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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.
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.
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 ...
For the pair a, b there are 2 2 =4 possible interpretations: 1) both are assigned T, 2) both are assigned F, 3) a is assigned T and b is assigned F, or 4) a is assigned F and b is assigned T. Given any truth assignment for a set of propositional symbols, there is a unique extension to an interpretation for all the propositional formulas built ...
Set-builder notation can be used to describe a set that is defined by a predicate, that is, a logical formula that evaluates to true for an element of the set, and false otherwise. [2] In this form, set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the ...
The notion of a predicate in traditional grammar traces back to Aristotelian logic. [2] A predicate is seen as a property that a subject has or is characterized by. A predicate is therefore an expression that can be true of something. [3] Thus, the expression "is moving" is true of anything that is moving.
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.