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A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.
If "predicate variables" are only allowed to be bound to predicate letters of zero arity (which have no arguments), where such letters represent propositions, then such variables are propositional variables, and any predicate logic which allows second-order quantifiers to be used to bind such propositional variables is a second-order predicate ...
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that is not defined or specified (thus being a free variable), which leaves the statement undetermined.
A predicate evaluates to true or false for an entity or entities in the domain of discourse. Consider the two sentences "Socrates is a philosopher" and "Plato is a philosopher". In propositional logic, these sentences themselves are viewed as the individuals of study, and might be denoted, for example, by variables such as p and q.
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.
If, abstractly, the subject category is named S and the predicate category is named P, the four standard forms are: All S are P. (A form) No S are P. (E form) Some S are P. (I form) Some S are not P. (O form) A large number of sentences may be translated into one of these canonical forms while retaining all or most of the original meaning of ...