 2001 in the example above, HIV may be the dominant cause, but if unprotected sex at an earlier time is considered then the HIV would be screened off by the unprotected sex. Looking at the causes of HIV infection, it can be seen that while unprotected sex may be a common cause of HIV it is not the only one. There is also sharing of needles, infusion with HIV infected blood, etc. So there may be many causes of a disease given a broad background population like all humans even though there may only be one cause for a specific person who contracts HIV. There can also be a common cause for the several symptoms of a disease. Finally, it is rare that there is a single cause for an event. It is usually the case that there are several events that contribute to any future event and we will explore the concept of casual relevance below. Causation is a far more complex concept than most people realise. The concepts presented in this article, and more thoroughly by Sadegh-Zadeh [1], provide some valuable tools for assessing causation and making more thorough use of the concept.

Causal Relevance

The concept of causal relevance is useful metric for answering the question: What event is causally more relevant to a particular disease? Causal relevance can be defined as:

(17) cr(A,B,X) = p(B|X∩A) – p(B|X)

This states that causal relevance is simply the difference in the probability of B given the background context X and causal event A and the just the probability of B given the background context X. An example would be:

In a given year:

p(Myocardial infarction | normal humans) = 1%

p(Myocardial infarction | normal humans ∩ smoking) = 2%

cr           = p(Myocardial infarction | normal humans ∩ smoking) – p(Myocardial infarction | normal humans)

= 0.02 – 0.01 = 0.01

The numbers are just estimates, but they suggest that while smoking may double the chance of myocardial infarction (MI) it does not have a high causal relevance within a one year period.

Some examples that demonstrate causal relevance [1, p277]:

causal irrelevance amounts to cr(A,B,X) = 0 (no relevance) eg. causal relevance of your healthcare number to myocardial infarction

positive causal relevance is cr(A,B,X) > 0 (causing) eg. smoking to myocardial infarction

negative causal relevance is cr(A,B,X) < 0 (discausing, preventing) eg. statins to myocardial infarction

maximum positive causal relevance cr(A,B,X) = 1 (maximum efficiency) eg. mechanically clamping your coronary artery to myocardial infarction

maximum negative causal relevance cr(A,B,X) = −1 (maximum prevention) eg. no example

Causal relevance as defined here is not a probability at least due to its range from −1 to +1. It is simply a quantitative function that provides a measures of the context-relative causal impact of events.

Causal relevance can also be used to compare the relative importance of different events to an outcome by comparing their causal relevance.

If cr(A1, B, X) > cr (A2, B, X), then A1 is causally more relevant to B in X than A2.

For example,

cr(smoking, myocardial infarction, normal humans) > cr (healthcare number, myocardial infarction, normal humans)

This says that smoking is a stronger cause of myocardial infarction than is your healthcare number.

In later articles or versions of this article, we will explore how the concepts of causation and relative causation might be applied to the Research Analysis model and platform.


  1. Sadegh-Zadeh, Kazem. Handbook of analytic philosophy of medicine. Dordrecht: Springer, 2014.

Version 1.0, 19th March, 2017

Representation of individual medical event claims

In the previous article, the logical representation of medical science claims was investigated. Scientific claims have the goal of compressing experimental evidence into rules or models that reliably represent the evidence and make good predictions about future events. In this article, a step is taken back and the representation of individual medical events is investigated. For example, the individual events that together make up the evidence used to come to a medical science claim.

Individual medical events are simpler to model and appear to be well modeled by the standard Davidsonian analysis discussed in the previous article (for discussion of why this analysis is used refer to the previous article). Below is an example discussed in the previous article:

(1) a.     Statins reduce myocardial infarction in normal humans

  1. ꓱe (REDUCE(statin, myocardial infarction, e) & IN(e, normal human))
  2. “There is at least one case, such that statin administration reduced myocardial infarction, where the case was in a normal human”

This Davidsonian analysis of the statement (16a) was taken as a step in the investigation (provided above as (1)), but it was decided that that the existential quantifier was not the correct analysis of the statement and that scientific claims like that in (1a) should to be interpreted as universal quantification. If an individual participant in the clinical trial is considered, the following statement could be made:

(1) a.     Statins reduced myocardial infarction in John Smith

  1. ꓱe (REDUCE(statin, myocardial infarction, e) & IN(e, John Smith))
  2. “There is at least one case, such that statin administration reduced myocardial infarction, where the case was in John Smith”

Here an important difference can be seen between the individual cases and the claims that can be made via statistical analysis of a large number of individual cases as a group. It may be that the statins did reduce the likelihood of a myocardial infarction in John Smith. However, given that the actual event of a myocardial infarction is an irregular occurrence and is dependent on a large number of factors (eg. lifestyle, high physical/stress events, etc), and these factors are uncertain, there is no way of being confident that the statins had any effect from the evidence of one individual. This is why clinical trials are required. So that outside factors can be controlled to some degree and the number of participants can be such that statistically we can have reasonable confidence that the medical scientific claim is valid.

