Provers Originally Presented by Peter Lucas Department of Computer Science Utrecht University Presented by Sarbartha Sengupta 10305903 Megha Jain 10305028 Anjali Singhal 10305919 ID: 927417
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Slide1
The Representation of Medical Reasoning Models in Resolution-based Theorem Provers
Originally Presented byPeter LucasDepartment of Computer Science, Utrecht University
Presented
by
Sarbartha
Sengupta
(10305903)
Megha
Jain (10305028
)
Anjali
Singhal
(10305919)
(14
th
Nov, 2010)
Slide2Introduction
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
.
Slide3Medical Reasoning Models
Diagnostic
Anatomical
Causal Reasoning
Slide4Logic as a language for representation of medical knowledge.
First order predicate logic: language to express knowledge concerning objects and relationship between objects.
Motivation
Slide5Logic: 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.
Slide7P(t1,t2
,…,tn)
P : relation
t
i
:
o
bjects
First Order Logic
Slide8P(t1,t2
,…,tn)
P : relation
t
i
:
o
bjects
Atom
Individual Object
Constant
Class of Objects
Variable
Dependencies upon other Objects
Function
First Order Logic
Slide9In 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 :
Slide10Logic 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
)
Slide11Medical Reasoning Models
Diagnostic
Anatomical
Causal Reasoning
Slide12Diagnostic Reasoning
Logical representation of diagnostic reasoning is viewed as a deductive process instead of abductive processAspects 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.
Slide13Attempt to reformulate the HEPAR system.HEPAR System: a rule based expert system for the diagnosis of disorders of liver and biliary tract.
Slide14sex (patient1 ) = femaleage(patient1
) = 12Complaint(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.
Slide15patient (name = patient1 ;sex = female;age = 12;...
complaint = [arthralgia ];...)The representation of patient data in logic seems straightforward.
Slide16Diagnostic medical knowledge is represented in HEPAR system using production rules. Object-attribute-value
According to the declarative reading of rules,
Slide17Diagnostic 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
Slide18More 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.
Slide19The 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.
Slide20Anatomical 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.
Slide21Only 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))
Slide22Formalization 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
Slide23Axiomatization 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)
Slide24Relation 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 ) )
Slide25Relation 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)))
Slide26Relation 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)))
Slide27Using 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 ) } ⊢ □
Slide28Connected predicate for facial nerve:
Example taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers
, Artificial Intelligence
Slide29Relation 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
Slide30Example taken from: Peter
Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence
Slide31Relation 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
Slide32Example taken from: Peter
Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem Provers, Artificial Intelligence
Slide33For 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 ) } ⊢ □
Slide34Causal 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
Slide35Cause 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
.
o
f causal reasoning
: Negative Feedback Process
Slide36Negative Feedback Process
S
r
1
r
1
’
r
2
r
n-1
’
r
n
.
.
.
r
n
’
~s
Where s, r
i
, r
i
’ , 1≤i≤n, n≥1 are literals
Slide37Image taken from: Peter Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem
Provers, Artificial Intelligence
Slide38Example taken from: Peter
Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem
Provers
, Artificial Intelligence
Slide39Example taken from: Peter
Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem
Provers
, Artificial Intelligence
Slide40Example taken from: Peter
Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem
Provers
, Artificial Intelligence
Slide41Logic Implication
Example taken from: Peter
Lucas, The Representation of Medical Reasoning Models in Resolution-based Theorem
Provers
, Artificial Intelligence
Slide42Now how will negative feedback used in theorem prover?
The numeric or qualitative state of a substance is change. Theorem prover tries to match with predicate of the form cause -> effect.
Slide43Accordingly effect of cause is found, now it 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.
Slide44We 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
Slide45References
[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
.
Slide46Questions ?
Slide47Thank You