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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 Winter '12
 MichaelGoodrich
 Sue, Jim, Tim, Ann, Zed

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