In the example above, the frequency of myocardial infarction is low in an individual and the result often catastrophic. For this reason, studies of drugs for diseases like heart disease generally need to be long term and inclusive of end points (eg. death). If a disease that involved continuous or frequent disease events is considered, then a sentence like that in (1a) may make sense in that the frequency of disease events prior to introduction of the drug can be compared to the frequency afterwards. Take for example antibiotic treatment for bacterial infection:

(2) a.    Antibiotics reduce bacterial infection in John Smith

  1. ꓯe (REDUCE(antibiotics, bacterial infection, e) & IN(e, John Smith))
  2. “In all cases, antibiotics reduce bacterial infection, where the case is in John Smith.”

In this example, bacterial infection nay occurred in John Smith a large number of times during his life. To assess the validity of the claim in (2) there would need to be a number of bacterial infections where no antibiotics were administered and then a number of bacterial infections where antibiotics were administered to allow for a comparison of the control events (no antibiotics) to treatment events. Where the difference was significant, the treatment might be considered a success and the claim (2) might be considered as true (uncertainty discussed further below). However, here again we see the importance of a clinical trial to assess the efficacy of a drug. The claim in (2) is specific to “in John Smith” and the claim cannot be extended to “normal humans” generally. While John Smith is a human, he also has a unique genome, diet, lifestyle and life history generally. The effectiveness of a drug in one human is certainly support for its effectiveness in other humans, but it is always possible that the drug only works with John Smith’s specific genetic profile for example. There is also the possibility that the bacterial infection went away by chance at the same time John Smith began receiving the antibiotic or that it resolved by the placebo effect. This last point highlights the fact that the reduction does not actually imply causation.

In the case of heart disease, the primary cause of myocardial infarction, there may be an indicator of disease other than myocardial infarction. Atherosclerosis describes the formation of lesions in the arteries. Atherosclerosis in the coronary arteries (arteries that supply blood to the heart) is a primary indicator of heart disease and increases the chance of myocardial infarction. The atherosclerotic lesions in the arteries (lesions from here on) exist prior to diagnosis of heart disease and after the commencement of treatment. So in theory they could be measured at many time points prior to treatment and after treatment with statins. If the lesions regressed after treatment, then this could be an indicator within one individual that statins reduce heart disease and by extension myocardial infarction. Unfortunately, lesion progression prior to diagnosis is rarely measured outside of specialised scientific studies. So there is no significant series of events prior to treatment. Secondly, lesions rarely regress significantly and the goal is usually to slow progression of lesions. To assess reduced progression would require the collection of far more time series events that included measures of magnitude and not just the presence or absence of lesions. Unlike say a skin infection, where the infection is visible externally with accompanying pain, the progression of atherosclerotic lesions is painless and difficult to assess given their location with our current technology. Finally, the evidence that lesion stage or size is positively correlated with myocardial infarction events is not definitive. For heart disease and many other diseases, the assessment of the performance of a drug is not possible within an individual, either due to the lack of time series data, the lack of a reliable indicator of disease or the requirement to base the assessment on the reduction of death in a cohort.

We have discussed the need for group based research, such as clinical trials, as necessary for making statements about the correlation between drugs and diseases. Well-designed clinical trials should be able to substantially exclude the placebo effect and take into account the performance of drugs based on end points like death, but it should be noted that chance can still never be ruled out as a factor. In studies involving chemicals or cells the sample size can be made very large, but with humans it is difficult to get very large sample sizes and to control all important variables. However, the statin meta analyses included over 90,000 participants through the consolidation of many large studies.

Version 1.0, 30th September, 2016

Representation of the meaning of scientific claims

Researchers in medical science work hard to express their views and findings in language which is unambiguous and consistent, but natural language is not well suited to the task, for example:

(1)    a. “Statin therapy can safely reduce the 5-year incidence of major coronary events, coronary revascularisation, and stroke by about one fifth per mmol/L reduction in LDL cholesterol, largely irrespective of the initial lipid profile or other presenting characteristics.” [2]

b. “Clinical trials in patients with and without coronary heart disease and with and without high cholesterol have demonstrated consistently that statins reduce the relative risk of major coronary events by ≈30% and produce a greater absolute benefit in patients with higher baseline risk.” [3]

c. “Statins can lower LDL cholesterol concentration by an average of 1.8 mmol/l which reduces the risk of IHD events by about 60% and stroke by 17%.” [4]

Are all of the scientific claims in (1) above expressing the same meaning? No, there are significant differences that effect the specific meaning of each sentence. If we assume that “IHD events” has the same meaning or denotation as “coronary events”, then can we say that all of the claims in (1) mean at a high level that “Statins reduce coronary events”? (see this claim in Research Analysis: These are the sorts of questions that it would useful to be able to answer reliably using sematic methods and tools.

Focusing on the high level claim, consider the following:

(2)    a. Statins reduce coronary events

b. Coronary events are reduced by statins

Sentences (2a, b) have different written forms but the same truth condition. A way is need to represent meaning that is unambiguous and consistent and for this logic can be used.

Logic is a system for reasoning. Below some of the high level terms and elements of logic are briefly outlined:

  • Propositional logic primarily involves the analysis and combination of propositions.
  • Propositions: The term has broad use, but the following is appropriate for our use:
    • refers to the meaning of declarative sentences.
    • affirms or denies a predicate (is true of false)
  • Predicate: A statement that is true or false depending on its arguments.
  • Predicate logic: involves the analysis of the inner structure of simple propositions

For example:

(2)    Statins are drugs

  • Predicate: are drugs
  • Argument: statins
  • This is a one-place predicate
  • It is true if statins are drugs, otherwise false.

