The Library of Dresan: Dr. Anthony G. Francis, Jr.'s Weblog

Introduction to Artificial Intelligence with Applications to Public Health

Rollins School of Public Health at Emory University
Instructor: Dr. Anthony G. Francis, Jr.

Lecture 10: Knowledge Representation

All but the simplest artificial intelligence programs need information about the world they inhabit. When this information takes the explicit form of a data structure that can be manipulated, we call the information knowledge and the form its representation --- or knowledge representation for short. While not all artificial intelligence systems use explicit knowledge representations, many powerful knowledge representation techniques have been developed, including graph notations such as frames and semantic networks, logics such as propositional logic and first order predicate calculus, and specialized representations such as conceptual dependency, STRIPS operators, and structure-behavior-function models. Some of the issues to consider in knowledge representation include its clarity, representational power, inferential efficiency and adequacy, procedural or declarative representation, the presence of absence of formal syntax and semantics, and presence or absence of a content theory of the kinds of information that the representation can store.

Outline

  • What Is a Knowledge Representation?
  • Issues in Knowledge Representation
  • Kinds of Knowledge Representations
  • Symbolic Graphs
  • Semantic Networks
  • Frame Systems
  • Propositional Calculus
  • Predicate Calculus
  • Conceptual Dependency
  • Rule-Based Systems

What Is a Knowledge Representation?

  • Representation: Storing Knowledge
  • Inferences: Deriving New Conclusions
  • Syntax: The Structure of the Language
  • Semantics: The Meaning of the Representation
  • Content Theory: Why the Language Stores What it Stores

Issues in Knowledge Representation

  • Representational Power
  • Inferential Adequacy
    • Soundness
    • Completeness
  • Inferential Efficiency
  • Formal Semantics vs Clarity
  • Tradeoffs in Knowlege Representation
    • Inferential Efficiency vs Representational Power
    • Inferential Efficiency vs Inferential Adequacy
    • Procedural vs Declarative Representation

Kinds of Knowledge Representations

  • Graph Representations
    • Symbolic Graphs
    • Semantic Networks
    • Frame Systems
    • Conceptual Graphs
    • Bayesian Networks
  • Formal Logics
    • Propositional Calculus
    • Predicate Calculus (FOPL)
    • Higher Order Logics
  • Commonsense Knowledge
    • Modal Logic
    • Temporal Logic
    • Fuzzy Logic
    • Description Logic
  • Rule Based Systems
    • Production Systems
    • Probabilistic Rules
    • STRIPS Rules

Symbolic Graphs

Primitive symbols combined into hierarchical expressions
  • Primitives: Atoms, S-Expressions
  • Inference Rules: Unspecified
  • Representational Power: Turing Complete
  • Inferential Adequacy: Unspecified
  • Formal Semantics: None
  • Typical Usage: To construct more constrained representations

Semantic Networks

Graphs of nodes and links representing concepts and relations
  • Primitives: Nodes, Links
    • Node: Kirk
      • IsA: Human
      • Captain-of: Enterprise
    • Node: Enterprise
      • IsA: Starship
      • Type: Constitution-class
  • Inference Rules: Inherited properties based on defaults
  • Representational Power: Subset of First Order Predicate Calculus
  • Inferential Adequacy: Subset of First Order Predicate Calculus
  • Formal Semantics: Representation yes, inferences no
  • Issues: Meaning of link categories must be defined
  • Typical Usage:
    • Representing concepts and relationships
    • Inferring inherited properties
    • Determining conceptual similarity

Frame Systems

Detailed representations of concepts using slots and fillers
  • Primitives: Frames, slots, fillers, defaults, procedures
    • Frame: ELEPHANT
      • Slot: Filler (Default: Value)
      • IsA: MAMMAL
      • Legs: (Default: 4)
      • Has-Part: Trunk
  • Inference Rules: Inherited properties based on defaults
  • Representational Power: Overlaps First Order Predicate Calculus
  • Inferential Adequacy: Subset of First Order Predicate Calculus
  • Formal Semantics: Representation yes, inferences no
  • Issues:
    • Largely equivalent to semantic networks
    • Procedures on slots can make inferences complex
  • Typical Usage:
    • Detailed representation of concepts
    • Fast lookup of local properties

