Semiotica 149 (2004), 361-376.
In previous studies, we have examined the rules by which an image reader combines or distinguishes between Roentgen signs in the process of clinical diagnosis (Cantor 2003, 2004). These rules entail the performance of logical operations on the interpretants of Roentgen signs. In this study, we will examine those types of inference that are involved in the use of Roentgen semiotic operators. This approach to Roentgen diagnosis will be based on the categorical logic of Charles S. Peirce. On this foundation, we distinguish fundamental differences between clinical logic and scientific logic as it is characterized by Peirce. We maintain that inference by mental association plays a greater role in clinical diagnosis than logical inference. We conclude with the demonstration of a semiotic modeling system for clinical diagnosis.
In diagnostic radiology, abnormal anatomic events in the human body are detected, localized and identified by means of Roentgen images. The interpretation of such images is based on the interpretation of Roentgen signs. A Roentgen sign is a triadic relation (a Peircean sign) comprised of an image (the representamen), an anatomic event (the object) and an interpretation by an image reader (the interpretant). For Roentgen signs, the object determines the representamen by physical causation. However, the representamen does not physically determine the interpretant of a Roentgen sign. An interpretant is produced in the mind of the interpreter when a precept of an image is compared with the memory of a concept of its object. Hence, a Roentgen sign cannot be interpreted without some prior knowledge of its object. The irreducibly triadic relation of a Roentgen sign results from the necessary condition that the interpreter have prior knowledge of the object of the sign. Prior knowledge of normal anatomy is necessary for the detection of an abnormal event. Prior knowledge of imaging conventions is necessary for the precise localization of an abnormal event. Prior knowledge of human pathology is necessary for the identification of an abnormal event. Furthermore, identification presupposes localization and localization presupposes detection (Cantor 2002). In the next section, we begin this study of clinical logic with an examination of the concept of clinical truth.
In the process of reading Roentgen images, abnormalities are described before they are interpreted. In the radiological report, 'findings' are recorded as assertions of fact. These assertions are the immediate interpretants of Roentgen signs (cf., Houser 1992: xxxvii, on the types of interpretants). The radiologic report is concluded with a summary interpretation that is based on dynamic interpretants. In what follows, assertions are statements (declarative sentences) that express perceptual judgments (Peirce 1903a: 155; Peirce 1903b: 191). According to Peirce, an assertion entails an act of mental acceptance and a justification for action (Peirce 1903b: 191; 1903f: 278; 1904:313). In Roentgen diagnostics, the justified action is the release of a report to a referring clinician to be used as a basis for treatment.
In this study, a correspondence between a thought and a measure of its acceptance will be termed a valuation. Therefore, a perceptual valuation is a correspondence between a perceptual judgment and a measure of its acceptance by the image reader (Peirce 1901: 87). In general, two types of perceptual valuations are used in clinical practice. These may be termed valuations of certainty and valuations of uncertainty. A perceptual judgment that is not accompanied by a feeling of doubt is expressed by an assertion with an implicit valuation of certainty. Examples of such assertions are 'There is no radiographic abnormality', 'There is left lower lobe pneumonia', 'There is no fracture', etc. A perceptual judgment that is accompanied by a feeling of doubt is expressed by an assertion with an explicit valuation of uncertainty. Valuations of uncertainty are expressed by words such as 'likely', 'unlikely', 'possible', 'probable' or 'indeterminate'. Examples of such assertions are 'This mass is possibly malignant', 'This joint is probably infected', 'This pulmonary nodule is indeterminate for malignancy', etc. In clinical practice, an image reader employs perceptual valuations that are appropriate for the case at hand. In contrast with perceptual valuation, a truth valuation is a correspondence between a statement and a measure of its acceptance. The conventional truth-values of statements are 'true' and 'false', where truth entails complete acceptance and falsity entails complete rejection. In Roentgen diagnostics, the primary sources of truth valuations are in consensus and authority (cf., Peirce 1877, on 'fixation of belief' by the methods of science and authority). As such, they are independent of the image reader. Truth valuation by consensus (the method of science) is determined by a community of minds (Peirce 1868: 52). This type of truth valuation assumes the existence of a physical reality that is independent of any individual mind (Peirce 1903c: 240). Hence, a truth valuation by consensus is based on the collective experience of a community of minds while a perceptual valuation is based on the perceptual judgments of an individual mind. In contrast, truth valuation by authority is based on the acceptance of statements from a trusted colleague or written source for which there may or may not be a consensus. When a practitioner consults an atlas, reference book or article in the peer reviewed literature, it is more often an appeal to authority than to consensus (granted, authorities are often assumed to represent consensus). Unfortunately, truth valuation by predilection (cf., Peirce 1877, on 'fixation of belief' by tenacity and the a priori) may also occur in clinical practice and is a major source of error. In summary, perceptual valuations are measures of acceptance of perceptual judgments and truth valuations are measures of acceptance of statements. Furthermore, truth valuations are determined by consensus, authority or predilection.