Predicates can be represented using notation that uses the main word, without tense, without the copula be (for example “are” in this case) and some prepositions. The entities (people or things) that the predicate is related to are its arguments. The standard notation uses upper case for the predicate and lower case letters for names. For the example above, the notation would be as follows:

(3)    DRUG(statins) = TRUE

In this case the name statins has been used as the argument for the proposition, but any name can be inserted into the proposition. The proposition will be true or false depending on the argument.

Propositions can have more than one argument, for example:

(4)    Statins reduce coronary events

  • Predicate: reduce
  • Subject: statins
  • Object: coronary events
  • True if Statins do reduce coronary events, otherwise false.
  • Notation: REDUCE(statins, coronary events)

This is an example of a two place predicate. In natural language, predicates can occur with three or possibly four arguments. Adicity is the number of arguments that a predicate can take. Each predicate has a fixed acidity or number of arguments. Some predicates from natural language can have different or extended meanings with different numbers of arguments, but each of these is considered to be a unique predicate in logic with a fixed number of arguments.

In natural language, predicates are sometimes used with an argument missing. These are known as elliptical sentences. Elliptical sentences are regularly used in common language e.g. “Give statins.” Give to who? From the context of the conversation it is assumed that the statins are to be given to the patient. From a syntactic point of view this sentence is incomplete as it is missing the object noun phrase. The way to understand these sentences is to assume that there is an ellipsis (in this case the patient) that is given by the context of the situation to fill the required argument in the predicate.

In the case of “Give statins to”, it is obvious as a native English speaker that this sentence is incorrect. In the case of our high level claim (4), the sentence sounds fine and this is because it is a syntactically complete sentence. But it could be asked, reduced compared to what? To assess the truth of the predicate, a comparison set is needed to assess whether there was a reduction. In science, and phrases like (4), the comparison set is usually taken to be the pre-treatment population sample that is represented by the control group in the experiment. The control group is a group of entities (e.g. people, mice, cells) that are the same as the experimental group, but where the experimental condition has not been applied (e.g. the drug has not been administered). The term control group will be used to refer to the comparison set.

An analysis of the full sentences in (1), but without detailed linguistic analysis, provides the following control group for each of the three sentences:

  1. “largely irrespective of the initial lipid profile or other presenting characteristics” suggests that the reduction would apply to any human receiving the treatment.
  2. “patients with and without coronary heart disease and with and without high cholesterol” again suggests that the reduction would apply to any human receiving the treatment.
  3. The sentence doesn’t provide a control group and publication must be investigated further to find out the context of the sentence. In the method it is found that “We included all double blind trials, irrespective of participants’ age or disease. Participants in most trials were healthy with above average lipid concentrations.”. While they note the bias towards above average lipid concentrations, they also note elsewhere that the results are adjusted to take into account variations in the participant groups. So it is reasonable to assume that at a high level they are also making the claim relative to the group of all humans. Though in this case it would also be reasonable to take healthy humans with above average lipid concentrations as the control group.

Taking the control group as “normal humans” (we could have a second claim for hyperlipidemic humans), (4) is updated as follows:

(5)    Statins reduce coronary events in normal humans

  • Predicate: reduce
  • Subject: statins
  • Object 1: coronary events
  • Object 2: normal humans (control group)
  • True if Statins do reduce coronary events in normal humans, otherwise false.

Notation: REDUCE(statins, coronary events, normal humans)

Is the reduce predicate a two place or three place predicate? Syntactically reduce with two arguments is sufficient. Scientists strive for the maximum generality possible in their theories and reduce with two arguments may suggest that the relationship applies to all sets of things. But our example is clearly ridiculous when applied to machines or plants that have no concept of coronary events. In the case of a plant, the denotation of the coronary artery would be false due to the non-existence of the organ in the case of a plants and thus the claim would be false based on Russell’s theory of descriptions [6] or meaningless on a classical analysis. So while the two argument reduce predicate is syntactically correct and may have a meaning, the broad meaning is not implied by the sentences in (1) and is false or meaningless outside the set of animals with coronary arteries. I believe that to represent the sentences in (1) and to be a scientifically useful claim, the reduce predicate must be combined with a control group. In semantics, the identification of arguments and non-arguments is not straightforward and remains an unresolved topic [1].

There are some alternatives means of linking the control group to the reduce predicate without making it an argument:

  1. Consider the control group as a noun modifier for the object of the reduce predicate.
  2. Consider the control group as an adverbial phrase attached to the reduce predicate that provides a location for the reduction.


Control group as noun modifier

If the control group is treated as a noun modifier for the object, then “coronary events in normal humans” is the object that is reduced and this would be represented by (5.1) below

(5.1) REDUCE(statins, coronary events in normal humans)

This doesn’t appear to obviously wrong, since on a simple reading coronary events do occur in the normal humans. However, I do not believe that this representation is logically correct and doesn’t correctly represent the claim in (1). The concept in (1) is that statins are given to normal humans and that this results in a reduction in coronary events. The predicate in 5.1 suggests that the reduction is seen in normal humans, but humans that have received statins are actually no longer “normal humans” because statins alter their metabolism. It is only in these humans with a metabolism altered by statins that the reduction in coronary events is claimed to occur. On the other hand, the predicate in (5.1) does not make clear that the statins or the metabolic effects of statins occur in the humans, because the “in normal humans” only modifies the coronary events argument. The interpretation of the control group as a noun modifier to the object argument does not appear to be correct.

