The Status of Knowledge

• How does knowledge fit in
  • Place of knowledge in an intelligent agent
  • Knowledge is "required" to guide the search
  • What is knowledge
    • Knowledge is justified true belief
    • May want to deal with weaker notions than knowledge
      • Things that are not (fully) justified
      • Things that are "probably true"
      • Things that are "true most of the time"
  • What is knowledge representation?
    • Representation is encoding into a data structure
    • KR is encoding justified true beliefs into a data structure
    • DS needs to represent justification, truth, belief
  • Knowledge base
    • A KB is KB₀ and a derivability relation |-_L
    • X is in KB iff KB₀ |-_L X
    • Deduction, abduction, induction
    • Insert real examples here

• Epistemic status
  • The degree of commitment to the information - weaker forms of information such as belief.
  • Knowledge is justified true belief
    • Truth is the assertional status, discussed below (computed by the semantic theory in use).
    • Epistemic status deals with justification, which establishes commitment.
  • Belief - anything in the KB.
    • Expected to be reasonable - no contradictory beliefs in KB₀
    • May not be what should be known, e.g., may not reflect reality due to an inaccessible environment.
    • K(X) means "X is in the knowledge base", so K(X) captures beliefs.
  • Hypothesis is a justified belief
    • Justification is not always absolute, especially in natural kind terms.
    • Hypothesis is different from knowledge as it's not fully justified, i.e., an agent is not fully commited to hypotheses.
  • Knowledge is absolutely justified
    • Knowledge is that which we will not give up (easily), and is taken as axiomatic.
    • K(X) => X equates belief to knowledge
    • Some "knowledge" turns out not, e.g., the earth is flat
  • Belief ... Justified belief ... Justified true belief. E.g.,
    • At start of semester I believe I'll pass
    • After assessment I hypothesize I'll pass
    • After results I know I've passed.
  • Low(er) commitment to belief.
    • May want to retract beliefs and hypotheses, but not knowledge
    • May want to modify (retract and add a different one)
  • Justification of inferred knowledge
    • Deduction - take weakest epistemic form
    • Abduction and induction - take weakest, but K+K=H
  • Representation to be studied soon, in terms of "uncertainty".

• Assertional status
  • Confidence in the information - may not be true always, may have exceptions, etc
  • Example "Elephants are grey"
    • All elephants are grey - reasonable, but false
    • Elephants are grey - with a degree of truth (greyness)
    • Elephants are grey with some exceptions
  • First case is the traditional theory of meaning
    • Meaning of elephant is determined by its properties
    • All statements are true and non-contradictory
    • Not useful for natural kind terms
  • Second is prototype theory
    • Terms are given prototype information
    • If some information is untrue, that reduces assertional status
    • Prototype theory is the basis for frames KR
    • Example - "He is tall"
  • Third case allows definitional error.
    • Exceptions are permitted, e.g., albino elephants
    • Use of KB must deal with this
  • Representation to be studied soon, in terms of "imprecision".

• Semantics
  • Determine what syntactic terms and statements in the KB designate in the domain of discourse.
    • Syntactic terms are interpreted as (designate) objects in the domain.
    • Syntactic statements are interpreted (designate) epistemic and assertional values.
  • A structure that provides this information is called an interpretation.
    • An interpretation typically includes a domain, corresponding to objects (yes, it's overloaded).
    • An interpretation typically includes a mapping from terms to domain elements.
    • An interpretation typically includes a mapping from statements to epistemic and assertional values.
    • An interpretation that interprets a statement as true, i.e., with absolute assertional status, is a model of the statement.
  • Example: The pictures of the ambiguous sentence
  • Example: Tarskian semantics for FOL (Geoff and Jim)
  • Semantics can provide strong guidance in AI search

Exam Style Questions

• Give a definition of "knowledge representation", based on appropriate definitions of "knowledge" and "representation".
• Give the formal definition of a knowledge base.
• What are deductive, abuductive, and inductive reasoning?
• Differentiate between the epistemic status and the assertional status of knowledge. Give examples to illustrate.
• The epistemic status of a statement describes the commitment to that statement. In this light differentiate between belief, hypothesis and knowledge.
• Explain how the epistemic status of an inferred statement is derived the epistemic statuses of its parents.
• What is the assertional status of a statement? Give a simple example to illustrate three possible assertional statuses.
• What is provided by the semantics of a syntactic representation?
• Define "interpretation" and "model" in semantics.
• Describe the three things typically included in an interpretation.