A truth valuation for compound statements of implication may be termed validation. The conventional truth-values for implications are 'valid' and 'invalid'. Perceptual, sentential and inferential valuations are interrelated. Hence, a statement is assumed to be true if it is an assertion with the perceptual value of certainty or if it is the consequence of a 'valid' implication with a 'true' statement as antecedent, since implication is assumed to preserve truth-value. In this section, we have seen that standards of clinical truth differ from the standards of scientific truth. Later we shall see that the same holds for the validity of arguments. In the next section, we briefly summarize the Peircean (triadic) typology of logical arguments for later use in our study of clinical inference.
In general, an inference is a binary relation between statements termed antecedent (premiss) and consequent (conclusion). Peirce (1895: 12) distinguished 'non-rational' inference (implication) from 'rational' inference (argument). An implication is an inference with a simple statement as antecedent. In sentential logic, an implication is valid if the consequent is true or the antecedent is false. This is termed material implication. However, in practice, an implication is considered to be valid only if both the antecedent and the consequent are true.
An argument is an inference with an antecedent (premiss) that is a compound statement formed by the conjunction of two statements termed the major premiss and the minor premiss. Peirce described three elementary types of logical argument, which he termed deduction, induction and abduction (cf., Peirce 1878d). He defined a deductive argument as the inference of a 'result' from a 'rule' (implication) and a 'case'. The rules of deductive inference are given in standard books on Logic (cf., Copi and Cohen 2000). Similarly, Peirce defined an inductive argument as the inference of an observational regularity (a 'rule') from a statement based on selected observations (a 'case') and a general statement (a 'result'). Peirce defined an abductive argument to be the inference of a hypothesis (a 'case') from an implication (a 'rule') and a statement of fact (a 'result'). For an inductive argument to be valid, the 'result' must be a predesignated type of event and the 'case' a set of observations of events of that type that is randomly selected and sufficiently large. Random sampling avoids observer bias that will affect the conclusion. A large sample size reduces the effect on the conclusion of random fluctuations in observations. For an abductive argument to be valid, the 'rule' must consist of a valid deductive argument. There is a logical opposition between deduction and abduction since deduction is reasoning from antecedent to consequent while abduction is reasoning from consequent to antecedent (Peirce 1868; 35). The mental operations involved in induction and abduction remain to be clarified.
In practice, statements are logically related by argumentation. Argumentation is the sequential arrangement of elementary arguments (deductive, inductive or abductive) to form an inferential chain with arguments as links. For a nonterminal link of an inferential chain, the premise contains the conclusion of the preceding argument and the conclusion is contained in the premise of the succeeding argument.
Peirce developed graded valuations for the elementary types of rational inference. These valuations, based on the attributes of uncertainty and novelty, reveal non-formal relations between the argument types. According to Peirce (1903e:233), the 'result' of a deductive argument is a necessity, the 'rule' of an inductive argument is a probability and the 'case' of an abductive argument is a possibility. In this way, the three types of argument are graded by measures of acceptance of their conclusions. The measure of certainty is 'necessity'. Measures of uncertainty are 'possibility' and 'probability'. Hence, the conclusion of a valid deductive argument (the 'result') is a necessity and without doubt. The conclusion of a valid inductive argument (the 'rule') is expressed as a probability that is based on experience and as such is uncertain. The conclusion of an abductive argument (the 'case') is only a possibility and more uncertain than a probability.
Peirce also graded the conclusions of logical arguments on the basis of their novelty. According to Peirce (after Kant) deduction infers things that are implicit in what is known i.e. the 'result' is implicit in the 'case' and is not truly new (Peirce 1901: 82-83,96-97). Induction infers things that are similar to what is known. Hence, something that is true about a certain selection of events of some type is probably true about other events of the same type i.e. the rule is statistically determined by the 'case'. In contrast, abduction infers things that differ from what is known i.e. the 'case' is only suggested by the 'result' (Peirce 1878d: 194,197). Peirce concludes that deduction (involving implicity) and induction (involving similarity) do not produce truly new ideas and that true novelty is produced only by abduction (Peirce 1901: 82-83; 1903c: 205; 1903d: 216). Peirce referred to those types of argument that increase knowledge by similarity or novelty (i.e. induction or abduction) as ampliative (synthetic) and the type of argument that does not increase knowledge (i.e. deduction) as explicative (analytic) (Peirce 1878c: 161-162; 1878d: 194).
