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)
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.
Medical Reasoning
Models
Causal Diagnostic Anatomical Causal
Reasoning
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.
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.
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.
First Order Logic
P(t
1,t
2,…,t
n)
P : relation ti : objectsFirst Order Logic
P(t
1,t
2,…,t
n)
P : relation ti : objectsAtom Atom
Individual Object Class of Objects Dependencies upon other Objects
Constant Variable Function
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 :
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 tract
diagnosis of disorders of liver and biliary tract.
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.
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-value Object attribute value
According to the declarative reading of rules,
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
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.
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 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.
• 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))
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
• 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.
• Relation between anatomical structures and signs that may
• Relation between anatomical structures and signs that may arise due to facial nerve lesion.
xy ( 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.
• 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)))
• 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)))
• 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 Intelligence
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 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
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 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
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
• 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
Negative Feedback Process Negative Feedback Process
S
r
1S
r
1r
1’ r
2.
r
n-1’ r
n. .
r
n’ ~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 Logic Implication
Example taken from: Peter Lucas, The Representation of Medical Reasoning Models p , p g in 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 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.
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.