Course Summary

Last Update: 2 May 2005 Note: or material is highlighted

1. Course Description:
   An introduction to the field of knowledge representation and reasoning, the branch of artificial intelligence concerned with the techniques for representing and reasoning about the information to be used by an AI program. Topics will include: the knowledge representation hypothesis; ontologies; syntax and semantics of classical propositional and predicate logic; and semantic networks. As time permits, we may also discuss some or all of the following (as well as others): non-classical logics (e.g., modal logics); logics of knowledge and belief; non-monotonic, defeasible, and default logics; truth maintenance and belief revision; frames; description logics; commonsense reasoning; and knowledge sharing.
2. 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."
   • 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 cognition:
       • AI as computational psychology:
         • Goal = to write programs as theories or models of human cognitive behavior
       • AI as computational philosophy:
         • Goal = Is cognition computable?
3. 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?
       • BUT: "things that we take to be"
4. Issues for any KR language:
   • syntax:
     
     • grammatical syntax
       • Which sequences of symbols are wffs?
     • proof theory
       • Which sequences of wffs are proofs?
       • I.e., which wffs are theorems?
       • ( ) iff there is a derivation of from premises in via rules of inference
     • semantics:
       • meaning/interpretation
       • model theory
         • ( ) iff every model of is also a model of
     • ideally, syntax (what computers are good at) precisely captures ("represents") the semantics
     • reality:
       • KRR systems are sound ( => )...
       • ...but incomplete (some truths are not provable)
5. Propositional Logic
   • syntax:
     • grammar: propositions, connectives
     • proof theory: natural-deduction system
       • intro/elim rules
       • subproofs
   • semantics
     • truth tables
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!
           
           • limitations of FOL language:
             • wffs can't be arguments of wffs
               • can't represent belief, knowledge, "says that"
             • can't represent modal expressions
             • can't represent general quantifiers (most, many...)
       • 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
           
           • Or: 2 rules of inf: Resolution, ¬Elim;
             single use of ¬Elim wrapped around multiple uses of Res
         • algorithm for using Resolution in FOL:
           Unification (generalized pattern matching)
   • semantics:
     • interpretation mapping of non-logical symbols to domain
     • assignment of values to variables (bindings)
     • satisfaction of wff by interpretation-mapping & variable-assignment
     • recursive definition of truth in an interpretation
7. Semantic networks
   • "object-oriented", taxonomic hierarchy, inheritance networks
   • SNePS
     • example of a full & fully-functioning KRR system
     • overcomes some limitations of FOL
     • propositional
     • intensional
     • inference engines:
       • node- (or formula-) based (like FOL)
       • path-based (generalized inheritance)
       • belief revision
8. Ontology:
   • PHI: theories of what there is
     • how to carve reality up in order to understand and reason about it
   • AI: computational theories of domain knowledge
     • "macro"-ontology: computational theories of everything
       • e.g., CYC's upper-level ontology
     • "micro"-ontology: computational theories of particular domains
       • e.g., time, wine, geographical landforms
9. Fundamental problem of KRR:
   • Combining information from different sources
10. Intelligence without representation or reasoning? (Brooks)