Logic Terms

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Last updated 8:32 PM on 6/2/26
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9 Terms

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Valid Propositional

If for all variable assignments the formula is True

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Satisfiable Propositional

If there is at least one variable assignment that makes the formula is True

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Unsatisfiable Propositional

If there are no variable assignment that makes the formula is True

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Valid Predicate


If it evaluates to true in every possible structure under every possible variable assignment

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Satisfiable Predicate

If there exists at least one structure and at least one variable assignment such that the formula evaluates to True

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Unsatisfiable Predicate

If there exists no structures and no variable assignments such that the formula evaluates to True

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Soundness

A proof system is sound if everything that can be proven using its rules is actually semantically True

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Completeness

A proof system is complete if everything that is semantically true can actually be proven using its rules.

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Logic is Sound and Complete

It means the proof system is correct and exhaustive; a formula can be proven if and only if it is universally true.