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Chapter 8 Identity and Function Symbols

Chapter 8 Identity and Function Symbols. Mathematical functions, e.g., +, –, , δ Identity = (“is”) can be treated as either a dyadic predicate or a function: =(x,y), x=y Definition of Terms : Constants (in the book), combination of constants, and function symbols.

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Chapter 8 Identity and Function Symbols

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  1. Chapter 8Identity and Function Symbols • Mathematical functions, e.g., +, –, , δ • Identity = (“is”) can be treated as either a dyadic predicate or a function: =(x,y), x=y • Definition of Terms: Constants (in the book), combination of constants, and function symbols.

  2. Functions and Predicates • Individual variables can be used to do substitutions: =(a, b) / =(x, y), for any a, b • “There is at least two Fs”: xy(Fx & Fy & ≠(x, y)) Adding functions makes quantified predicate logic more powerful

  3. Identity Introduction (=I) • n. c = c =I • Example: • Show for all x, x = x • |Show a = a, for any a • | | a = a =I

  4. Identity Elimination (=E) • n. t = u m. A ------------------- p. A[t // u] or A[u // t] n, m, =E Here A[t // u] is any result of substituting t for some or all occurrences of u throghout A. e.g., A[c // d] could be: Fcd, Fdc, Fcc.

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