Peirce's concept of truth is based on his model of scientific investigation. By this account, scientific investigation is an activity of a community of minds that is not limited in time or space (Peirce 1868: 52). He assumes that unrestricted thought within such a community will ultimately lead to a faithful representation of reality that is independent of any individual mind i.e. truth (Peirce 1878a: 136-137). However, these assumptions are not applicable in a clinical setting. The process of Roentgen diagnosis operates under severe temporal constraints since diagnostic conclusions are intended for use in patient care. Also in Roentgen diagnostics, questions are usually addressed by one or a very small number of minds rather than by an unlimited community. Furthermore, diagnostic judgments are usually immediate, except in exceptional cases where judgment may be delayed in order to allow for consultation or the acquisition of additional information.
Scientific abduction, requiring deductive verification, is infrequently used in clinical diagnosis. In an emergent setting, a diagnostic judgment may be nothing more than an unverified hypothesis based on clinical intuition. Even in non-emergent cases, limited clinical information, limited interpretation time or limited interpreter capacity may preclude the deductive verification of hypotheses that constitutes the 'rule' in scientific abduction (cf., Peirce 1903e: 231). Furthermore, scientific induction is not applicable to clinical diagnosis. In induction the 'case' must consist of numerous observations of a predesignated type whereas a clinical 'case' involves a single observation. (cf., Peirce 1878b: 147). However, a 'degenerate' form of induction or inference from experience is used in clinical practice. This may be termed clinical induction where the 'case' consists of a single observed event together with a personal memory of similar previously observed events. In the next section, we will examine mental association. This is a nonrational form of inference that is frequently used in clinical diagnosis.
Association is an involuntary mental operation by which consciousness of one thought evokes the consciousness of another. Hence, association is a binary relation between thoughts. Based on the three Peircean categories of thought, binary relations can be mediated in only three ways i.e. by similarity (Firstness), contiguity (Secondness) and conventionality (Thirdness) (Peirce 1868:50-51; cf., Cantor 2003, on categorical relations) where 'similarity' entails a commonality of attributes, 'contiguity' a commonality of place and 'conventionally' a commonality of meaning by agreement. Hence, the three categorical types of association are mediated by resemblance (similarity), contiguity and custom (conventionality) (after Hume 2000; cf., Peirce 1868:50). Since real events have both spatial and temporal attributes, an association between two events must involve both spatial and temporal associations. The categorical associations of spatial attributes may be termed resemblance, collocation and necessitation. Resemblance denotes a similarity of visual attributes of events. Collocation denotes the occurrence of events in the 'same' place, where sameness may mean spatial coincidence or proximity. Necessitation denotes a customarily recognized relation of compulsion between one event and another. The categorical associations of temporal attributes may be termed covariance, concurrence and succession. Covariance denotes a similarity of temporal variations of events. Temporal variations include rate of change and 'sense' of change, where 'sense' refers to the increase or decrease of an attribute with time. Concurrence denotes the occurrence of events at the 'same' time, where sameness may mean temporal coincidence or proximity. Succession denotes the customary temporal ordering of events. The Third Category associations of spatial necessitation and temporal succession constitute mental habits acquired from repeated past experience. These associations characterize causation (cf., Hume (2000 : 86, 116).
Concepts of causation
Causation may be thought of as a binary relation between events termed 'cause' and 'effect'. Two distinct types of causation were recognized in ancient Greek medicine. These involved containing and antecedent causes (for an excellent survey of these concepts, see Hankinson 1998: 376-379). Expressed in terms of the categorical typology of associations, containing causation entails the spatial associations of resemblance collocation and necessitation with the temporal associations of covariance and concurrence. In containing causation, spatial collocation and temporal concurrence denote coincidence in space and time. Furthermore, a containing cause of disease originates within the body. In contrast, antecedent causation entails the spatial associations of collocation and necessitation and the temporal associations of concurrence and succession. In antecedent causation, collocation and concurrence denote the proximity of cause and effect in space and time. Futhermore, an antecedent cause of disease originates outside of the body. Clearly, both containing causation and antecedent causation are Third Category associations.
