The Representation of Medical Reasoning Models in l b d hResolution-based Theorem Provers

Originally Presented byg y y

Peter LucasDepartment of Computer Science, Utrecht University

Presented byPresented bySarbartha Sengupta (10305903)

Megha Jain (10305028)Anjali Singhal (10305919)

(14th Nov, 2010)

Introduction

• Several common reasoning models in medicine arebeing investigated, familiar from the AI literature.

• The mapping of those models to logicalrepresentation is being investigated.

• The purpose of translation is to obtain ah drepresentation that permits automated

interpretation by a Logic-based TheoremProver.

Medical Reasoning

Models

Causal Diagnostic Anatomical

Causal Reasoning

Motivation

Logic as a language for representation of medicalknowledge.

First order predicate logic: language to expressknowledge concerning objects and relationshipbetween objects.between objects.

Logic: One of the major candidate of knowledgerepresentation language in future expert system.p g g p y

• Most other knowledge-representation languagesare not completely understoodare not completely understood.

L i i h if i f k f i i• Logic is the unifying framework for integratingexpert systems and database systems.

Hypothesesyp

• The use of logic language: Revel the underlying g g g y gstructure of a given medical problem.

• First order logic – sufficiently flexible for the representation of a significant fragment of medical k l dknowledge.

First Order Logic

P(t1,t2,…,tn) P : relationti : objects

First Order Logic

P(t1,t2,…,tn) P : relationti : objects

AtomAtom

Individual Object Class of ObjectsDependencies upon 

other Objects

Constant Variable Function

In logic-based Theorem Prover, the syntax of fo m lae is est icted to cla sal fo mformulae is restricted to clausal form.

Clause: a finite disjunction literals.

Literals: an atom (positive literals)or negation of an atom (negative 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 …

Si l V l d U i i i f • Single Valued: Unique at a certain point of time.

Age(johnson) = 30

• Multi Valued : Several fill-ins may occurs at the same time

g (j )

the same time.

Sign(johnson, jundice)Sign(johnson spide angiomas)Sign(johnson, spider_angiomas)

Medical Reasoning

Models

Causal Diagnostic Anatomical

Causal 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.g g

Attempt to reformulate the HEPAR system.

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

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

Th t ti f ti t d t i l i The representation of patient data in logic seems straightforward.

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

Object-attribute-valueObject attribute value

According to the declarative reading of rules,

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

Object-attribute-valueObject 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-HEPAR system could only be represented in nonHorn clauses.

So, a Horn-Clause based Theorem Prover is insufficient.

Diagnostic reasoning in medicine typically involves Diagnostic reasoning in medicine typically involves reasoning about diagnostic categories.

Resolution based Theorem Prover

The data of a specific patient represented as

A collection of unit clause D,The diagnostic theory Tg y

The diagnostic problem solving can be established as

x: patient name.y: possible discloser.

Anatomical Reasoningg

Automated reasoning in which knowledge concerning the anatomy ofthe human body is applied.

Point of departure is the axiomatization of the basic anatomicalrelations.

• Only certain anatomical structures are connected to each other in a qualitative wayother in a qualitative way.

• This is axiomated by the connected predicate.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))

li i f l d b f i l l di• Formalization of Knowledge base for Facial Palsy disease : 

This is paralysis of part of the face caused by non functioningThis 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 p y g gspecific fill‐in for connected predicate.

connected(x , y) 

It means facial nerve runs from  level  x up to level y.

• Relation between anatomical structures and signs that may• Relation between anatomical structures and signs that may arise due to facial nerve lesion. 

x y ( Lesion( x )  Connected(y , x) → Lesion( y ) )

Si i t d ith l i t t i l l i l d llSigns associated with a lesion at certain level x includes all the signs of a lesion at a lower level y.

• Relation between a lesion at a certain level and the specific anatomical structures that will be affected by the lesionanatomical 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 thiscomplaints for this. 

(Affected(structure) ↔ (sign(x₁)  sign(x₂)  ….sign(xₐ)))

(Affected(structure) ↔ (complaint(x₁)  complaint(x₂)       ….complaint(xₐ)))….complaint(xₐ)))

• Using  this Logical theory Expert system  can derive:

T  { Lesion(level)}  {⌐Sign( x )}  {⌐Complaint( y ) }  □

For a level the values corresponding to x and y can be 

calculated using the knowledge base.

• Connected predicate for facial nerve:Connected predicate for facial nerve:

Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers Artificial Intelligencein 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 l i f hicomplaints 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

T { Lesion(stapedius nerve)} {⌐ Sign( x )} {⌐ Complaint( y ) }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 

i fi i l k l tparesis_superficial_neck_musculature

For y we have hyperacuasis dry mouth andFor y we have hyperacuasis, dry_mouth and 

taste_loss_anterior_part_tongue

Causal ReasoningCausal Reasoning•Reasoning about cause – effect relationships is

Causal Reasoning

g pcalled causal reasoning.

• The representation of causal knowledge in logic The representation of causal knowledge in logic may be represented by means of collection of logical implications of the form :

cause effect

• Cause and effect are the conjunction of literalsCause and effect are the conjunction of literals.They represent state of some parameter.

E L l f b t i bl d It b • Eg. Level of a substance in blood. It may be qualitative or numeric

(bl d di ) 125conc(blood, sodium) = 125

conc(blood, sodium) = decreased( , )

• Eg. of causal reasoning: Negative Feedback ProcessProcess

Negative Feedback ProcessNegative Feedback Process

S r1S r1r1’ 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 ImplicationLogic Implication

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

N h ill ti Now how will negative feedback used in theorem prover?

•The numeric or qualitative state of a substance is change.

• Theorem prover tries to match with Theorem prover tries to match with predicate of the form cause -> effect.

•Accordingly effect of cause is found, now it will try to find effect generated due to this will try to find effect generated due to this effect and so on.

•Now in the example taken here it will end up proving a contradiction.

• Hence the effect due to the initial cause is nullified.

Conclusion

• We investigated the applicability of logic as a language for h i f b f di l ithe 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 modelsthese models.

• Generally, in translating domain knowledge into logic, many f th btl ti th t b d i t l lof the subtleties that can be expressed in natural language 

are lost. In our study, it appeared that this problem was less prominently present.

References

[1] Peter Lucas, The Representation of Medical Reasoning Models inResolution based Theorem Provers Artificial Intelligence PublishedResolution-based Theorem Provers, Artificial Intelligence, Publishedin: Artificial Intelligence in Medicine, 5(5), 395{414}, 1993.

[2] M. H. VAN EMDEN AND R. A. KOWALSKI, University of Edinburgh,[ ] , y g ,Edinburgh, Scotland, The Semantics of Predicate Logic as aProgramming Language, Journal of the Association for ComputingMachinery, 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 1982Volume 51, 1982 .

[4] P.J.F. Lucas, R.W. Segaar, A.R. Janssens, HEPAR: an expert systemfor the diagnosis of disorders of the liver and biliary tract, published inthe journal of the international association for the study of the liver,Liver 9 (1989) 266-275.

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