Artificial Intelligence in Medicine HCA 590 (Topics in Health Sciences)

Artificial Intelligence in MedicineHCA 590 (Topics in Health Sciences) Rohit Kate 2. Knowledge Representation

References • Chapter 2, Principles of Biomedical Informatics by Ira J. Kalet, Academic Press, 2008. • Nardi, D., & Brachman, R. J. (2002). An introduction to description logics. In F. Baader et al. (Eds.), Description logic handbook. Cambridge: Cambridge University Press. • http://vision.unipv.it/IA2/aa2004-2005/IntroductionToDescriptionLogics-01.pdf

What is Knowledge Representation (KR)? • Intelligence in a domain, for e.g. biomedical domain, is impossible without sufficient knowledge • Representing knowledge of a domain in a computer processable form to enable Artificial Intelligence • Automated reasoning • Automated discovery • Organizing knowledge

A Small Motivating Example • Given the knowledge: • If a particulate material is being moved and is dry then it will be airborne • If particulates are toxic and airborne they will increase incidence of asthma • If there are more incidences of asthma then there will be more clinical visits • What all can be concluded if we are given that some particles that are being moved are dry and toxic? • What can be concluded if we are given an increase in clinical visits? • Can all this be done automatically by a computer? • Yes, if the knowledge is represented in a suitable formalism which enables automated reasoning by only symbol manipulation

What are different formalisms of KR? • Logic • Propositional Logic • First-order Logic • Description Logic • Semantic Networks and Ontologies

Propositional Logic: Syntax • Statements about the world is represented using some constants, symbols and connectives • Logical constants: True, False • Propositional Symbols: e.g. P, Q, Airborne, Dry • Represent facts about the world • Can be either True or False • Atomic sentences/Atomic formulas • Sentences/formulas are combined by connectives to form larger sentences/formulas: and [conjunction] or [disjunction] implies [implication] not [negation]

Propositional Logic: Examples • Particulate is dry: dry • Particulate is being moved: moved • Particulate is airborne: airborne • Particulate is dry and being moved: dry moved • Particulate is dry or being moved: dry moved • Particulate is not dry: dry • If particulate is dry and being moved then it will be airborne: dry moved  airborne • If particulate is not dry and being moved then it will not be airborne: dry moved  airborne

Propositional Logic • User decides the propositional symbols, e.g. dry and airborne, to represent the ideas • User gives meaning to each propositional symbol, i.e. what they stand for in the real world • Well-formed sentences are formed using symbols and connectives and other sentences • Knowledge can be encoded using a set of sentences, this is called a knowledge base

Propositional Logic • Given • If a particulate material is being moved and is dry then it will be airborne • If particulates are toxic and airborne they will increase incidence of asthma • If there are more incidences of asthma then there will be more clinical visits • Knowledge base in propositional logic moved ^ dry => airborne toxic ^ airborne => more-asthma more-asthma => more-clinical-visit • A knowledge base is implicitly a conjunction of all its sentences (moved ^ dry => airborne) ^ (toxic ^ airborne => more-asthma) ^ (more-asthma => more-clinical-visit)

Propositional Logic • In a possible world, each symbol has a truth value of True or False • Truth value of a sentence can be computed from the truth values of the symbols it contains Truth table

Propositional Logic • In a possible world, each symbol has a truth value of True or False • Truth value of a sentence can be computed from the truth values of the symbols it contains Truth table What is the truth table for (P^Q)v( P^Q)  Q?

Entailment • A sentence S1 is said to be entailed by a sentence S2 if whenever S2 is true S1 is also true, written as S2 |= S1 • Typically, we want to know if something, say S, is true given the knowledge base, i.e. whether KB |= S • One way to do determine entailment is to compute truth tables and check for every combination of truth values for the symbols whether S2 is true whenever S1 is true • Example,  (P V Q) |=  P ^  Q

Rules of Inference • But for n symbols it would require computing 2^n rows of truth tables which is computationally very expensive • An alternate is to use rules of inference • Purely symbol-based manipulation of formulas to derive new formulas • Modus Ponens: If P and P=>Q then Q • Elimination: If P^Q then P • Introduction: If P then P v Q • Implication elimination: If P => Q then  P v Q • Unit resolution: If P v Q and  Q then P • Resolution: If P v Q and  Q v R then P v R

Rules of Inference • Inference rules can be verified by truth tables • Determining whether a sentence or a knowledge base entails a sentence can be done using the inference rules, this is much more efficient than directly through truth tables

Applying Rules of Inference • Given the knowledge base moved ^ dry => airborne toxic ^ airborne => more-asthma more-asthma => more-clinical-visit moved dry toxic Does this knowledge base entail/prove more-clinical-visit? If moved ^ dry => airborne and moved ^ dry then airborne [modus ponens] If toxic ^ airborne => more-asthma and toxic ^ airborne then more-asthma [modus ponens] If more-asthma => more-clinical-visit and more-asthma then more-clinical-visit [modus ponens]

