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Representation

Temporal Reasoning and Planning in Medicine Frame-Based Representations and Description Logics Yuval Shahar, M.D., Ph.D. Representation. Knowledge systems are a model of a domain, a process, or a task Representations enable making distinctions and inferences appropriate for relevant tasks

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Representation

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  1. Temporal Reasoning and Planning in MedicineFrame-Based Representations and Description LogicsYuval 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, E> • V: set of vertices (nodes) Vi • E: set of edges (links) Ei,j: (Vi, Vj) • If edges are ordered pairs the graph is directed • if edges are nonordered pairs the graph is undirected E1,2 V1 V2 V3 V4

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

  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 Legs: 4 AKA AKA AKA Bats Humans Lions Legs: 2 Legs: 2 IS-A IS-A IS-A Jim John Bibi Age:27 Age:16

  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 structure on 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 C1 a subset of C2?) • 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

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