1. Temporal Reasoning and Planning in Medicine Frame-Based Representations and Description Logics Yuval Shahar, M.D., Ph.D.

2. Representation Knowledge systems are a model of a domain, a process, or a task Representations enable making distinctions and inferences appropriate for relevant tasks Representations can differ with respect to expressiveness and/or computational complexity of answering certain queries

3. A Representation: First-Order Logic Constants: Mr_Smith, Dr._Jones, anemia Variables: X, Y Functions: Address(X), Age(Y) Predicates: Diagnosis(X, anemia); Male(Y); Patient(Z) Negation: ¬Male(X); ¬Name(X, Smith) Connectors: –Conjunction (AND): Patient(X)  Male(X) –Disjunction (OR): Doctor(X)  Nurse(X) –Logical implication: Female(X)  ¬Male(X) Quantifiers: –Universal quantifier:  X (Patient(X)  Doctor(X)) –Existential quantifier:  Y (Patient(Y)  Name(Y, Jones))

4. Graphs A graph G: a set –V: set of vertices (nodes) V i –E: set of edges (links) E i,j : (V i, V j ) If edges are ordered pairs the graph is directed if edges are nonordered pairs the graph is undirected V1V1 V2V2 V3V3 V4V4 E 1,2

5. A Semantic Network A directed graph where V i are concepts and E i,j are relations Jim Person IS-A Disease 5 Days Mumps Has Duration Diagnosis Patient 27 years Age Mamal AKA

6. Semantic Networks: Arity of Relations Unary relations –Person(Jim): IS-A link Binary relations –Age(Jim, 27 years): Age link N-ary relations –Disease(Jim, Mumps, 5 days): By creating a reified disease-relation object with several cases (patient, diagnosis, duration)

7. Frames (Minksy, 1975) Semantic networks Typically represented graphically as hierarchies of concepts such as person Concepts have roles, or properties, (also known in OOLs as slots), such as age Frames encapsulate more meaningful chunks of knowledge (e.g., birthday party)

8. A Frame Representation Mammals Humans Jim AKA IS-A Legs: 2 Age:27 Legs: 4 John Age:16 IS-A Lions AKA Bats AKA Legs: 2 Bibi IS-A

9. Inheritance Assume property P for class C, then:  x (IS-A(x, C) => P(x)) That is, all instances of C have property P Exceptions can be handled by allowing for overriding values of properties if there is an intervening node with a different value for P Values of properties are thus only defaults

10. Implications of Inheritance Determination of properties of instances involves a search of the semantic-network graph Default reasoning is enabled –high-level nodes can have values that are inherited by many lower-level nodes unless these values are overridden –Exceptions imply a nonmonotonic logic Multiple inheritance is possible, but might be ambiguous when conflicts occur

11. Advantages of Frames Classes and instances organize a flat knowledge base (unlike FOL) by introducing structureon an epistemological level –E.g., specialization of subclasses through restriction of a range of values for a property Simple; easy to understand Inheritance is captured in a natural, modular fashion Efficient inference (e.g., for validation) by following links, compared to standard logics

12. Problems with Frames Negation cannot be represented –Jim does not have pneumonia Disjunction cannot be represented naturally –Jim has Mumps or Rubella Qualification is not a part of the language –All of Jim’s diseases are infectious => Thus, procedural attachments are often added The semantics of the links are often not well defined [“What’s in a Link,” Woods, 1975]

13. Description Logics A subset of FOL designed to focus on categories and their definitions in terms of existing relations More expressive than semantic networks Major inference tasks: –Subsumption (is category C 1 a subset of C 2 ?) –Classification (Does Object O belong to C?)

14. Examples of Definition Logics KL-One: The first, prototypical language Classic Krypton Loom Grail (medical ontologies; part of Galen project)

15. KL-One A structured inheritance network Basic elements: –Concepts generic individual –Roles: Conceptual subpieces of an entity parts, attributes, function arguments, linguistic cases –Structured descriptions: Relations among roles

16. A Classic Example A patient with at least 2 diseases, both of which have a diagnosis of either Mumps or Rubella: And (Patient, Atleast (2, Diseases), All(Diseases, Fills(Diagnosis, Mumps, Rubella)))

17. Features of description Logics Subsumption is derived from category descriptions Inference is tractable (polynomial) –However, that must preclude representation of certain models –Complex models might require exponential representations –Users might be tempted to circumvent the language Negation and disjunction typically do not exist

18. Summary There are multiple representation formalisms Frames are a type of semantic networks A fundamental tradeoff exists in all formalisms [Levesque and Brachman, 1984], between: –1. Expressive power of a representation language –2. computational tractability of inference with it