15-Interps

15-Interps - Discussion #15 Interpretations Discussion #15...

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Discussion #15 Chapter 2, Section 2.2 1/16 Discussion #15 Interpretations
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Discussion #15 Chapter 2, Section 2.2 2/16 Topics Interpretations Closed World Assumption Interpretation Examples for Class Project
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Discussion #15 Chapter 2, Section 2.2 3/16 Interpretations Provide Meaning Consider the problem of giving meaning to the expression: sibling(x, Lynn) married(x). Can’t just assign T or F to a predicate expression with variables Truth depends on the values assigned to the variables E.g. assign Zed to x; then if Zed is indeed Lynn’s sibling and is married, we can say that this expression is true. E.g. for 5 x(sibling(x, Lynn) married(x)), we can look through the list of all possibilities (i.e. look through the domain) and see if at least one of them is a sibling of Lynn and is married; if so we can say that this expression is true. To provide an interpretation, we need A domain that provides values for the arguments of the predicate A way to determine the truth value of all predicates for each possible assignment of domain values to the variables
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Discussion #15 Chapter 2, Section 2.2 4/16 Interpretation An interpretation for an expression E Specify a domain, D. For each predicate of E, specify T or F for every possible substitution. Select a value in D for each free variable, if any. Example: 5 yP(x, y) D = {1, 2} P(x, y) = ? 1 1 T 1 2 F 2 1 F 2 2 F x = 1: 5 yP(x, y) = P(1, 1) P(1, 2) = T F = T x = 2: 5 yP(x, y) = P(2, 1) P(2, 2) = F F = F
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Discussion #15 Chapter 2, Section 2.2 5/16 Interpretation An interpretation for an expression E Specify a domain, D. For each predicate of E, specify T or F for every possible substitution. Select a value in D for each free variable, if any. Example: 5 yP(x, y) D = {1, 2} P(x, y) = ? 1 1 T 1 2 F 2 1 T 2 2 F x = 1: 5 yP(x, y) = P(1, 1) P(1, 2) = T F = T x = 2: 5 yP(x, y) = P(2, 1) P(2, 2) = T F = T Observe that the truth of a statement depends on the interpretation.
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Discussion #15 Chapter 2, Section 2.2 6/16 Interpretation An interpretation for an expression E Specify a domain, D. For each predicate of E, specify T or F for every
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15-Interps - Discussion #15 Interpretations Discussion #15...

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