Lecture_16_09 - Lecture 16 Lecture 16 Syntax Syntax...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

This note was uploaded on 02/27/2011 for the course PHILOSOPHY 101 taught by Professor H during the Spring '11 term at Columbia College.

Ask a homework question - tutors are online