<logic, discipline> the branch of logic dealing with propositions in which subject and predicate are separately signified, reasoning whose validity depends on this level of articulation, and systems containing such propositions and reasoning. Also called quantification theory or predicate calculus. predicate first-order theory
First-order predicate logic
Predicate logic in which predicates take only individuals as arguments and quantifiers only bind individual variables.
Higher-order predicate logic
Predicate logic in which predicates take other predicates as arguments and quantifiers bind predicate variables. For example, second-order predicates take first-order predicates as arguments. Order n predicates take order n-1 predicates as arguments (n > 1). See Grelling's paradox.
Inclusive predicate logic
Predicate logic that does not exclude interpretations with empty domains. Standard predicate logic excludes empty domains and defines logical validity accordingly, i.e. true for all interpretations with non-empty domains. Also called inclusive quantification theory.
See existential import, logical validity
Monadic predicate logic
Predicate logic in which predicates take only one argument; the logic of attributes.
Polyadic predicate logic
Predicate logic in which predicates take more than one argument; the logic of n-adic predicates (n > 1); the logic of relations.
Predicate logic with identity
A system of predicate logic with (x)(x=x) as an axiom, and the following axiom schema, [(x=y) => (A =>A')]^c, when A' differs from A only in that y may replace any free occurrence of x in A so long as y is free wherever it replaces x (y need not replace every occurrence of x in A), and when B^c is an arbitrary closure of B. See first-order theory with identity, identity
Pure predicate calculus
A system of predicate logic whose language contains no function symbols or individual constants. As opposed to a number-theoretic predicate calculus which contains these things.
[Glossary of First-Order Logic]
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