Representation 2

Transition

Reasoning as search
Search procedures tell us nothing about
- How to represent knowledge of different sorts
- How to extend a problem state
Particular kinds of representations, together with techniques for extending states, may facilitate reasoning enormously

Internal Representations and the World

Facts in the world
Internal representations of facts
- Translating facts into internal representations
  - Using natural language as an intermediate representation, translation via a natural language understanding interface
  - Perception: vision, audition, etc.
Reasoning programs
- Manipulate internal representations
- Reasoning leads to inferences, further fact representations, which are supposed to correspond to actual facts in the world which must be true given the truth of the original facts
- Reasoning as search through the space of possible inferences
- Responding on the basis of the inferences
  - Natural language generation system which reports the inferences
  - Action based on the inferences, e.g,, reaching (of a robot), deletion of a file

Basics of Symbolic Representations

The world consists of objects and relations between them.

Symbols in some knowledge representation language represent the objects and relations in the world. The actual form of the symbols is arbitrary (unrelated to the things referred to in the world).

Symbol structures (typically implemented as lists) represent facts.

Internal representations (symbol structures) are manipulated on the basis of their syntax alone.

Inference
- Property inheritance
  - (Representations of) particular objects and facts and generalizations over objects and facts are stored in a hierarchy (a semantic network or frame system)
  - Neighbors in the hierarchy are related by the isa relation or the instance relation.
    - TURNIP8 is an INSTANCE of TURNIP, which ISA ROOT-VEGETABLE, which ISA FOOD and ISA ROOT.
  - Property values may be stored along with instances or generalizations in the hierarchy.
    - (diameter turnip8 8cm)
    - (taste turnip bitter)
  - If a property is not stored explicitly with a concept, it can be inherited from a concept higher in the isa hierarchy.
    - Inherit (taste turnip8 bitter) from TURNIP.
- Production systems
  - A set of productions, if-then rules implementing general (long-term) knowledge about (a) how to behave or (b) how to reason under certain circumstances
  - A working memory of facts representing specific (short-term) knowledge which defines the current problem
  - A general procedure for applying the productions to the facts in working memory by attempting to unifying (match) the facts with the left-hand sides of the productions and executing the right-hand side of a matching production
- Theorem proving
  - Begin with a set of axioms, assumed true, and prove one or more facts that must be true, given the axioms.
  - Uses an inference procedure, usually resolution, which makes extensive use of unification
  - Encompasses reasoning production systems
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Representation and Reasoning: Predicate Calculus

Last updated: 29 January 1996
URL: http://www.indiana.edu/~gasser/Q351/representation2.html
Comments: gasser@salsa.indiana.edu
Copyright 1996, The Trustees of Indiana University