Control group as an adverbial phrase

I believe that the correct interpretation of the adjunct “in normal humans” is that the process or event of reduction occurs within the normal human. This is a word group that qualifies the main reduce predicate and is not a required argument of the reduce predicate. This is an example of an adverbial phrase that is attached to the verb, reduce, and provides a location for the event(s) or process. In the example, the statin is taken by the patient and the effect of the statin occurs within the patient by altering their metabolism and leads to a reduction of coronary events. In this example the location is within the body of any human included in the set of “normal humans”. I believe that this representation allows the interpretation that the process that the statins trigger in the normal humans to alter their metabolism resulting in reduced coronary events occurs from the starting point of a normal human, even though the result of the process will be an altered human with reduce coronary events.

Davidsonian Analysis

The semantic concepts introduced by Davidson in his 1967 paper “The Logic Form of Action Sentences” [8] can be used for the analysis of the reduce predicate and its associated adverbial phrases. Before analysing the sentences in (1), the Davidsonian approach will be reviewed with a simpler example:

“In 1976 we published two papers reporting the discovery and characterization of compactin, the first statin.” [5]

The following simpler sentence that takes some information from elsewhere in the paper will be used:

(6)      Akira Endo discovered compactin in 1976 in Japan

Before Davidson’s work, the standard logical analysis would have included the adverbials as arguments of the predicate [1].

(7)     DISCOVERED(Akira Endo, compactin, 1976, Japan)

Because a predicate has a fixed number of arguments, we can see that this analysis results in a number of DISCOVERED predicates with different numbers of arguments:

(8)     a. Akira Endo discovered compactin

DISCOVERED’(Akira Endo, compactin)

b. Akira Endo discovered compactin in 1976

DISCOVERED’’(Akira Endo, compactin, 1976)

The argument structure in (7) can be represented generally as (9):

(9)    DISCOVERED’’’(discoveree, discoverer, time, place)

There are problems with this analysis:

  1. The arguments of the predicate should be necessary to give it meaning. The discoveree and discoverer appear to be essential to the meaning of the DISCOVERED predicate. But the adverbial expressions are more loosely connected to the predicate.
  2. Action verbs can be modified by a variable number and type of adverbials in difference combinations. The difference combinations of the predicts would express different predicates, which results in a very complex group of related predicates.

It does not seem to make sense that the multitude of predicates that this produces related to different verb meanings. Intuitively it seems that there is one core predicate that appears in all of the sentences, with the adverbs specifying additional information.

Davidson pointed out that sentences like (7) and (8a&b) are related by entailment in a way which seems to require that the same predicate appears in all sentences [1, This example paraphrases Kearns’ example in chapter 11 and it should be referred to for a general introduction]. For example:

The entailments of (6) include:

(10)    Akira Endo discovered compactin in 1976

(11)    Akira Endo discovered compactin in Japan

And the entailment of both (10) and (11) is:

(12)    Akira Endo discovered compactin

Davidson observed that every entailment of this kind resembles entailments which ‘drop conjuncts’, in this case adverbial phrases. He proposed that the parts of the entailing sentence which can be dropped to produce the entailed sentence should be represented as logical conjuncts [1]. The central basic proposition can then be conjoined with the adverbials to provide a proposition that expresses the meaning of the whole sentence.

(13)    Akira Endo discovered compactin in 1976 in Japan

DISCOVERED (Akira Endo, compactin) & p & q

p expresses “in 1976”

q expresses “in Japan”

The next step is to link the propositions p and q to the central proposition. Davidson argued that the adverbials are referring to the action or event described by the central basic proposition eg. “The discovery event occurred in 1976”, “The discovery event occurred in Japan”. Davidson proposed that the event itself should be included as an additional argument and that the propositions should all refer to this event. Using our example:

(14)    a. Akira Endo discovered compactin in 1976 in Japan

b. ꓱe DISCOVERED (Akira Endo, compactin, e) & INYEAR(e, 1976) & INCOUNTRY(e, Japan)

c. “There was an event, which was the discovery of compactin by Akira Endo, and the discovery was in 1976 and the discovery was in Japan.”

The variable e is a restricted variable in logic and ranges over all events. The existential binding of the event variable in this proposition requires that there is at least one event for which the remainder of the proposition is true for the whole proposition to be true. The adverbials (eg. time, place, manner) are now expressed as logical conjuncts with each represented by its own predicate with the event as an argument. The result of the Davidsonian approach is just one core predicate for the action verb (in this case DISCOVERED), to which can be added as many or as few adverbials as needed by using separate predicates for each and conjoining them to the core action predicate.

Davidsonian Analysis of Medical Science Claims

Returning to the analysis of the medical science claim (5), Davidsonian analysis would produce the following:

(15)      a. Statins reduce coronary events in normal humans

b. ꓱe (REDUCE(statin, coronary events, e) & IN(e, normal human))

The word “events” in “coronary events” is confusing here and shouldn’t be confused by the reduction event represented by e in the predicate REDUCE. “Coronary events” here is the object of the predicate and refers to a category of adverse medical events related to the coronary artery, for example a myocardial infarction. To avoid confusion, from here on “myocardial infarction” will be used to replace coronary events as the most common coronary event.