According to David Hume, a causal relation is distinguished by its necessity. In this context, 'necessity' refers to the feeling of expectation that is produced by the memory of a constant conjunction of objects or events in past experience (Hume 2000 : 62,105). Necessity in this sense entails a relation of compulsion. Hence, constant conjunction is the essential spatial characteristic of causation. Hume also believed that the relation of causation involves regular succession or an expected temporal ordering of events determined by repeated past experience. (Hume 2000 : 61; Mackie 1980, on the regularity theory of causation). Hence, regular succession is the essential temporal characteristic of causation. It follows that Humean causation involves Third Category spatial and temporal associations. Hume considered resemblance (i.e. similarity) and contiguity to be of secondary importance in the characterization of causal association (Hume 2000 : 76).
Since deductive inference has 'necessity' as an attribute, we would expect there to be a relation between the 'necessity' of implication and the 'necessity' of causation. We have seen that causation is a binary relation between events termed 'cause' and 'effect' and that implication is a binary relation between sentences termed 'antecedent' and 'consequent'. Hume has taught us that causational necessity may be thought of as a feeling that accompanies the memory of a constant conjunction of pairs of events. By introspection, one also finds that implicational necessity is a feeling that accompanies the memory of preestablished conventions (laws of inference) that mediate pairs of sentences. In both cases, the feeling of necessity is the satisfaction of a certain expectation. Just as statements are used to represent events, relations of implication are used to represent relations of causation. In fact, causation may be represented by an implication in more than one way. An implication that partially captures the necessity of causation is the counterfactual conditional i.e. 'X causes Y' means 'If X had not occurred in the circumstances, then Y would not have occurred' (Mackie 1980:Chapter 2, on conditional analyses). Since the purpose of medical treatment is the elimination of morbid or undesirable effects, counterfactual conditionals provide a rational basis for intervention. In cases where the cause of disease is still operative, treatment involves the elimination or mitigation of the cause in order to prevent or lessen its effects. In cases where the cause of disease is no longer operative, treatment may involve the elimination or mitigation of residual effects or the prevention of recurrence of disease either by changing the circumstances in which the cause produces effects or avoidance of repetition of the cause.
Concepts of cause
Aristotle distinguished four types of causal agents, which he termed material, efficient, formal and final causes (cf. Hankinson 1998: 132-133). Peirce derived a realist version of the Aristotelian typology from two binary relations between attributes of events (Peirce 04: 315-316). In one relation, causes may be physical or mental events. In the other, causes may be inside or outside their effects. These two relations yield four combinations of attributes that represent the four Aristotelian causes. Hence, material causes are physical and internal to their effects, efficient causes are physical and external to their effects, formal causes are mental and internal to their effects and final causes are mental and external to their effects. In what follows, we adapt this modified Aristotelian typology for practical use in medical diagnostics. Since the 'effects' considered in medical diagnosis (i.e. the injuries and diseases for which 'causes' are sought) are within the body of a patient, the second dichotomy is more conveniently expressed as 'injury or disease originates either inside or outside the body'. With the assumption that the physical world is independent of mind, it is convenient to express the first dichotomy as 'injury or disease may either depend on mind or be independent of mind'. As a further concession to contemporary medical custom, 'mind' means 'human mind'. Hence, endosomatic causes are inside the body and independent of mind, exosomatic causes are outside the body and independent of mind, autopsychic causes are inside the body and dependent on the mind of the patient, allopsychic causes are outside the body of the patient and dependent on another mind. For example, autopsychic causes are thoughts in the mind of the patient that have produced effects in the body, either intentionally or unintentionally. Allopsychic causes are thoughts in other minds that have produced effects in the body of the patient, either intentionally or unintentionally. As examples, malingering, factitious disorders and Münchhausen syndrome have autopsychic causes; assault, battered child syndrome and Münchhausen syndrome by proxy have allopsychic causes; congenital, developmental and degenerative diseases have endosomatic causes; natural accidental injuries, infectious diseases and environmental diseases have exosomatic causes.
In this section, we present examples of associations that frequently arise in clinical practice. For each categorical type of association, three examples will be cited from each of three basic anatomic domains: the chest, the abdomen and the skeleton. In practice, any such association may be tested by further image sampling or imaging before it is accepted as valid.
Association by resemblance
In the lungs, a rounded opacity suggests a neoplasm, although some nonneoplastic lesions may have a similar appearance (i.e. granuloma, abscess, round atelectasis). An amorphus opacity with fading edges suggests pneumonia, although other conditions may have a similar appearance (e.g. atelectasis, contusion or infarct). An opacity containing a circumscribed radiolucency suggests cavitation.