Propositional Calculus

Boolean Algebra Applied to Propositions About the World
  • Primitives: Atoms, Logical Connectives
    • Atoms: True, False, A,B,C, ELEPHANTS_HAVE_4_LEGS
    • Connectives: Or, And, Not, Implies
    • "Meta-level conveniences": Parentheses, implication, derivation
  • Inference Rules: Boolean Algebra, Modus Ponens, Resolution
  • Representational Power: Less than First Order Predicate Calculus
  • Inferential Adequacy: Less than First Order Predicate Calculus
  • Formal Semantics: Yes
  • Issues:
    • Propositions are very large grained
    • Expensive to represent facts about objects
    • Difficult to represent concepts like "for each" and "for all"
  • Typical Usage: Fast inferences where simple representation is sufficient

Predicate Calculus

Logical predicates operating over universes of objects
  • Primitives: Predicates, Values, Logical Connectives, Quantifiers
    • Predicates: True, False, On(x,y), CaptainOf(y,z), Legs(x,y)
    • Values: Kirk, Enterprise, Elephants
    • Connectives: Or, And, Not, Implies
    • Quantification: Exists, ForAll
    • "Meta-level conveniences": Parentheses, implication, derivation
    • ForAll Elephant e: IsA(e,Mammal)
    • Exists Elephant e: Color(e,White)
  • Inference Rules: Boolean Algebra, Modus Ponens, Resolution
  • Representational Power: Extremely Broad
  • Inferential Adequacy: Extremely Broad
  • Formal Semantics: Yes
  • Issues:
    • Covers an extremely wide range of facts
    • Inferences can be more expensive
    • Tricky to represent default values and for-all at the same time
    • Cannot represent higher-order concepts, like properties of predicates
  • Typical Usage: Where more complex logical representations are required

Rule Based Systems

If-then rules encompassing specific knowledge
  • Primitives: Rules
    • Condition: usually in an extended logic with variables
    • Action: logical or probabilistic conditions
  • Inference Rules: Backward and forward chaining, Conflict Resolution
  • Representational Power: Depends on underlying logic
  • Inferential Adequacy: Depends on rulebase
  • Formal Semantics: Yes (no if probabilistic)
  • Issues:
    • Can be extremely effective at narrow tasks
    • Hard to extract knowledge
    • Difficult to scale
    • Probabilities difficult to track
  • Typical Usage: Nasrrowly specified expert tasks

Conceptual Dependency

Similar Meanings Should Have Similar Structure
  • Primitives: Primitive Conceptual Dependencies, Actors and Objects
    • Types of Conceptual Dependency
      • Primitive Acts: Actor Object Agent
      • Demonstrative: Object Is State
      • Causality: Causes, Ensables, Disables...
    • Primitive Acts: 11
      • ATRANS
      • PTRANS
      • MTRANS
      • ATRANS
    • Actors: John, Mary, Bob
    • Objects: Food, Money, Gun
  • Inference Rules: Knowledge-Based
  • Representational Power: Constrained
  • Inferential Adequacy: Constrained
  • Formal Semantics: No
  • Issues:
    • Covers a specific content domain - Natural human actions
    • Inferences are informal but fast and powerful
    • Similar concepts have similar representations
    • Easily extensible
  • Typical Usage: Memory and reasoninmg about day to day life

Resources

  • Semantic Networks: ????
  • Frame Systems: ????
  • Propositional Logic: ????
  • Predicate Calculus: ????
  • Description Logic: ????
  • Fuzzy Logic: ????
  • Conceptual Dependency: ????
  • Rule-Based Systems: ????
  • Semantic Web: ????
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