The Representation of Medical Reasoning Models in Resolution-based Theorem Provers

1. The Representation of Medical Reasoning Models in Resolution-based Theorem Provers Originally Presented by Peter Lucas Department of Computer Science, Utrecht University Presented by SarbarthaSengupta (10305903) Megha Jain (10305028) Anjali Singhal (10305919) (14th Nov, 2010)

2. Introduction • Several common reasoning models in medicine are being investigated, familiar from the AI literature. • The mapping of those models to logical representation is being investigated. • The purpose of translation is to obtain a representation that permits automated interpretation by a Logic-based Theorem Prover.

3. Medical Reasoning Models Causal Reasoning Diagnostic Anatomical

4. Motivation Logic as a language for representation of medical knowledge. First order predicate logic: language to express knowledge concerning objects and relationship between objects.

5. Logic: One of the major candidate of knowledge representation language in future expert system. • Most other knowledge-representation languages are not completely understood. • Logic is the unifying framework for integrating expert systems and database systems.

6. Hypotheses • The use of logic language: Revel the underlying structure of a given medical problem. • First order logic – sufficiently flexible for the representation of a significant fragment of medical knowledge.

7. First Order Logic P : relation ti : objects P(t1,t2,…,tn)

8. First Order Logic P : relation ti : objects P(t1,t2,…,tn) Atom Individual Object Class of Objects Dependencies upon other Objects Constant Variable Function

9. In logic-based Theorem Prover, the syntax of formulae is restricted to clausal form. Clause: a finite disjunction literals. Literals: an atom (positive literals) or negation of an atom (negative literals) Horn clause: contains at least one positive negation. Null clause :

10. Logic Data Representation in Medicine • Individual Objects : patients, substances … • Properties of the objects : physiological states, level of substances … • Single Valued: Unique at a certain point of time. • Multi Valued : Several fill-ins may occurs at the same time. Age(johnson) = 30 Sign(johnson, jundice) Sign(johnson, spider_angiomas)

11. Medical Reasoning Models Causal Reasoning Diagnostic Anatomical

12. Diagnostic Reasoning • Logical representation of diagnostic reasoning is viewed as a deductive process instead of abductive process • Aspects of formalization of medical diagnostic reasoning: • Some suitable logical representation of patient data must be chosen. • We have to decide on the logical representation of diagnostic medical knowledge.

13. Attempt to reformulate the HEPAR system. HEPAR System: a rule based expert system for the diagnosis of disorders of liver and biliary tract.

14. sex (patient1 ) = female age(patient1 ) = 12 Complaint(patient1,arthralgia ) time course(patient1,illness ) = 150 ... Signs(patient1,Kayser Fleischer rings) ... ASAT(patient1,labresult,biochemistry ) = 200 urinary copper (patient1,labresult,biochemistry ) = 5 ... In this case, the representation language is primarily viewed as a term manipulation language, not as a logical language.

15. patient (name = patient1 ; sex = female; age = 12; ... complaint = [arthralgia ]; ... ) The representation of patient data in logic seems straightforward.

16. Diagnostic medical knowledge is represented in HEPAR system using production rules. Object-attribute-value According to the declarative reading of rules,

17. Diagnostic medical knowledge is represented in HEPAR system using production rules. Object-attribute-value According to the declarative reading of rules, Translation of most production rules is straightforward. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

18. More than 50% of the production rules in the HEPAR system could only be represented in non-Horn clauses. So, a Horn-Clause based Theorem Prover is insufficient. Diagnostic reasoning in medicine typically involves reasoning about diagnostic categories.

19. Resolution based Theorem Prover The data of a specific patient represented as A collection of unit clause D, The diagnostic theory T The diagnostic problem solving can be established as x: patient name. y: possible discloser.

