Agents, Knowledge and Uncertainty

PSU CS441/541 Lecture 6
November 1, 2001

• Resolution Refutations and 1^st-Order Logic
  • FOL is semi-decidable (subsets are NP-hard)
  • Prolog
    • Horn clause is (-a or -b or c) = (a and b implies c)
    • Prolog (c :- a, b) captures same idea
    • Use MGU (text 16.1) to chain
    • Backward chaining from goals to facts
  • FW chaining is RBS idea
    • ``Expert Systems'' example
    • Book e.g.: loan payments
    • Ginsberg/Rod Ludwig: Meadowlark/GIB
• TMSs and Non-Monotonic Logic
  • Idea: keep track of truth or falsity of goals as facts change
  • Some facts may be ``undefined''
  • non-monotonicity: may have to retract conclusions
  • Inductive learning of logical rules
• Commonsense and Naive Knowledge
  • KR: logic?
  • objects & materials, space, time, physics
  • Allen temporal interval logic
  • Taxonomies, semantic nets, frames
• Probabilistic Logic
  • Idea: chance and likelihood are important concepts for real reasoning
  • Method: assign probabilities to events and combinations of events
  • Formulation
    • pr(p) is probability of event
    • pr(p|q) is probability of q given p (easy to get backward)
    • pr(p and q) = pr(p) pr(q|p) = pr(q) pr(p|q)
    • pr(not p) = 1 - pr(p)
    • pr(p or q) = pr(not (not p and not q))
    • equivalent sentences have same probability
  • Reasoning
    • Bayes' Rule: given
      • effect E with prior probability pr(E)
      • cause C with pp pr(C)
      • probability pr(C|E) of the effect given the cause
      prove from above and compute
      • pr(E|C) = pr(C|E) pr(C) / pr(E)
    • problem: everything depends on everything else
      • need to know impossible number of prior and conditional probabilities to conclude anything
      • Bayes Net (BBN, influence diagram): indicate which priors and conditionals have significant influence in practice
    • problem: probabilities may be meaningless
      • difference between 0.5 and ``don't know'' and ``don't care''
      • MYCIN and probabilities v. ``likelihoods''
      • problems obtaining realistic numbers
• More about Bayes Nets
  • causal/top-down: p(M|L) = p(M,B|L) + p(M,-B|L)
  • diagnostic/bottom-up: p(-L|-M) = p(-M|-L)p(-L)/p(-M)
  • D-separation: coping with uncertain evidence
  • Polytrees: special case for easy computation
  • Learning with BBNs: to cover later
• Programming
  • HW: Programming and minimax search
    • SE
    • Recursion, DFS, and negamax
  • Project: Gothello
    • Rules (AFAIK)
    • Teams (1-2)
    • Requirements
      • All
        • play legal games
        • use some AI technique to play better than randomly/heuristically
        • reasonable writeup (dead trees)
        • submitted code (probably for tourney) works with ref
      • Graduate
        • implement search w/ AB, ID, ttables
        • locate research paper, use idea, report
    • Tourney
      • Referee for auto-play
      • Strictly voluntary, non-graded
      • Small prize