(16)    a. Statins reduce myocardial infarction in normal humans

b. ꓱe (REDUCE(statin, myocardial infarction, e) & IN(e, normal human))

c. “There is at least one event, such that statin administration reduced myocardial infarction, where the event was in a normal human”

Note that the plural has been removed from “statins” and from “normal humans”. This is because in the Davidsonian analysis the predicate REDUCE now applies to a single even e. In each case there is only one statin administered to one human (we’ll ignore the case here that multiple statins are administered).

The concept of an event in common language gives the impression that the statin administration reduced the myocardial infarction over a short period of time. The effects of a single statin administration on the metabolism of cholesterol in humans does occur over a short period of time, but this altered cholesterol metabolism needs to persist for a long period of time to result in a significant reduction in myocardial infarction. Heart disease patients are often administered statins for the remainder of their life. In this way the statin administration has its reduction effect on myocardial infarction via a long term process rather than over a short period implied by the word event. Process may be a better word to use than event. I would like to suggest “case” as an alternative to event as a word that is better suited to the medical field. I believe that the concept of a case suggests that the time period and medical process will be appropriate to the specific disease treatment paradigm. I will continue to use the variable e for event as it is standard in logic, but will use case and event interchangeably in the verbal descriptions.

(16)    d. “There is at least one case, such that statin administration reduced myocardial infarction, where the case was in a normal human”

While the research claims in (1) certainly do suggest that there is a least one event or case where statins reduced coronary events, the existential quantifier doesn’t give the full strength of the claims made. In the introduction to Davidsonian analysis above the past tense of discover, discovered, was used to refer to Endo’s discovery. This signifies the historical nature of the discovery and implies that it isn’t expected to occur again. Rediscoveries can occur due to lost knowledge, but in modern science there is an assumption that there is a first discover and discovery of a scientific claim. In contrast, the claim in (15a) uses the infinitive, reduce, which implies that the reduction will occur in all or many events. A primary goal of science is to identifying models or rules that allow for the reliable compression of large amounts of evidential information about events in the world into a much more compact form that allows us to make good predictions about future events. To this end scientific claims ideally would apply to all events or at least most events that fit the conditions of the claim. The nature of empirical knowledge is that we can’t ever know anything with certainty, but we seek to verify claims that have as broad a scope as possible. Based on this goal of science, I would interpret the claim (16a) with the following logical proposition:

(17)    a. ꓯe (REDUCE(statin, myocardial infarction, e) & IN(e, normal human))

b. “In all cases, statin administration reduces myocardial infarction, where the case is in normal human.”

I believe that (17a) is the correct logical representation of the claim in (5) & (16a) and is a good representation of the core claim in the sentence of (1).

It was shown that considering the control group, “in normal humans”, as a noun modifier to the myocardial infarction (or coronary events) resulted in the scope of the control group only applying to the myocardial infraction. Davidsonian analysis applies the control group to the whole event. This has the effect of placing the reduction event, the statins and the myocardial infarction in a normal human. I believe that this is the correct logical interpretation.

One of the primary reasons for considering the Davidsonian approach was to remove the need for additional arguments in the REDUCE predicate and here this approach adds an additional argument. However, the benefit of the addition of the event argument is that is can be used to introduce other adjuncts to the REDUCE predicate without the need for any arguments beyond three. For example: “reduced by how much?”. Each of the sentences in (1) gives a description of the size of the reduction. For (1b), the following summary sentence could be made: Statins reduce myocardial infarction in normal humans by 30%, and the logical proposition could be made:

(18)    ꓯe (REDUCE(statin, myocardial infarction, e) & IN(e, normal human) & BY(e, 30%))

This BY adjunct does seem to be optional unlike the control group IN predicate, as without it the truth value of the statement (16) and (17) could be assessed by assuming that any reduction greater than zero will be sufficient. I believe that there are some adjuncts that are essential to have a valid scientific meaning and others that may improve the specificity of the claim, but are not essential to the core scientific claim. Interestingly the addition of the BY predicate introduces clear conflict between the three claims in (1). For (1b) we have the claim in (18) and for (1c) we would have:

(19)    ꓯe (REDUCE(statin, myocardial infarction, e) & IN(e, normal human) & BY(e, 60%))

The differences may be due to differences in the meaning of coronary events, as (1b) refers specifically to IHD events, though generally they are assumed to be the same concept. This clear identification of contradiction or conflict between claims is one of the key reasons for representing claims in this this logical structure and of the key goals for Research Analysis. The contradictions raise questions about the structure of the claims and the descriptions of medical objects and events, and I believe that these clearly defined questions are what drives science forward. Arguments are constantly happening in medical science, but often they occur without the parties having a clear understanding of the other parties claims. The use of standardised language and formal descriptions of claims will improve the quality of these arguments and science.

