first-order logic
(foldoc) | first-order 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:
F1 ^ F2 conjunction - true if both F1 and F2 are true,
F1 V F2 disjunction - true if either or both are true,
F1 => F2 implication - true if F1 is false or F2 is
true, F1 is the antecedent, F2 is the
consequent (sometimes written with a thin
arrow),
F1 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.
["The Realm of First-Order Logic", Jon Barwise, Handbook of
Mathematical Logic (Barwise, ed., North Holland, NYC, 1977)].
(2005-12-27)
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