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

Originally Presented by

Peter LucasDepartment of Computer Science, Utrecht University

Presented bySarbartha Sengupta (10305903)

Megha Jain (10305028)Anjali Singhal (10305919)

(14th Nov, 2010)

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.

Medical Reasoning

Models

Diagnostic AnatomicalCausal

Reasoning

Logic as a language for representation of medical knowledge.

First order predicate logic: language to express knowledge concerning objects and relationship between objects.

Motivation

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.

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.

P(t1,t2,…,tn)P : relationti : objects

First Order Logic

P(t1,t2,…,tn)P : relationti : objects

Atom

Individual Object

Constant

Class of Objects

Variable

Dependencies upon other Objects

Function

First Order Logic

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 :

Logic Data Representation in Medicine

1.Individual Objects : patients, substances …

2.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)

Medical Reasoning

Models

Diagnostic AnatomicalCausal

Reasoning

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.

Attempt to reformulate the HEPAR system.

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

sex (patient1 ) = femaleage(patient1 ) = 12Complaint(patient1,arthralgia )time course(patient1,illness ) = 150...Signs(patient1,Kayser Fleischer rings)...ASAT(patient1,labresult,biochemistry ) = 200urinary copper (patient1,labresult,biochemistry ) = 5...

In this case, the representation language is primarily viewed as a term manipulation language, not as a logical language.

patient (name = patient1 ;sex = female;age = 12;...complaint = [arthralgia ];...)

The representation of patient data in logic seems straightforward.

Diagnostic medical knowledge is represented in HEPAR system using production rules.

Object-attribute-value

According to the declarative reading of rules,

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

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.

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

Resolution based Theorem Prover

x: patient name.y: possible discloser.

Anatomical Reasoning

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.

• 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))

• 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

• 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)

• 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 ) )

• 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)))

• 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)))

• 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 ) } □∪ ∪ ∪ ⊢

• Connected predicate for facial nerve:

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

• 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

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

• 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

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

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_mouth and taste_loss_anterior_part_tongue

T { Lesion(stapedius_nerve)} {⌐ Sign( x )} {⌐ Complaint( y ) } ∪ ∪ ∪ ⊢□

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 :

cause effect

Causal Reasoning

• 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

Negative Feedback Process

S r1

r1’ r2

rn-1’ rn

.

.

.

rn’ ~s

Where s, ri , ri’ , 1≤i≤n, n≥1 are literals

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

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

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

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

Logic Implication

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

• 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.

Conclusion

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, pp 733-742, 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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