COURSE SUMMARY

1. What is AI?
   • 2 complementary definitions:
     • Minsky:
       • "The science of making machines do things that would require intelligence if done by humans."

     • Boden:
       • "The use of computer programs and programming techniques to cast light on the principles of intelligence in general and human thought in particular."

   • Shapiro's 3 goals of AI research:
     • AI as advanced CS, or as engineering:
       • Goal = to extend frontiers of what we know how to program

     • AI as computational psychology:
       • Goal = to write programs as theories or models of human cognitive behavior

     • AI as computational philosophy:
       • Goal = Is cognition computable?

2. What is KR&R?
   • KRR =def branch of AI concerned with techniques for:
     • representing info
     • reasoning about/with it.

   • what should be represented?
     • facts about world?
     • cognitive agent's beliefs about world?

   • how much should be:
     • represented explicitly?
     • inferred?

   • KRR system requirements:
     • representation language
     • inference mechanism
     • ontology (theory of domain knowledge)

   • representation of external world is always...
     • incomplete
     • error-prone
     • therefore, need belief revision

   • declarative vs. procedural knowledge vs. acquaintance
     • knowing that, propositions
     • knowing how, procedures
     • knowing who/what, objects

   • Brian Cantwell Smith's KR Hypothesis:
     • any AI system needs things that we take to be declarative representations of the world, which play a causal role in the system's behavior
     • antithesis of Brooks (see below)?
       • BUT: "things that we take to be"

3. Issues for any KR language:
   • syntax:
     • grammatical syntax (definition of wff)

     • proof theory
       (Δ |- α) iff there is a derivation of α from premises in Δ via rules of inference

   • semantics:
     • meaning/interpretation

     • model theory
       (Δ |= α) iff every model of Δ is also a model of α

   • ideally, syntax (what computers are good at) precisely captures ("represents") the semantics

   • reality: KRR systems are sound (|-α => |=α)
               but incomplete (some truths are not provable)

4. Semantic networks
   • "object-oriented", taxonomic hierarchy, inheritance networks

   • SNePS
     • example of a full & fully-functioning KRR system

     • propositional

     • intensional

     • inference engines:
       • node-based (like FOL)

       • path-based (generalized inheritance)

       • belief revision

5. Propositional Logic
   • syntax:
     • grammar: propositions, connectives

     • proof theory: natural-deduction system
       • intro/elim rules

       • subproofs

       • Proof Giver (partial strategy)

   • semantics
     • truth tables
     • Johnson-Laird's theory of Mental Models

6. First-order predicate logic (FOL)
   • syntax:
     • grammar
       • terms:
         • atomic: variables, constants
         • molecular: function symbols (take terms as arguments)

       • predicates (property symbols, relation symbols)
         • take terms as arguments
         • therefore, canNOT take wffs as arguments!

       • connectives; quantifiers (universal, existential)

       • wffs

     • proof theory:
       • natural-deduction system

       • automated theorem proving:
         • clause form
           wff converted to sets of conjoined clauses, each of which is a set of disjoined literals

         • single rule of inference: Resolution

         • strategy: Refutation

         • algorithm for using Resolution in FOL:
           Unification (generalized pattern matching)

   • semantics:
     • wff satisfied by assignment of values to variables (bindings)
     • truth in an interpretation

7. Ontology:
   • PHI: theories of what there is
     • how to carve reality up in order to understand and reason about it

   • AI: theories of domain knowledge
     • Allen's ontology for temporal information
     • CYC

8. Frames (Minsky)
   • representing stereotypical objects with defaults
   • frame systems: frames arranged taxonomically

9. Description logics
   • Woods:
     • distinguish between structural & assertional information
     • need to provide semantics!

   • KL-ONE

   • T-Box, A-Box

10. General issue: What are the differences between different KR systems?
    • semantic networks vs. FOL
    • frames vs. semantic networks vs. FOL

11. Default reasoning & belief revision
    • inference from partial information in the presence of noise
    • to plausible, but uncertain & defeasible conclusions
    • Frame Problem: how to represent & reason about info that is invariant under changing circumstances?

12. Intelligence without representation? (Brooks)