Standard claims used in Research Analysis

The sentences in (1) use the predicate reduce as the relationship between the subject and object. Reduce is clearly just one of many predicates that could be used in medical science. Increase, as the opposite of a reduction, would be another obvious example. In Research Analysis, at the date of writing, three predicates have been proposed as a summary of all predicates. They are:

  1. Increases: The subject has the effect of increasing the object
  2. Decreases: The subject has the effect of decreasing the object
  3. Not Significant: There is no significant relationship between the subject and object. From a statistical point of view, the relationship is not present at a level that is sufficient to exceed the threshold of significance as defined by the authors.

Decrease is a synonym for reduce, as well as other verbs like lower, shrink, etc. In each case, the words may have slightly different usage in natural language, but they share a common concept. In Research Analysis, we use decrease to represent all of these verbal predicates. For the opposite concept we use increase to represent all verbs like raise, expand, etc. Finally, we use the term Not Significant to represent relationships where the subject has no significant effect on the object based on the statistical measure used by the authors of the scientific claim.

Using this model, we can represent (17) as:

(20)    a. ꓯe (DECREASE(statin, myocardial infarction, e) & IN(e, normal human))

b.“In all cases, statin administration decreases myocardial infarction, where the case is in normal human.”

This claim can be found in Research Analysis here where it is linked with the sentences and references in (1).

Causation and Confidence/Determinism

The use of “reduce” in the claims in (1) appears to suggest a relationship of causation between the statins and the reduction in coronary events. Most people would also associate verbs like increases and decreases as suggesting that there is a causal link between the subject and object of the sentence. Bertrand Russell in his paper, “On the notion of cause” [7], states “the word “cause” is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable”. This is a very strong view, but it is clear that causation is a complicated concept and that it should be used with care. The concept of causation and its formal representation will be reviewed in more detail in a later article.

Through the practical use of the Research Analysis model, examples have been found that do not suit a causal model. For example, there may be an association between increased c-reactive protein and myocardial infarction, however the researchers don’t believe that the c-reactive protein causes the myocardial infarction. Instead they believe that both are caused by some other common cause eg. late stage atherosclerosis. In these cases, the use of increase in a claim could be interpreted as “c-reactive protein is found to increase with myocardial infarction”. This use of increase does not imply causation. Increase and decrease in Research Analysis are intended to be used to represent scientific claims that propose causation as well as those that do not.

The formal representation of claims is in (20a) and in Research Analysis are declarative statements that don’t include any hedging of the claim. The claim “statins reduce myocardial infarction in normal humans” suggests that the reduction will occur in all normal humans, not that it will occur most of the time or 95% of the time. This is representative of the claims made in (1), where the core claim in (20a) is made without any hedging, though there is some uncertainty on the quantum of the effect. Is this type of declarative statement appropriate given that modern science relies on statistical tools (eg. t-testing) that acknowledge that we can never have complete certainty about any real world associations. I believe that unhedged declarative statements are the appropriate representation of scientific claims, as Research Analysis seeks to represent the clearly stated core of the hypothesis being tested by the research that becomes the claim found to be support by the results of the scientific process. Modern science is largely based on the philosophy of Karl Popper [9] that requires a scientist to begin their work with a hypothesis that can at least theoretically be falsified by experimental findings. A hypothesis that involves any hedging, cannot ever be falsified definitively as the defender of the hypothesis can always claim that a negative result was only due to chance. The claims in Research Analysis aim to capture the core of these hypotheses that could have been falsified, but were found to be supported, but remain open to having their mettle tested.

Through this investigation, it was identified that the terminology of “not significant” does not align with the declarative and unhedged statements that are intended to be collected in Research Analysis. For this reason, it will be replaced with “no relation” in the next version as in “hair colour has no relation to myocardial infarction”. This language and concept removes the hedging that is implied by the concept of “not significant”. With this language new language, a claim from another publication that found an increase or decrease relationship between the subject and object would provide evidence against or falsify the claim of “no relation”, whereas the old language leaves open the possibility of statistical luck.


Is the model presented in this article a perfect representation of the semantics of scientific claims in medicine? Of course not. We expect to improve the model over time as we learn from application and the input of peers. But we do believe that scientific claims collected using the existing model can provide value through clarification of meaning, more efficient search and tools that can compare and contrast claims.

The writing of this article raise a number of issues for us and we hope to explore them in future articles. They include:

  • Related to Davidsonian analysis:
    • Consider a neo-Davidsonian analysis of our medical science claim model.
    • Does Davidson’s event model extend to situations where the medical claim relates to an association that occurs only after a substantial time.
  • Investigation into the probabilistic representations of medical claims.
  • Research Analysis currently allows for the specification of an organ or organ cell model to be associated with the claim predicate. This would specify “in heart” for the claim in this article. Is this another adverbial phrase or a modifier to “in normal human”?
  • Are there other adverbial phrases or adjuncts that are essential to the core medical scientific claim?
  • Investigation of the different types of terms that can be used as subject and object in medical claims. For example:
    • Events: coronary events, myocardial infarction (blockage of the coronary arteries)
    • Disease process: atherosclerosis (development of lesions in the arteries)
    • Groups or sets of things vs individual things: eg. brain cells, coronary events.
  • An investigation into the validity of causation claims and their representation.
  • Application of the model to individual medical cases or small groups of cases that do not significantly show a general correlation.
  • The use of lambda calculus to represent claims, construct claims and extract claims from natural language into a formal structure in a systematic way. In this article we rephrased sentences before abstracting them into a logical form. Lambda calculus may provide tools that can leverage the syntactic structure of sentences to algorithmically extract formal claims from natural language.
  • Why is it relatively easy for scientists to make linguistic claims, but hard to define the same claims in a logical language?
  • Finally we have discussed several ideas that are not cited. Some of these should have citations from work that we have already read, but couldn’t identify at the time of writing. Others we have not yet found appropriate works to support our approach, but we will keep searching.


