predicate,
n. (Logic) 1a. an expression that ascribes a property to some thing or things (its subjects); a predicate with more than one subject is a relation.
b. a property, characteristic or attribute that may be affirmed or denied of something. The categorial statement all men are mortal relates two predicates,... is a man and... is mortal. See syllogism.
c. the term of a categorial proposition that is affirmed or denied of its subject; in the same example, all men is the subject and is mortal is the predicate in this sense.
2a. formally, in some treatments of the predicate calculus, a term that is derived from an atomic sentence by the deletion of a name, these being the primitive terms of the system; in other treatments, names and predicates are primitive, and an atomic sentence is defined to be the result of combining them by replacing each variable in the predicate by a name. Predicates are usually written in functional notation, as, for example, F(x) and R(x, y), and yield well-formed sentences when an appropriate sequence of referring expressions replaces the variables in order, or when all the variables are bound by quantifiers. A predicate cannot itself be true or false, but it is sometimes said to be true if its universal closure is true, that is, if it holds for every element in the relevant domain. It is satisfied by, or is true of, a sequence of referring expressions if the uniform replacement of each of its variables by the elements of the sequence in order yields a true sentence.
b. consequently, in semantics, a function from individuals or sequences to truth-values, the truth set of the function being the extension of the predicate. In this context it is sometimes a useful device, due to Tarski, to treat sentences as zero-place predicates.
b. a property, characteristic or attribute that may be affirmed or denied of something. The categorial statement all men are mortal relates two predicates,... is a man and... is mortal. See syllogism.
c. the term of a categorial proposition that is affirmed or denied of its subject; in the same example, all men is the subject and is mortal is the predicate in this sense.
2a. formally, in some treatments of the predicate calculus, a term that is derived from an atomic sentence by the deletion of a name, these being the primitive terms of the system; in other treatments, names and predicates are primitive, and an atomic sentence is defined to be the result of combining them by replacing each variable in the predicate by a name. Predicates are usually written in functional notation, as, for example, F(x) and R(x, y), and yield well-formed sentences when an appropriate sequence of referring expressions replaces the variables in order, or when all the variables are bound by quantifiers. A predicate cannot itself be true or false, but it is sometimes said to be true if its universal closure is true, that is, if it holds for every element in the relevant domain. It is satisfied by, or is true of, a sequence of referring expressions if the uniform replacement of each of its variables by the elements of the sequence in order yields a true sentence.
b. consequently, in semantics, a function from individuals or sequences to truth-values, the truth set of the function being the extension of the predicate. In this context it is sometimes a useful device, due to Tarski, to treat sentences as zero-place predicates.