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Handbook of Practical Logic and Automated Reasoning by John Harrison

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3

First-order logic

 

 

We now move from propositional logic to richer first-order logic, where propositions can involve non-propositional variables that may be universally or existentially quantified. We show how proof in first-order logic can be mechanized naively via Herbrand’s theorem. We then introduce various refinements, notably unification, that help make automated proof more efficient.

3.1 First-order logic and its implementation

Propositional logic only allows us to build formulas from primitive propositions that may independently be true or false. However, this is too restrictive to capture patterns of reasoning where the truth or falsity of propositions depends on the values of non-propositional variables. For example, a typical ...

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