Automated Proof Methods • The whole objective of translating biomedical knowledge into formulas using logical symbols is to enable a computer program to prove an assertion or compute various entailments • Three main methods of automated proofs • Backward chaining • Forward chaining • Resolution

Forward Chaining • Works for a subset of sentences called Horn clauses, these are either a single assertion or an implication (e.g. previous example) • Previous proof was an example of forward chaining • Keep concluding the right side of the implication till the query sentence can be concluded or nothing more can be concluded • Easy for humans to follow the proof • Based on Modus Ponens inference rule

Backward Chaining • Also restricted to Horn clauses • Works backwards, in order to prove the query sentence what all should be true and so on • Based on Modus Ponens inference rule • To prove more-clinical-visit, more-asthma should be true • To prove more-asthma, airborne and toxic should be true • To prove airborne, moved and dry should be true • These are given to be true hence more-clinical-visit is true

Resolution • More general, not restricted to Horn clauses • Based on the resolution inference rule • Requires converting formulas into conjunctive normal form (can be done automatically) moved ^ dry => airborne will get converted to  moved v  dry v airborne • Proof tries to show that negation of the query sentence reaches a contradiction

Resolution • The proof is generally not very readable/understandable by humans • Resolution is less efficient than backward and forward chaining methods • All these methods can be programmed to work automatically

Unsound Inferences • Abduction If P => Q and Q then conclude P • Although unsound but used all the time in medicine • If disease => symptoms and symptoms are true then conclude the disease • Induction If P ^ Q then conclude P => Q • Although unsound, used in generating hypothesis • Could be a mere correlation

Limitations of Propositional Logic • Requires a separate symbol for every fact • To encode John is Mary’s brother you need a new symbol John_brother_Mary, instead of stating that brother is general relation by which John and Mary are related • Can’t represent generalities: • If any X is Y’s brother then Y is X’s brother or sister • First-order logic remedies these limitations brother(John,Mary) for all X,Y brother(X,Y) => brother(Y,X) v sister(Y,X)

First-order Logic • Extends propositional logic by introducing variables, predicates and functions • Constants: Individual objects of the world, e.g. John, Mary • Functions: Used to map individuals to other individuals, e.g. father-of(John) = Jack • Predicates: Used to represent relations of individuals, e.g. brother(John,Mary), predicates carry truth values of true or false • Variables: Placeholders for constants, e.g. A, B • Connectives: Same as in propositional logic • Quantifiers: • Universal:  A (for all A) • Existential:  A

First-order Logic • An atomic sentence is simply a predicate applied to a set of constants, variables and functions • brother(John,Mary) • brother(X,father-of(John)) • Connectives can be used to form complex sentences, variables in them could be quantified •  X,Y brother(X,Y) => brother(Y,X) v sister(Y,X) •  X,Y  Z brother(X,Y) => mother(Z,X) ^ mother(Z,Y) (if X is Y’s brother then there exists some Z who is mother of X and mother of Y)

Encoding in First-order Logic • Encoding knowledge of a domain in first-order logic requires making decisions about what should be the constants, functions, predicates etc., part of knowledge engineering • If a nodule is getting bigger it may be either a malignancy or a reactive node •  X, bigger(X) => malignant(X) v reactive(X) • Malignancies need treatment •  X, malignant(X) => need-treatment(X) • Reactive modules do not need treatment •  X, reactive(X) => not need-treatment(X) • If a patient does not need treatment the patient will be ok •  X,Y contained-in(X,Y) ^ not need-treatment(X) => OK(Y) • If a patient has a nodule that needs treatment and an effective treatment is available then the patient will be ok •  X,Y,Z contained-in(X,Y) ^ need-treatment(X) ^ effective(Z,X,Y) => OK(Y)

Encoding in First-order Logic • There is a 3 mm nodule in the right lower lobe (of the lung of patient Patient1), corresponding to a 1.5 mm nodule seen on the previous scan; for all nodules, effective treatment IL2 is available to Patient1 bigger(N) contained-in(N,Patient1)  X, effective(IL2,X,Patient1)

Inference in First-order Logic • The inference methods from propositional logic have suitable extensions in first-order logic • Requires an operation of substitution, i.e. substituting a variable with a constant  X,Y,Z contained-in(X,Y) ^ need-treatment(X) ^ effective(Z,X,Y) => OK(Y) • Substitute Patient1 for Y and IL2 for Z  X contained-in(X,Patient1) ^ need-treatment(X) ^ effective(IL2,X,Patient1) => OK(Patient1) • One can ask questions like who are Mary’s brothers, brother(X,Mary) • The forward chaining, backward chaining and resolution proof techniques work analogously with suitable search for substitutions • Prolog is a logic programming language based on first-order logic

Limitations of First-order Logic • If a proof exists then resolution method will find it, we say first-order logic is complete • But there is no method that will find a proof if it exists, and stop in finite number of steps in every case when the proof does not exist, first-order logic is semi-decidable • Sometimes finding a proof may take too long and no way to know how long it may take, may be weeks or months, called intractable

