FOPL, Part Deux

1
FOPL, Part Deux

• Lecture 8-1
• November 16th, 1999
• CS250

2
First-Order Logic

• World consists of objects and predicates on
  objects
• Get to keep Boolean operators
• Add quantifiers
• Example
• The wumpus is dead could be Dead(wumpus)
• All wumpi are dead could be
• ?x Wumpi(x)?Dead(x)

3
Return to the Land of the Wumpus

• Use Tell to add assertions to the knowledge base
• Use Ask to pose queries
• Answers to Asked queries are binding lists (aka
  substitutions)

Tell(KB,Percept(Smell, Breeze, None,5))
Ask(KB,?a Action(a, 5))
Does the KB entail any particular action at t5?
a/Shoot (Thats a yes)
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A Little Syntax

• Given a sentence S, and a substitution, ?
• S ? denotes the result of plugging ? into S

S Smarter(x, y) ? x/Hillary, y/Bill S ?
Smarter(Hillary, Bill)
What does Ask(KB, S) do in these terms?
Returns some (or all) ? such that KB S?
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KB for WW

• Represent perceptions more abstractly
• Write rules to transform percepts into predicates
• Map from predicates to actions
• Why is this a better approach?

6
The Only Constant is Change

• How do we reason about changing situations?
• Minimal internal state, but story history of
  percepts
• Build an internal model of the world
• Need diachronic rules
• Already use time, but not the whole context

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Be here now.

• Predicate calculus doesnt have time for time
• For all x means for all x, today, tomorrow and
  the day after, and the day after that...
• Fine for the immutable things in this world, but
  need a fix for changing predicates

8
Threes Company

• Add situations to predicate calculus

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Ever-Changing Predicates

• Add a situation argument to properties that
  change over time, Si
• Actions move from one situation to the next
  situation
• Result(action, situation)
• Actions have effects
• Example If something thats portable is
  present, then if you grab it, youll be holding
  it

?(x, s) Present(x, s) ? Portable(x) ? Holding(x,
Result(Grab,s))
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Tracking Action Effects

• If the agent is at a location with gold, and
  grabs the gold, the agent is then holding the
  gold in the next situation

Portable(Gold) ?s AtGold(s) ? Present(Gold, s)
?x,s Present(x,s) ? Portable(x) ? Holding(x,
Result(Grab, s))
And if the agent releases the gold?
?x,s ?Holding(x, Result(Release, s))
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Flavors of Axioms

• State the effects of actions (Effect axioms)
• What about the non-effects of inaction? (Frame
  axioms)
• If the agent is Holding an object in a situation,
  and performs any action except Release, then the
  agent is Holding the object in the resulting
  situation
• Dont forget about not Holding!

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Frame Problems

• Representational frame problem
• Writing down what doesnt change
• Inferential frame problem
• Reasoning about what doesnt change
• Situation calculus requires carrying every
  property through time - even if it doesnt change
• What if most of the world doesnt change?

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A New Flavor Combination

• Successor state axioms combine effect and frame
  axioms
• Each axiom is about a predicate

true afterwards ? an action made it true ? true
already and no action made it false
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Other problems?

• Qualification problem
• Exactly describing when a an action will occur
• Ramification problem
• Inferring what goes with what

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Doin the Sherlock Thing

• Squares are near a breezy pit
• Diagnostic - infer cause from effect
• Causal - infer effect from cause
• Model-based reasoning versus diagnostic approaches

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Planning

• Special search systems for reasoning about
  actions
• Different representations
• Making good choices
• Preferences among actions