In the abdomen, a lamellated calcific density suggests a calculus regardless of location. A smooth curvilinear calcific density suggests a thin walled cavity filled with fluid e.g. cyst or aneurysm, although some solid masses may have a similar appearance e.g. fibroid tumor. Parallel linear calcific densities suggest calcification of a tubular structure e.g. an artery.
In the skeleton, certain patterns of abnormal opacity subadjacent to convex articular surfaces, with or without signs of subchondral fracture, suggest osteonecrosis e.g. in the femoral head, humeral head, lunate etc. An unexpected radiolucent line within the image of a bone suggests brittle fracture. Multifocal osteolytic or osteoblastic lesions suggest metastatic disease.
Association by contiguity
In the chest, widening of the subcarinal angle suggests the presence of a subcarinal mass e.g. tumor, enlarged lymph nodes, enlarged left atrium. Focal widening of the paraspinal stripe suggests the presence of a lesion in the spine e.g. fracture, infection, tumor. The absence of an expected interface, for example, between the heart and an adjacent pulmonary opacity suggests contiguity and permits localization of the opacity within a specific lobe. (cf., Cantor 2000, on the Separation Signs).
In the abdomen, displacement of a gas filled viscus away from its expected position or impression of its contour suggests the presence of a mass. Separation of gas filled bowel loops suggests the presence of contiguous fluid within the peritoneal cavity. Visualization of serosal surfaces of bowel loops suggests the presence of contiguous free air in the peritoneal cavity (cf., Cantor 2000, on the Separation Signs).
In the skeleton, focal erosion of the surface of a bone suggests the presence of a contiguous soft tissue mass e.g. periosteal metastasis, soft tissue tumor, or aneurysm. A circumscribed absence of trabecular bone suggests the presence of a space occupying lesion e.g. tumor, cyst. In a Roentgen image of a joint, superposition of the articular surfaces suggests dislocation.
Association by causation
In the chest, cardiomegaly with pulmonary edema and pleural effusions suggests congestive heart failure. Acute opacification of a hemithorax with ipsilateral shift of the mediastinum suggests pulmonary collapse. Vascular clips on the surface of the heart in the distribution of the coronary arteries suggest previous coronary artery bypass surgery.
In the abdomen, distension of the colon that terminates abruptly, with little or no gas distally, suggests colonic obstruction. Spontaneous pneumoperitoneum with signs of peritonitis suggests bowel perforation. Surgical clips in the iliac fossa on one side of the pelvis in a patient with uremic osteopathy suggest the presence of a transplanted kidney.
In the skeleton, a fracture of the radius with resultant shortening, in the absence of an ulna fracture, suggests dislocation of the distal radioulnar joint. Posterolateral flattening of the humeral head suggests impact fracture from prior anterior dislocation. In a Roentgen image of a knee, the presence of surgical tunnels containing bone plugs and screws in customary positions suggest previous anterior cruciate ligament reconstruction.
In this section, we define two irreducible semantic structures that are of fundamental importance in Roentgen diagnosis. These structures are defined on binary relations and are termed ordering and markedness. The meaning conveyed by ordering is 'succession' and the meaning conveyed by markedness is 'difference'. Subsequently, we will use these semantic structures to construct a semiotic modeling system for Roentgen diagnosis.
A binary relation is an ordered pair of terms consisting of a predecessor and a successor (see Tarski , Chapter III for an exposition of the Theory of Relations). In sentential logic, implication is a reflexive and transitive binary relation between sentences (cf. Copi and Cohen 2000: 344, Principle of Identity; 282, Hypothetical Syllogism). This type of relation determines a quasi-ordering (Suppes 1960:72) of sentences. In common experience, the notion of causation entails an asymmetric and transitive binary relation between events. Since the relation is asymmetric, it cannot be reflexive. For if it were, it would imply its own negation. Hence, causation is an irreflexive, asymmetric and transitive binary relation between events. This type of relation is usually referred to as strict partial ordering. (Suppes 1960:72). In what follows, it will be termed causal ordering.