  1. Kearns, Kate. “Semantics. Palgrave Modern Linguistics 2ndEngland: Palgrave Macmillan (2011).
  2. Cholesterol Treatment Trialists. “Efficacy and safety of cholesterol-lowering treatment: prospective meta-analysis of data from 90 056 participants in 14 randomised trials of statins.”The Lancet 9493 (2005): 1267-1278.
  3. Maron, David J., Sergio Fazio, and MacRae F. Linton. “Current perspectives on statins.” Circulation2 (2000): 207-213.
  4. Law, Malcolm R., Nicholas J. Wald, and A. R. Rudnicka. “Quantifying effect of statins on low density lipoprotein cholesterol, ischaemic heart disease, and stroke: systematic review and meta-analysis.” Bmj7404 (2003): 1423.
  5. Endo, Akira. “A historical perspective on the discovery of statins.”Proceedings of the Japan Academy, Series B5 (2010): 484-493.
  6. Russell, Bertrand. “On denoting.”Mind 56 (1905): 479-493.
  7. Russell, Bertrand. “On the notion of cause.”Proceedings of the Aristotelian society. Vol. 13. Aristotelian Society, Wiley, 1912.
  8. Davidson, Donald. “The logical form of action sentences.” (1967).
  9. Popper, Karl. The logic of scientific discovery. Routledge, 2005.

Version 1.3, 20th September, 2016

Previous versions can be provided on request.

Acquaintance and Knowledge About the World – Descriptions in Medical Science

  • Denotation involves the interpretation of denoting phrases such as: a cell, some cell, every cell, all cells, the zygote that developed into Bertrand Russell, the unfertilised ovum that developed into Bertrand Russell. The theory of descriptions, developed by Bertrand Russell beginning with his work On Denoting [1], provides a means of extracting the logical form of denoting phrases from natural language expressions.
  • The topic of denotation is important to Russell from a theory of knowledge point of view, that is, theory about what we can know about the world. Russell at the time saw two distinct types of knowledge:
    1. acquaintance: things that we can directly perceive.
    2. knowledge about: things with which we have no immediate acquaintance, but understand by description.
  • Descriptions of objects are denoted by phrases composed of words with whose meanings we are acquainted.

Acquaintance is a special type of knowledge about

  • Many texts on Russell’s theory of descriptions suggest that direct perception and the naming of objects by ostensive definition, by pointing, are unproblematic. This may have been Russell’s view too in his early writings.
  • However, in Russell’s later writings on human knowledge [2] he took a pragmatic empirical view that I would summarise as follows:
    • He accepts Hume’s position that there is no certain knowledge of the real world
    • However, he believes that there is a pragmatic and practical basis for believing in knowledge that has strong empirical support.
  • Acquaintance with the name of a thing is gained through a series of events where the name is associated with the physical perception of the thing.
  • Through this empirical acquaintance we link the name of the thing with the mental description of the object that we keep in our mind and use to recognise the object.
    • The name of the object is just the short hand link to the mental description of the object we keep. The mental description that is used by our brains to interpret the inbound perceptual information from our senses (for example, information from our eyes delivered by our optic nerve to our brain).
    • This is essentially the same as the short hand identifier used by a computer to link to a detailed description or model for recognising an object. A model that is used by the computer to interpret inbound information from its sensory devices (for example, information from a camera delivered by binary information to the CPU).
    • Symbols are used to denote things, usually we think of words, words in any language, but the language could be a computer language of binary bits, those bits physically held in memory, our memories stored in the structure of physical neural networks.
  • If acquaintance is taken to be empirical as discussed above, then really it is just another form of knowledge about things. Traditionally it is considered to be knowledge gained where there is no intermediate unnatural translation of the description from the “natural world” (light travelling to our eyes from the object) and our perception (the receipt of the light by our eyes). But even in this natural case, the simple name we give to a perceived thing is denoted by the description held in our minds of the object, the description used to recognise the object. This description of the object is an incomplete description and created through imperfect senses and thus empirical in nature.
    • Even knowledge of our selves is empirical, in that it necessarily involves one part of the self-perceiving another and in the same way this must be incomplete.
  • Some examples of acquaintance being a special type of knowledge about:
    • Direct sense perception: Practical medical science provides an opportunity for physical acquaintance with physiological, biological and other medical objects. Names are associated with the physical objects by ostensive definition, pointing out, of objects by demonstrators and peers. As discussed, I argue that even here the objects are being denoted by descriptions in our minds that will be used to link future acquaintances with the name given to the object.
    • Magnified perception: When our practical science moves to the microscopic level the empirical nature of naming and denotation becomes clearer. Here we don’t have direct perception of the objects and must rely on the images provided by magnification devices. We treat the images as if they were simply the perceptions we would have if our eyes could achieve the same magnification, however this assumption is an empirical one.
    • Assay perception: At the molecular level, the empirical nature of perception becomes obvious. When we run an assay on a biological sample (eg. ELISA) and interpret the results, it is impossible to treat it as a direct perception of the molecular make-up of the sample. This is acknowledged by the use of statistical analysis to interpret the results and their quality.
  • I would argue that the direct sense perception of medical objects is, from a theory of knowledge point of view, no different to the perception of assay results. Both rely on the translation of sensory perception into description/denotation/model in our brains that is then linked to a name for the object. The difference being only that the assay perception involves external additional descriptions of the object and the direct sensory perception only involves internal human descriptions of the object in our brains.
  • This equivalence can further be demonstrated by the following examples:
    • Instead of a physical practical experience with the object, you could instead learn the name for an object from a textbook where the exact same image that you would have seen in an in person medical practical is provided in the text book. Certainly some of the quality of the acquaintance with the object will be lower (eg. loss of 3 dimensions, you can’t feel it), but it is not a completely different experience and you would gain similar acquaintance and knowledge about the object.
    • It may be that the image in the textbook was damaged, but there remains an extremely detailed description of the object in the book and you would gain a lower but again somewhat similar acquaintance and knowledge about the object.
    • Other similar examples would be a high quality replica wax model of the object, a diagram of the object that is drawn to highlight important attributes of the object (good ways of describing or recognising the object), etc
  • Perception, as it is used here, is simply a name for a type of knowledge about things in the world that doesn’t involve the interposition of descriptions of the object between a human and the object in the real world. However, there remains descriptions within the human, that makes perception a form of knowledge about the object.
  • Thus all human knowledge is knowledge about the world and is thus subject to Russell’s theory of descriptions and denotation.

