# Lect6 - Announcement Homework 1 due Verify your in-class...

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Announcement Homework 1 due Verify your in-class score on Compass Start reading Chapter 10, Classical Planning 1

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SEMANTICS Θ Universe of Possible Worlds Intuitive meaning in our world Student means “is a student” Happy means “is happy” and all students are joyful in this world Student means “is a giraffe” Happy means “has a short neck” and there are no giraffes in this world Student means “can drive” Happy means “can swim” in our world   x [Student(x) Happy(x)] 2
Componential Semantics WFFs express constraints Meaning of a WFF is the set of possible worlds that satisfy Intersect sets Union sets Complement set 3

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Entailment An axiom set contains n axioms: i i=1,n These are implicitly conjoined:   i iff holds in all possible worlds of i=1,n PW( ) PW( ) PW 4
Overloaded “model” Logic specific usage A model for a sentence is any possible world in which a WFF holds (recall that for us a possible world is a world and a denotational correspondence) Let M( ) be the models of WFF then is equivalent to M( ) M( ) Previous slide uses the less formal PW To avoid confusion we will minimize this use of “model” 5

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Entailment An axiom set contains 3 axioms:   i (    1 2 3 ) i=1,3 1 2 3 Possible Worlds Any WFF that completely includes this intersection is logically entailed 6
An axiom set contains 3 axioms:   i (    1 2 3 ) i=1,3 1 2 3 Possible Worlds Any WFF that completely includes this intersection is logically entailed 7 Does ? Does

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Lect6 - Announcement Homework 1 due Verify your in-class...

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