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Lecture_16_09

Lecture_16_09 - Lecture 16 Lecture 16 Syntax Syntax...

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Unformatted text preview: Lecture 16 Lecture 16 Syntax Syntax inductively defined set of terms inductively defined set of formulas binding conventions scope bound variables, free variables substitution More on substitution More on substitution Consider the following problematic substitution: ∃ x(y < x)[x/y] = ∃ x(x < x) We avoid such problems by restricting substitution to cases where t is free for x in ϕ . What about “substitution” of bound variables? 8.1 style exercise 8.1 style exercise Consider the first­order language (with equality) over the following signature: c (constant), S (binary relation symbol), P and M (three­place relation symbols) Consider the following (standard) Consider the following (standard) interpretation on the natural numbers: c ≡ 0 S(x,y) ≡ “y is the successor of x” P(x,y,z) ≡ “x + y = z” M(x,y,z) ≡ “x * y = z” Write down wffs that formalize the following: Write down wffs that formalize the following: x is even x is larger than y x is divisible by y x is prime x and y have a common prime factor x is a square root of y ...
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• Spring '11
• H
• binary relation symbol, common prime factor, problematic substitution, formulas binding conventions, three­place relation symbols

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