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The Representation of Medical Reasoning Models in
Resolution-based Theorem Provers
Originally Presented by
Peter Lucas
Department of Computer Science, Utrecht University
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
representation is being investigated.
to
logical
• The purpose of translation is to obtain a
representation
that
permits
automated
interpretation by a Logic-based Theorem
Prover.
Medical
Reasoning
Models
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.
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.
First Order Logic
P(t1,t2,…,tn)
P : relation
ti : objects
First Order Logic
P(t1,t2,…,tn)
P : relation
ti : objects
Atom
Individual Object
Class of Objects
Dependencies upon
other Objects
Constant
Variable
Function
In logic-based Theorem Prover, the syntax of
formulae is restricted to clausal form.
Clause: a finite disjunction literals.
Literals: an atom
or negation of an atom
(positive literals)
(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.
Age(johnson) = 30
• Multi Valued : Several fill-ins may occurs at
the same time.
Sign(johnson, jundice)
Sign(johnson, spider_angiomas)
Medical
Reasoning
Models
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.
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 ) = female
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;
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 nonHorn clauses.
So, a Horn-Clause based Theorem Prover is
insufficient.
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 T
The diagnostic problem solving can be established as
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
relations.
axiomatization of the basic anatomical
• 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.
connected(x , y)
It means facial nerve runs from level x up to level y.
• Relation between anatomical structures and signs that may
arise due to facial nerve lesion.
∀x∀y ( Lesion( x ) ∧ Connected(y , x) → Lesion( y ) )
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
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:
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:
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
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
paresis_superficial_neck_musculature
For y we have hyperacuasis, dry_mouth and
taste_loss_anterior_part_tongue
Causal Reasoning
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
• 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’
rn-1’
rn’
.
.
.
r1
r2
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
Conclusion
• 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.
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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