Markedness is an irreducible semantic structure that represents the relation of 'difference'. A binary opposition is a binary relation with a marked predecessor and an unmarked successor (cf., Cantor [2000,2003], after Roman Jacobson). There are two types of markedness for binary oppositions. These are termed the 'general' and the 'specific' types (after Jacobson). In the general type of markedness, the marked term has an attribute that is not present in the unmarked term. In the specific type of markedness, the marked term has more or less of an attribute than the unmarked term. In Roentgen semiotics, the unmarked term of a binary opposition has an attribute that is expected on the basis of past experience. It follows that markedness of the general type in Roentgen semiotics is either the presence of an unexpected attribute or the absence of an expected attribute of a Roentgen image. The specific type of markedness in Roentgen semiotics is the presence of more or less of an expected attribute of a Roentgen image. The awareness of markedness is accompanied by a feeling of 'surprise' or 'dissatisfaction' provoked by the non-fulfillment of an expectation.
The process of Roentgen diagnosis begins with the recognition of the normal or the abnormal in an image. The normal is that which is expected. The abnormal is the absence of the normal. Therefore, the recognition of the normal is the fulfillment of an expectation while the recognition of the abnormal is the non-fulfillment of an expectation. This recognition of the presence or absence of the normal is based on two mental operations, which we will term conformation and discrimination. Conformation is the recognition of a sameness between an image and what is expected in the image. Hence, conformation is a binary relation between a perception and an expectation with the same attributes. In the recognition of the normal, the image conforms to the expectations of the reader. Discrimination is the recognition of a difference between an image and what is expected in the image. Hence, discrimination is a binary opposition between a perception and an expectation where the perception is marked and the expectation is unmarked. In Roentgen semiotics, binary oppositions are used as detectors of abnormality and as discriminators in differential diagnosis (Cantor 2000,2003).
Causation and implication
In general, association is a mental event in which thoughts with attributes in common occur in succession. Hence, an association is a binary relation between thoughts. We have seen (after Hume) that causation is an association between events in constant conjunction and regular succession in past experience. Hence, causation is a binary relation between events. Since causation involves regular succession, a cause is that event in a causal relation that is marked by the memory of precedence while its effect is unmarked. Therefore, causation may be thought of as a binary opposition between events. In sentential logic, implication is a binary relation between statements that involves logical succession. An antecedent is marked by the attribute of logical precedence while its consequent is unmarked. Therefore, the relation of implication is a binary opposition of statements. Markedness in both causation and implication is of the general type.
We recall that a triadic (Peircean) sign consists of a binary opposition between a representamen and an object that is mediated by an interpretant. In what follows, the representamen and object will be termed the correlates of a sign. When these correlates have the same ground, it will be referred to as the ground of the sign. An aggregate of signs all of which have the same ground will be called a semiotic domain. We have seen that an implication is a binary opposition between a 'case' and a 'result' that is mediated by a 'rule' (after Peirce). Hence, implication is a triadic sign with its ground in sentential logic. We have also seen that causation is a binary opposition between events termed 'cause' and 'effect' that is mediated by custom (after Hume). In this context, the term 'custom' refers to the memory of events in constant conjunction and regular succession. Hence, causation is a triadic sign with its ground in the physical world. A semiotic modeling system is a correspondence between different semiotic domains that preserves semiotic structure (cf., Sebeok and Danesi , on Modeling System Theory). One such system is the correspondence between sentential logic and the physical world that is produced by natural language. Recall that sentential logic is the semiotic domain of signs with sentences for correlates and that the physical world is the semiotic domain of signs with events for correlates. It follows that verbal representation provides a correspondence between logical and physical domains that preserves semiotic structure. For a pair of nonequivalent statements that represent a pair of distinct events, the logical relation between antecedent and consequent corresponds to the physical relation between cause and effect. With this correspondence, the semantic structures of ordering and markedness are preserved. Furthermore, the subjective 'necessity' of implication corresponds to the 'necessity' of causation (Figure 1). In this modeling system, a conjunction of statements corresponds to the copresence of events and the negation of a statement corresponds to the absence of an expected event. A causal chain is commonly understood to be a causally ordered sequence of events. Furthermore, a causal explanation of an event is a sequence of statements, ordered by implication that corresponds to a causal chain ending in that event. Hence, explanations are semiotic models produced by a language based semiotic modeling system.
A radiological report is a semiotic model of a selected anatomic region of a patient. This type of model is expressed in language and conveys diagnostic information. Roentgen diagnosis involves the detection, localization, identification and explanation of abnormal events in a patient as revealed by Roentgen signs. Clinical explanations consist of sequences of inferences that contain abductions i.e. inferences from effect to cause. The clinician, as pragmatist, prefers explanations that represent causal chains with treatable links.