Quantifiersgiveusawaytoevaluatepredicate

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Unformatted text preview: represents all values being considered. – The UofD is sometimes called the domain of interest, or simply the domain. • Arguments in predicates can be constants (values in the UofD), variables (whose value assignments come from the UofD), or terms (expressions that evaluate to values in the UofD). • Quantifiers give us a way to evaluate predicate calculus formulas with variables that range over the entire UofD. Discussion #14 Chapter 2, Section 1 6/20 Less Than a Well Known Predicate 2 arg nd < 2 < 3 3 < 2 <(2, 3) <(3, 2) <(x, y) True False True False ? 3 F T T 2 F F T 3 1st arg 2 1 • Examples: 1 F F F UoD = {1, 2, 3} • Predicate evaluation – Plug in constants from the UoD. – Sometimes we have pre­agreed meanings. – In general, we must specify the result. Discussion #14 Chapter 2, Section 1 7/20 Predicate Evaluation (continued…) • Sometimes we know the “meaning” but we don’t know which assignments hold until we are told. • For example: UoD = {Jim, Sally, Sara, Zed} Jim Sally Sara Zed F F T T Sally F F F F Sara T F F T Zed Discussion #14 siblingOf Jim siblingOf(x,y) T F T F Chapter 2, Section 1 8/20 Predicate Evaluation (continued…) • Sometimes we don’t know the “meaning” but we are “given” the assignments. UoD = {a, b, c} • For example: Facts: P a b c a F F T b F F T c P(x, y) T F F P(b, c) P(c, a) P(a, c) • Under a “closed world assumption,” we only need to list the facts (substitutions that evaluate to True). All others are False. Discussion #14 Chapter 2, Section 1 9/20 Instantiation • Instantiation is the substitution of a constant for a variable (or in general, the substitution of a term, which is an expression that yields a constant.) • Sxt A me...
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