20. Automated reasoning in which knowledge concerning the anatomy of the human body is applied. Point of departure is the axiomatization of the basic anatomical relations. Anatomical Reasoning

21. Only certain anatomical structures are connected to each other in a qualitative way. • This is axiomated by the connected predicate. • Connected predicate is defined as a transitive, irreflexive relation : ∀x ∀y ∀z(connected(x , y) ∧ connected(y , z) → connected(x , z)) ∀x(⌐connected(x , x))

22. Formalization of Knowledge base for Facial Palsy disease : This is paralysis of part of the face caused by non-functioning of the nerve that controls the muscles of the face. This nerve is called the facial nerve. Image taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

23. Axiomatization of anatomical relationships by giving a domain specific fill-in for connected predicate. It means facial nerve runs from level x up to level y. connected(x , y)

24. Relation between anatomical structures and signs that may arise due to facial nerve lesion. Signs associated with a lesion at certain level x includes all the signs of a lesion at a lower level y. ∀x∀y ( Lesion( x ) ∧ Connected(y , x) → Lesion( y ) )

25. Relation between a lesion at a certain level and the specific anatomical structures that will be affected by the lesion affected by the lesion, expressed by the unary predicate Affected. (Lesion(level) ↔ (Affected(structure 1) ∧ Affected(structure 2) ∧….Affected(structure n)))

26. Relation between structure affected and specific signs and complaints for this. (Affected(structure) ↔ (sign(x₁) ∧ sign(x₂) ∧….sign(xₐ))) (Affected(structure) ↔ (complaint(x₁) ∧ complaint(x₂) ∧….complaint(xₐ)))

27. Using this Logical theory Expert system can derive: For a level the values corresponding to x and y can be calculated using the knowledge base. T ∪ { Lesion(level)} ∪ {⌐Sign( x )} ∪ {⌐Complaint( y ) } ⊢ □

28. Connected predicate for facial nerve: Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

29. Relation between anatomical structures and signs that may arise due to facial nerve lesion. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

30. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

31. Relation between structure affected and specific signs and complaints for this. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

32. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

33. T ∪ { Lesion(stapedius_nerve)} ∪ {⌐ Sign( x )} ∪ {⌐ Complaint( y ) } ⊢ □ For x we have mouth_droops, cannot_whistle, cannot_close_eyes, Bell, flacid_cheeks, cannot_wrinkle_forehead, and paresis_superficial_neck_musculature For y we have hyperacuasis, dry_mouthand taste_loss_anterior_part_tongue

34. Causal Reasoning • Reasoning about cause – effect relationships is called causal reasoning. • The representation of causal knowledge in logic may be represented by means of collection of logical implications of the form : Causal Reasoning cause effect

35. Cause and effect are the conjunction of literals.They represent state of some parameter. • Eg. Level of a substance in blood. It may be qualitative or numeric • conc(blood, sodium) = 125 • conc(blood, sodium) = decreased • Eg. of causal reasoning: Negative Feedback Process

36. Negative Feedback Process rn-1’ rn’ r1’ r1 r2 rn ~s S . . . Where s, ri , ri’ , 1≤i≤n, n≥1 are literals

37. Image taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

38. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

39. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

40. Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

41. Logic Implication Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence

42. Conclusion • We investigated the applicability of logic as a language for the representation of a number of medical reasoning models. • It was shown that the language of first-order predicate logic allowed for the precise, and compact, representation of these models. • Generally, in translating domain knowledge into logic, many of the subtleties that can be expressed in natural language are lost. In our study, it appeared that this problem was less prominently present.

43. References [1] Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence, Published in: Artificial Intelligence in Medicine, 5(5), 395{414}, 1993. [2] M. H. VAN EMDEN AND R. A. KOWALSKI, University of Edinburgh, Edinburgh, Scotland, The Semantics of Predicate Logic as a Programming Language,Journal of the Association for Computing Machinery, Vol 23, No 4, pp733-742, October 1976. [3] Artificial Intelligence in Medicine, Randall Davis, Casimir A. Kulikowski, Edited by Peter Szolovits, AAAS Selected Symposia Series, Volume 51, 1982 . [4] P.J.F. Lucas, R.W. Segaar, A.R. Janssens, HEPAR: an expert system for the diagnosis of disorders of the liver and biliary tract, published in the journal of the international association for the study of the liver, Liver 9 (1989) 266-275.

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