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# first-order logic

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• US Pronunciation
• US IPA

## Definitions of first-order logic words

• noun Technical meaning of first-order logic (language, logic)   The language describing the truth of mathematical formulas. Formulas describe properties of terms and have a truth value. The following are atomic formulas: True False p(t1,..tn) where t1,..,tn are terms and p is a predicate. If F1, F2 and F3 are formulas and v is a variable then the following are compound formulas: The "order" of a logic specifies what entities "For all" and "Exists" may quantify over. First-order logic can only quantify over sets of atomic propositions. (E.g. For all p . p => p). Second-order logic can quantify over functions on propositions, and higher-order logic can quantify over any type of entity. The sets over which quantifiers operate are usually implicit but can be deduced from well-formedness constraints. In first-order logic quantifiers always range over ALL the elements of the domain of discourse. By contrast, second-order logic allows one to quantify over subsets. 1
• noun first-order logic (logic) A formal deductive system extended from propositional logic with the possibility to quantify over individuals of the domain of discourse. 0

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