Knowledge about is empirical

  • Knowledge about the world gained by acquaintance or through descriptions is inevitably empirical. In the case of acquaintance, the descriptions of objects that we build for objects in the world are strengthen and refined through the corroboration of our recurring observations of the object and the description we hold for the object. In the case of knowledge gained through descriptions, the descriptions to be useful must have been developed through empirical means by the person or community who created the description. It is possible that a description has been developed without an empirical foundation, but in this case we should not expect the description to be corroborated by our own observations of the world.
  • Most of our common sense knowledge about the world is established through our acquaintance with the world as we develop. We may not consciously think of this knowledge acquisition as a scientific process, but subconsciously our mind is gaining knowledge through the generation of hypotheses and the testing of these hypotheses in the course of our life.
  • Science and the scientific method is really just a formalisation of our natural approach to knowledge acquisition with a higher expectation on the required level of corroboration.
  • The goal of science is to gain high quality and reliable knowledge about specific things in the world, both objects and the processes that effect objects, to be able to describe or denote these specific things in a highly reliable way.
  • Very good scientific descriptions are those that would allow a person with no direct acquaintance with a thing to identify and make good predictions about that thing in the world.
  • The quality of the descriptions in science are important. Descriptions that are needlessly complicated or rambling will make their conversion into knowledge about the world difficult for the reader. Ockham’s razor suggests that descriptions should be as simple as possible, but no simpler.
  • Another goal of science is to make descriptions as broadly applicable as possible where that can be done without excessive additional complexity. Our preference is to create efficient scientific descriptions of “all cells”, rather than just “some cells”.
  • In physics, many of the descriptions are provided in the form of mathematical equations. On the other hand, in medical science, the majority of descriptions are given in the form of literature. Certainly medicine uses special scientific terminology, but the terminology is presented in natural language. There are some niches of medical science were more formal languages are used: for instance, in biochemical pathway analysis.
  • Mathematics is just a type of description where the symbols and words are used in a highly formal way. High quality natural language can be somewhat formal, but only to a dramatically lower level than formal languages like mathematics and first order predicate logic.
  • Our goal is to develop and promote more formal languages for expressing medical science knowledge. We seek to extract medical science knowledge out of the existing natural language literature and into such formal languages. Ideally one-day medical science will be coded directly into such formal languages and we believe that powerful and easy to use tools will be essential to achieving this goal.


  • Russell, Bertrand. (1905). “On Denoting”, Mind 14, pp. 479–493.
  • Russell, Bertrand. “Human knowledge: Its scope and its limits.” New York: Simon &Schuster (1948).

Version 1.0, 21st August, 2016

Semantics in Medical Science Literature – Introduction

This is the topic for a series of knowledge base articles that will provide an introduction to semantics with a focus on the medical science literature. We have found a number of introductory texts on semantics to be very valuable, but haven’t been able to find any that have a focus on science. Coming from the field of linguistics, it makes sense that these texts focus on general human language. Some of the advanced concepts in semantics deal with the complexity of human conversation where there is a large body of unspoken understanding and context between the speakers. Colloquial language makes it even harder. Scientific language on the other hand tends to be more formal and declarative, but it has its own complexities. There may be introductory texts addressing the semantics of scientific language, but we haven’t been able to find them. As a result, we will likely attempt explanations that have been made before and with more rigor. Where you know this is the case, please let us know and will correct the text and include references. We felt that these articles would be a valuable learning tool for our users and for us.

Research Analysis was developed before we gained an understanding of the formal semantic analysis methods and the sematic tools that have been developed. We expect the Research Analysis platform to evolve as a result of our better understanding of these semantic tools and techniques.

Version 1.0, 18st August, 2016