Reasoning Agents and Predicate Calculus

PSU CS441/541 Lecture 4
October 18, 2001

Search (continued)

• Nogoods
  • DFS for SAT does not use memory effectively
  • Keep nogoods around: partial assignments that fail
  • Resolve nogoods to shorter nogoods
  • Prune search using nogoods
  • What nogoods to keep?
    • short nogoods: does not work
    • "relevant" nogoods: RELSAT
• Search and SAT
  • Search space
  • Solution algorithms
  • Heuristics
• Local Search
  • Completeness of search
  • Hill climbing: problems
    • local maxima
    • plateaus
    • ridges
  • Noise
    • natural noise
    • introducing noise
    • convergence
    • restarts
    • simulated annealing
  • WSAT: local search for Boolean SAT
    • idea: start with total assignment and ``flip''
    • problem: can get stuck
    • solution: noise flips
    • algorithm
      1. Start with (random?) total assignment
      2. Repeatedly flip a coin and on
         • Heads: pick ``best'' variable in unsat clause, flip it
         • Tails: pick random variable, flip it
      3. If a solution is ever found, stop
    • ``walks'' through total assignment space
• Search and search control
  • imperative search control
    • e.g. ordered search: static, user-supplied
    • can be very efficient
    • encodes the answer
  • automatic search control
    • e.g. lookahead, general purpose heuristics
    • variable: ``cheapest-first'' (= most-constrained first)
    • value: least-constraining first
  • metalevel reasoning

Predicate Calculus

• WFFs of predicate calculus
  • constants (nullary predicates)
  • predicates
  • relations
• Relation of prop logic and predicate calculus
  • Models and interpretations
  • Finiteness and grounding
• Quantifiers: the general case
  • negation and flipping
  • generalization
  • elimination of exists by Skolemization
  • e.g.: forall h . [big(h) and exists p . house(h, p) implies work(h)]
    • Goal: forall h, p . [big(h) and house(h, p) implies work(h)]
    • Trick: existential negation
• Inference in predicate calculus
  • renaming
  • unification and bindings
  • resolution
  • normal forms
  • Skolemization
  • equality (and paramodulation)

Review: Midterm

• Lecture 1: Introduction
  • AI: Concept
  • AI: Implementation
  • AI: History
  • Limits of computation
  • Agents
• Lecture 2: Reactive Agents and Prop. Logic
  • KR
    • KR properties
    • Logic as KR
    • Other common AI KRs
  • Grid Space World
  • Reactive Agents
    • Concept
    • Production systems
  • Logic
    • model, interpretation, meaning
    • soundness, completeness
    • entailment, inference
    • standard inference rules
    • Horn clauses and resolution
    • why logic matters to AI
• Lecture 3-4: Search
  • pathfinding vs. constraint satisfaction
  • what is NP?
  • state spaces
  • blind search: DFS, BFS, Iterative Deepening
  • heuristic search: heuristics, A* pathfinding
  • local search: giving up completeness for efficiency
  • DP and WSAT for Boolean SAT search
• Lecture 4: Predicate Calculus
  • predicate calculus
  • first-order representation
  • advantages and disadvantages