MIT24_241F09_handout18

MIT24_241F09_handout18 - Logic I Fall 2009 Session 18...

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Unformatted text preview: Logic I Fall 2009 Session 18 Handout Formal semantics for PL • An interpretation for PL is a specification of each of the following: – A universe of discourse UD, where ∅ ⊂ UD. – For each sentence letter S of SL, a truth-value assigned to S . – For each n-place predicate letter F of PL, a set of n-tuples of members of UD assigned to F . E.g., if we are interpreting ‘Lxy’ to mean x lives in y , then to ‘L’ we would assign { Ephraim, Somerville , Damien, Somerville , Vann McGee, Boston , . . . } . – For each individual constant c of PL, an individual u assigned to c , where u is a member of UD. Denotations of individual terms on I and d : • – If t is a variable, then den I , d ( t ) = d(t) . – If t is an individual constant, then den I , d ( t ) = I(t) . • Variants of variable assignments: – d [u / x ] is the variable assignment that assigns u to x and is otherwise just like d ....
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This note was uploaded on 01/25/2012 for the course PHIL 201H1F taught by Professor Derekallen during the Fall '10 term at University of Toronto.

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MIT24_241F09_handout18 - Logic I Fall 2009 Session 18...

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