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The Representation of Medical Reasoning Models in

l b d h

Resolution-based Theorem Provers

Originally Presented byg y y

Peter Lucas

Department of Computer Science, Utrecht University

Presented by Presented by Sarbartha Sengupta (10305903) Megha Jain (10305028) Anjali Singhal (10305919) (14th Nov, 2010)

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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

h d

representation that permits automated interpretation by a Logic-based Theorem Prover.

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Medical Reasoning

Models

Causal Diagnostic Anatomical Causal

Reasoning

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Motivation

Logic as a language for representation of medical knowledge.

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

between objects.

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

• Most other knowledge-representation languages are not completely understood

are not completely understood.

L i i h if i f k f i i

• Logic is the unifying framework for integrating expert systems and database systems.

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Hypotheses yp

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

• First order logic – sufficiently flexible for the

representation of a significant fragment of medical

k l d

knowledge.

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First Order Logic

P(t

1

,t

2

,…,t

n

)

P : relation ti : objects

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First Order Logic

P(t

1

,t

2

,…,t

n

)

P : relation ti : objects

Atom Atom

Individual Object Class of Objects Dependencies upon  other Objects

Constant Variable Function

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In logic-based Theorem Prover, the syntax of fo m lae is est icted to cla sal fo m

formulae 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 :

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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)

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Medical Reasoning

Models

Causal Diagnostic Anatomical Causal

Reasoning

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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

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Attempt to reformulate the HEPAR system.

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

diagnosis of disorders of liver and biliary tract.

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sex (patient1 ) = female age(patient1 ) = 12

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.

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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.

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

Object-attribute-value Object attribute value

According to the declarative reading of rules,

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

Object-attribute-value 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

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More than 50% of the production rules in the

HEPAR system could only be represented in non- 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 Diagnostic reasoning in medicine typically involves reasoning about diagnostic categories.

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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.

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Anatomical Reasoning g

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.

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

other 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) ר connected(y , z) → connected(x , z)) 

׊x(⌐connected(x , x))

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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 functioning 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

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• Axiomatization of anatomical relationships by giving a domain p y g g specific fill‐in for connected predicate.

connected(x , y) 

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

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

Si i t d ith l i t t i l l i l d ll

Signs associated with a lesion at certain level x includes all  the signs of a lesion at a lower level y.

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• Relation between a lesion at a certain level and the specific  anatomical structures that will be affected by the lesion

anatomical structures that will be affected by the lesion  affected by the lesion, expressed by the unary predicate  Affected.

(Lesion(level) ↔ (Affected(structure 1) ר Affected(structure 2)  ר….Affected(structure n)))

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• Relation between structure affected and specific signs and  complaints for this

complaints for this. 

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

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

ר….complaint(xₐ)))

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• 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.

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• 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 Intelligence

in Resolution-based Theorem Provers, Artificial Intelligence

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• 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

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

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• Relation between structure affected and specific signs and  l i f hi

complaints for this. 

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

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

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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 t

paresis_superficial_neck_musculature

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

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Causal Reasoning

Causal Reasoning

Reasoning about cause – effect relationships is

Causal Reasoning

g p

called 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

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• 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 ) 125 conc(blood, sodium) = 125

conc(blood, sodium) = decreased( , )

• Eg. of causal reasoning: Negative Feedback Process

Process

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Negative Feedback Process Negative Feedback Process

S

r

1

S

r

1

r

1

’ r

2

.

r

n-1

’ r

n

. .

r

n

’ ~s

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

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

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

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

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

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Logic Implication Logic Implication

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

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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.

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•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.

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Conclusion

• We investigated the applicability of logic as a language for 

h i f b f di l i

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 these models.

• Generally, in translating domain knowledge into logic, many 

f th btl ti th t b d i t l l

of the subtleties that can be expressed in natural language  are lost. In our study, it appeared that this problem was less  prominently present.

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References

[1] Peter Lucas, The Representation of Medical Reasoning Models in Resolution based Theorem Provers Artificial Intelligence Published 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,

[ ] , y g ,

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

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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Questions ?

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Thank You

References

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