CS598EA Logic in AI LogicBased AI Lecture

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CS598-EALogic in AI / Logic-Based AILecture 3

• Professor Eyal Amir
• Spring Semester 2009

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Previously

• Logic propositional, first-order, equality

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Today Examples in FOL Situation Calculus
(Temporal Reasoning)

• Sitatuation Calculus
• Language inference in First-Order Logic
• Frame problem and Explanation Closure
• Other problems Ramification Qualification
• Action Languages
• Event Calculus
• Applications and tasks

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Situation Calculus

• A first-order language for describing the effects
  of actions and events over time
• Constants S0 initial state action constants
• Functions result(act,situation) do(act,sit.)
• Predicates fluents properties that change
  over time
• at(1, S0)
• at(x,s) ? at(x1,result(move_fwd,s))
• Query at(11,s) ? ?ans(s) ?

?at(11,s) ? ans(s)
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Situation Calculus

• Requires axioms describing effects and
  non-effects of actions/events
• Can be used for planning, projection, diagnosis,
  filtering (tracking)
• Frame Problem the compact and natural-language-li
  ke specification of effects of actions
• Qualification Problem the preconditions of
  actions

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Situation Calculus Details

• Types
• Situations S0, variables, result(act,situation)
• Actions action constants, functions
• E.g., go(agent,loc1,loc2)
• Fluents features (propositions, predicates,
  functions) that change over time
• E.g., at(agent1,loc1,situation)
• Atemporal features predicates, functions, object
  constant symbols

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Situation Calculus Details

• Basic axiom types
• Initial state description at(agent1,loc1,S0)
• Possibility of action Preconds(s) ? Poss(a,s)
• Effects of action Poss(a,s) ? fluents(do(a,s))
• Observations

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Situation Calculus Frame Problem

• How do we specify that things dont change?
• Frame Axioms
• Nonmonotonic techniques
• Explanation closure
• Successor-State axioms

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Situation Calculus Ramification

• How do we specify ramifications of our actions?
• Compilation into effect axioms
• State constraints

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Situation Calculus Details

• Basic axiom types
• Initial state description on(A,B,S0)
• Possibility of action
• PrecondsA(s) ? Poss(A,s)
• PrecondsA formula containing exactly one
  situation argument
• Effects of action
• Poss(a,s) ? (F(s) ? F(do(a,s)))
• F,F formulae that contain exactly one situation
  argument
• Observations
• On(A,B,do(pickUp(A,B,S0)))