Cognitive Science > Methods of AI > 7

Contents 1 Motivation 1.1 Possible extensions of our logic 1.2 Many-sorted Logics 2 Knowledge Representation 2.1 Definition of knowledge 2.2 Types of knowledge 2.3 Properties of knowledge 2.4 Representation formalisms 2.5 Applications 3 Historically important accounts 3.1 Semantic nets 3.2 Frames 3.3 Prototypes 3.4 Conceptual dependency theory 4 Feature constraint logics 5 Ontologies

[edit] Motivation

[edit] Possible extensions of our logic

• Predicate variables

  No complete calculus for so-called second-order logic

• Additional operators

  Modal, tense operators, generalized quantifiers

• More than two truth values (non-bivalent logic)

  Non-classical reasoning

• Change semantic evaluation of our formulas

  Intuitionistic logic, relevance logic

[edit] Many-sorted Logics

• Sorts of variables and constants
• Change language of logic slightly
• Motivation: Talk e.g. about time points, intervals, massterms, events, situations, ...
• Transformation of many-sorted logical expressions into FOL
• With many-sorted logic, expressive power cannot be increased

[edit] Knowledge Representation

[edit] Definition of knowledge

• No generally accepted definition
• "Relevant information"
• Traditional definition in philosophy: An agent X knows phi if and only if
  • phi is true
  • X believes that phi holds
  • X can justfy why phi holds
    • Kant distinguishes between ...
      • a priori (without experience)
      • a posteriori (after experience)
      • synthetic

        "5+7=12": synthatic a priori (Kant)

      • analytic

        Meaning coded in concept itself; bachelor = unmarried man

• Traditional defiition in psychology
  • Justified and subjective belief
  • Content of long-term memory
• Traditional usage in aI
  • Content of knowledge base of a system

[edit] Types of knowledge

• Three types according to Habel (1985)
  • Declarative/explicit knowledge

    Knowledge about facts; verbalizable, accessible, represented in form of propositions

  • Procedural/implicit knowledge

    Knowledge which immediately can be transformed into actions; not verablizable, not accessible

  • Knowledge about objects

    e.g. "every bird is an animal"

• World knowledge vs language specific knowledge
• Heuristic / strategic / meta / background knowledge
• Domain-specific vs common-sense
• Private vs common ground

[edit] Properties of knowledge

• Not clear
• Philosophical analysis: Know(a, phi) :<=> Believe(a, phi) and phi
• Deductive closure pf knowledge: (Know(a, phi -> psi) and Know(a, phi)) -> Know(a, psi)
• "Consciousness" of knowledge: Know(a, phi) -> Know(a, Know(a, phi))

[edit] Representation formalisms

• Predicate logic
• Non-classical logics
• Classical approaches: Semantic nets, frames etc
• KL-ONE langauge family (OWL, description logics)
• Prolog
• Non-symbolic approaches: Connectionist, statistical models; hybrid approaches

[edit] Applications

• Every computer application
• Epert systems
• Background for semantic web applications
• In linguistics, the formalism coding world knowledge

[edit] Historically important accounts

[edit] Semantic nets

• Labeled nodes and directed labeled edges
• The nodes in a semantic network correspond to concepts
• Labeled edges correspond to relations that hold between two nodes
• Direction of a link represents the asymmetry of the relation
• Class inclusion is a relation stating that one class is aa subset of another class

[edit] Frames

• Knowledge can be organized into more complex units that represent situations or objects in the domain (frames, schemas)
• Static data structure used to represent well-understood stereotypes situations
• Parts of a frame
  • Name: Concept name
  • Slots: Attribute or property (dimension along which concept can vary)
  • Facets: Slots of slots; can be associated with names for concepts
  • Fillers: Values a facet can have
• Correspond logically to existentially quantified first-order logic
• Possible to translate frames into semantic networks
• Alignment between frames
  • Compare frames
  • Alignable difference: Matching slot with mismatching value
  • Nonalignable difference: Slot with no corresponding slot

[edit] Prototypes

• Developed by Eleanor Rosch based on psychological experiments
• Prototype = Clearest case, best example of a category
• Non-protatype members tend towards an order from better to poorer examples
• Types of categories/concepts
  • Superordinate category: Very few attributes
  • Basic category: Significantly greater number of attributes ("natural kinds")
  • Subordinate category: Not significantly more attributes listed than basic level attributes
• Problem: No formally developed approach

[edit] Conceptual dependency theory

[edit] Feature constraint logics

[edit] Ontologies

• Top level ontologies
• Linguistics and ontologies