(Natural Deduction & Resolution)

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Last updated 2:12 AM on 4/20/24
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10 Terms

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Substitution

Replacing all free occurrences of a variable in a WFF with a term

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Composition of Substitutions

Applying one substitution followed by another in a specific order

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Prenex Normal Form

A form of WFF with quantifiers preceding a quantifier-free sub-formula

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Matrix of a WFF

The quantifier-free sub-formula in the prenex normal form of a WFF

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Skolemization

Converting WFFs to remove existential quantifiers

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Most General Unifier (MGU)

A unifier that can be composed with any other unifier to unify a set of terms

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Robinson’s Theorem

Every set of unifiable clauses has a Most General Unifier

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Equisatisfiable

Two WFFs are equisatisfiable if one is satisfiable if and only if the other is satisfiable

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Equivalence of WFFs

Two logically equivalent formulas are equisatisfiable

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Theorem on Equivalence

A WFF in predicate logic is equisatisfiable to its Skolem form