CSE 663, Fall 2006

Course Summary

Last Update: 7 December 2006

Note: or material is highlighted

What Is KRR?
- KRR is a branch of AI
  - AI tries to answer: "How much of cognition is computable?"
  - So, KRR tries to develop a computational theory of how a cognitive agent does/can/should represent and use (i.e., reason about and with) information...
    - ... about the world
    - ... about an agent's beliefs about the world
- Cognitive agent A knows/believes that α.
- Representation R represents world-fragment W for A.
  - The representation R has a syntax & a semantics:
    - Syntax: relations among the symbols ("markers") of the representation language
      - grammar:
        
        "shape", symbol manipulation;
        "term", "wff"
        which strings of symbols are wf
        Ontology(1): the non-logical details of the KR language
      - proof-theory:
        
        axioms, rules of inference
        which strings of wffs are theorems
    - Semantics: relations between symbols & what they represent
      - meaning, truth
      - Ontology(2): theory of the represented world
        what there is
        what kinds of things there are (categories)
        properties, relations
        "syntax" of the world
      - Brian Cantwell Smith's paradoxical observation: Semantic theory requires its own KR language!
Language of FOL
- (Grammatical) Syntax:
  - punctuation
  - connectives
  - variables
  - function symbols (including 0-place ones, i.e., constants)
  - predicates (including 0-place ones, i.e., atomic wffs)
  - terms
  - wffs (atomic, molecular [recursively defined])
- Proof-Theory (inferential syntax):
  - axioms
  - rules of inference
  - syntactic entailment
- Semantics:
  - interpretation (= domain + interpretation mapping)
  - denotation (of terms)
  - satisfaction (of wffs)
  - logical models
  - logical consequence & semantic entailment
- Relationship of syntax to semantics:
  - soundness: KB α => KB α
    - i.e., the KR doesn't represent too much
      - (it doesn't represent false things)
  - completeness: KB α => KB α
    - i.e., the KR doesn't represent too little
      - (it represents at least the provable things)
  - Gödel: if arithmetic+logic is sound & consistent, then it is incomplete.
Ontology
- In philosophy: the study of what there is.
  - ontology(3)?
- In KRR: the structure of the world that the KR language is about
  - decisions that a K-engineer must make or that are forced by the KR:
  - individuals
  - types (categories)
  - attributes (properties)
  - relations
  - functions
  - basic facts
  - complex facts
- The Alpine Ski Club world
Semantic Networks
- Quillian's "Semantic Memory"
  - network of words and their definitions
  - "full meaning" of a word is its location in the network
  - spreading activation (to find intersections)
- Schank's "Conceptual Dependency"
  - frame-like semantic network that represents events
  - primitive acts (ATRANS, PTRANS, etc.)
  - scripts: frame-like sequences of events
- SNePS
  - the CVA project
    - various KR techniques can be used to represent "prior" (or "background") knowledge
    - various reasoning techniques need to be used to "figure out"/compute a meaning
Production Systems
- not a KR language, but a way to organize a KRR system
- basis of "expert systems"
- 2 KBs (rule KB, working memory) + inference engine
- Newell & Simon's GPS
Minsky's Theory of Frames
- a kind of "schema" theory
- represent stereotypical situations/entities, instances of them
- slots & fillers, defaults, procedural attachment
- difference between a representation language and a programming language
Description Logics
- for representing objects in taxonomic hierarchies
- the language DL:
  - concepts (Thing, user-defined)
  - [ALL role concept]
    - all indivs related by "role" only to elements of "concept"'s extension
  - [EXISTS n role]
    - all indivs related by "role" to >= n other indivs
  - [FILLS role constant]
    - all indivs related by "role" to "constant"
  - [AND concept_1 .. concept_n]
    - anything described by concept_1 & ... & concept_n
- reasoning by subsumption
Inheritance Networks
- focus on the "isa" mechanism of inheritance
- strict inheritance
  - Clyde isa Elephant isa Gray-Thing, so Clyde is gray
- defeasible inheritance
  - Opus isa Penguin isa Bird isa Flying-Thing, so Opus flies, but Penguin isn'ta Flying-Thing, so Opus doesn't fly
  - Nixon diamond
- strategies:
  - shortest path
  - inferential distance
  - admissible paths
  - credulous vs. skeptical reasoning
Defaults
- generics: Birds fly. All? Some? Normal ones? Etc.
- non-monotonic reasoning:
- Reiter's Closed-World Assumption
  - "Birds fly":
    - if KB doesn't entail "Opus flies", then Opus doesn't fly.
    - if KB doesn't entail "Tweety doesn't fly", then Tweety flies.
- McCarthy's Circumscription
  - "Birds fly" = ∀x[Bird(x) ∧ ¬Ab(x) ⊃ Flies(x)]
  - "circumscribe" the Ab predicates to be as small as possible
- Reiter's Default Logic
  - add "default rules" (of inference?):
    - α, :Mβ δ
    - from α and "β is consistent with the KB", infer δ
  - "Birds fly" = any substitution instance of Bird(x), :M Flies(x) Flies(x)
- Moore's Autoepistemic Logic
  - [[Bα]] = it is believed to be the case that α
  - "Birds fly" = ∀x[Bird(x) ∧ ¬B¬Flies(x) ⊃ Flies(x)]
Modal Logics
- varieties of modalities:
  - alethic: possibly α, necessarily α
  - epistemic: agent a knows that α
  - doxastic: agent a believes that α
  - tense: it (always) will be the case that α
  - deontic:
    - it is obligatory (i.e., it ought to be the case)/permissible that α
    - agent a ought to do action A
- varieties of axiomatic systems:
  - K, T, S4, S5, B, etc.
- possible-world semantics, accessibility relations on possible worlds
  - varieties of semantics depend on varieties of accessibility relations
  - quantified modal logic: Barcan formula, problems with Leibniz's Law of equality
  - Moore's logic of knowledge and action