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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.
In the most typical cases, the predicand corresponds to the subject of a clause, and the predicate corresponds to a verb phrase (VP) that is the head of the clause. But there are also form-meaning mismatches, where the predicand is not a subject or where the predicate is not the head of the clause. Also, not every utterance has a predicand.
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.
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.
Quantity refers to the number of members of the subject class (A class is a collection or group of things designated by a term that is either subject or predicate in a categorical proposition. [3]) that are used in the proposition. If the proposition refers to all members of the subject class, it is universal.