Limitations of First-order Logic • Some important things are not easy to express or query for, for example, name all the relations of John • It is called first-order because the quantifiers range over constants and not predicates or functions • Second-order logic allows quantifiers over predicates and functions, for example: r transitive( r )  (xyz) r(x,y)  r(y,z)  r(x,z)) • Higher order logics are more expressive but is undecidable, i.e. no method that may find a proof even when it exists • Higher order logics are rarely used in practice

Description Logic • Often first-order logic is more powerful and more expressive framework than needed • If one only needs to encode categories, objects and relations in a domain then something simpler will suffice and will be more efficient • Description logic (DL) is one such very widely used framework • “Describes” things in a domain • More expressive than propositional logic, but less expressive than first-order logic • Some things are easily expressible in description logic but are difficult or awkward to express in first-order logic • All the patients who visited clinic at least twice but not more than five times

Description Logic • Concepts: Represents classes i.e. set of individuals (diseases, persons, mothers, etc.) • AND (П) construction represents intersection of concepts, for e.g. Person П Female • NOT () construction represents all those individuals that are not in that concept class, for e.g.  Female • Atomic concepts: Concepts that cannot be represented using other concepts • Woman Person П Female • Woman is not an atomic concept here

Description Logic • Roles: Represent relations between pairs of individuals, for e.g. hasChild • Roles are always used with some quantification: • Existential () •  hasChild.Female represents all those who have a female child • For all () •  hasChild.Female represents individuals whose all children are female • Value restriction • (>= 3 hasChild) П (<= 2 hasFemaleRelative) represents all individuals who have at least three children and at most two female relatives

An Example Person >= 1 hasChild Parent Female Woman Mother

An Example Person >= 1 hasChild Parent Female Woman Woman Person П Female Parent Person П >= 1 hasChild Mother Female П Parent Mother

An Example Person >= 1 hasChild Parent Female Woman Woman Person П Female Parent Person П >= 1 hasChild Mother Female П Parent Mother Is every Mother a Woman? Not explicit, but is implicit. Task of the knowledge representation system to determine this automatically.

Reasoning in DL • The basic inference on concept expressions in DL is subsumption, written as C D, meaning everyone in C is also in D • Basic query in DL is whether a concept C is subsumed by another concept D, for e.g. is every Mother a Woman • In DL, subsumption is: • Sound (there is an algorithm which when returns “yes” then subsumption is true) • Complete (there is an algorithm which when returns “no” then subsumption is not true ) • Efficient (the above algorithms run very fast) • Because of above theoretical results, DL is very widely used in practice • There are several versions of DL which usually differ in what operators and quantifications are defined over concepts and roles

DL Knowledge Base • A DL Knowledge base consists of two parts: TBox and ABox • TBox (terminology box): Describe general properties of concepts, for e.g. Person, Female, Woman etc. • ABox (assertion box): Specify individuals of the domain, for e.g. Female П Person (ANNA), hasChild(ANNA,JACOPO)

Basic Reasoning in DL • TBox • Subsumtion • Classification: Where to put a new concept in the hierarchy of concepts • Determine using subsumtion: place between the most specific concept that subsumes it and the most general concept that it subsumes • ABox • Instance checking: Whether an individual is an instance of a concept • Knowledge base consistency: Whether every concept admits at least one individual • Realization: Find the most specific concept an individual object is an instance of • Retrieval: Find the individuals that are instances of a conept The last three can be accomplished through instance checking. • There are algorithms to do all the above automatically

DL in Medicine • Many large-scale knowledge bases (hundereds of thousands of concepts) are common in medicine • GALEN (Generalized Architecture for Languages, Encyclopedias, and Nomenclatures in Medicine) [Rector et al. 1993] is a terminology resource for clinical systems built using Description Logic • SNOMED CT (Systematic Nomenclature of Medicine Clinical Terms) is a comprehensive biomedical terminology recently developed in Description Logic formalism

A Well Known Trade-off in Knowledge Representation • There is a trade-off between expressiveness of a representation language and the difficulty of reasoning over it [Brachman and Levesque, 1984] • The more expressive a language is, computationally more difficult the reasoning is • Description Logic is a good compromise and its expressiveness often suffices many applications

Conclusions • Knowledge representation formalisms enable automated reasoning and answering queries • Once properly represented, reasoning over the knowledge can be done through symbol manipulation hence it can be automated using a computer • Different formalisms have varying expressive power and computational complexity • Knowledge in any domain of biomedicine is typically large (huge terminology) and complex and its systematic organization and automated reasoning are indispensable

Homework 2 (Due next week) • Using truth tables show that (P => Q) v (Q => P) is always true. • Decide suitable concepts and roles to encode the following in description logic: • Pain in lower limb is a type of pain whose site is lower limb structure • Pain in calf is a type of pain whose site is calf structure • Calf structure is a type of lower limb structure (use the subsumption operator) What can be said about the relation between pain in calf and pain in lower limb?

Artificial Intelligence in Medicine HCA 590 (Topics in Health Sciences)