# Lect8 - Homework 2A is available Read Chapter 10 1 Clause...

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Homework 2A is available Read Chapter 10 1

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Clause Form (also clausal form) Set notation of CNF (conjunctive normal form - also POS) R & N stop with CNF we do not Write axioms as a conjunction of sentences Each sentence is a disjunction of literals (recall literal: atomic WFF or negated atomic WFF) Braces { } denote sets; comma separates literals 2
Convert FOPC to Clause Form 1. Eliminate equivalence and implication symbols 2. Move inwards forming literals 3. Standardize variables apart - unique variable names eliminating scoping conflicts 4. Skolemize 5. Drop universal quantifiers 6. Distribute AND over OR 7. Flatten nested ANDs and ORs yielding CNF (POS) 8. Write in set notation standardizing variables apart in different clauses 3

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Example: x y [( z (R(x, z) P(y, z)))   z Q(y,z)] 1. x y [( ( z (R(x, z) P(y, z))))   z Q(y,z)] 2. x y [( z ( R(x, z)   P(y, z)))   z Q(y,z)] 3. x1 y1 [( z1 ( R(x1, z1)   P(y1, z1)))   z2 Q(y1, z2)] 4. x1 [( z1 ( R(x1, z1)   P(Sk1(x1), z1))) z2 Q(Sk1(x1), z2)] 5. [( R(x1, z1)   P(Sk1(x1), z1)) Q(Sk1(x1), z2)] 6. [( R(x1, z1) Q(Sk1(x1), z2)) ( P(Sk1(x1), z1) Q(Sk1(x1), z2))] 7. [( R(x1, z1) Q(Sk1(x1), z2)) ( P(Sk1(x1), z1) Q(Sk1(x1), z2))] 8. { R(x2, z3), Q(Sk1(x2), z4)} { P(Sk1(x3), z5), Q(Sk1(x3), z6)} 4
7. [( R(x1, z1) Q(Sk1(x1), z2)) ( P(Sk1(x1), z1) Q(Sk1(x1), z2))] 8. { R(x2, z3), Q(Sk1(x2), z4)} { P(Sk1(x3), z5), Q(Sk1(x3), z6)} x L(x) M(x) is the same as w L(w)   v M(v) THIS DOES NOT WORK WITH Don’t rename between ORs x L(x) M(x) is NOT the same as w L(w)   v M(v) 5

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7. [( R(x1, z1)
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## This note was uploaded on 10/13/2011 for the course CS 440 taught by Professor Levinson,s during the Fall '08 term at University of Illinois, Urbana Champaign.

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Lect8 - Homework 2A is available Read Chapter 10 1 Clause...

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