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Predicate (grammar) The term predicate is used in two ways in linguistics and its subfields. The first defines a predicate as everything in a standard declarative sentence except the subject, and the other defines it as only the main content verb or associated predicative expression of a clause. Thus, by the first definition, the predicate of ...
First-order logic —also called predicate logic, predicate calculus, quantificational logic —is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than ...
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 Propositional Function, or a predicate, in a variable x is an open formula p ( x) involving x that becomes a proposition when one gives x a definite value from the set of values it can take. According to Clarence Lewis, "A proposition is any expression which is either true or false; a propositional function is an expression, containing one or ...
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.
A predicative expression (or just predicative) is part of a clause predicate, and is an expression that typically follows a copula or linking verb, e.g. be, seem, appear, or that appears as a second complement of a certain type of verb, e.g. call, make, name, etc. [1] The most frequently acknowledged types of predicative expressions are predicative adjectives (also predicate adjectives) and ...
A predicate symbol applied to the number of terms required by its arity, or; An operator applied to the number of propositions required by its arity, or; A quantifier applied to a proposition. For example, if = is a binary predicate symbol and ∀ is a quantifier, then ∀x,y,z [(x = y) → (x+z = y+z)] is a proposition. This more complex ...
Second-order predicate. In mathematical logic, a second-order predicate is a predicate that takes a first-order predicate as an argument. [1] Compare higher-order predicate . The idea of second order predication was introduced by the German mathematician and philosopher Frege. It is based on his idea that a predicate such as "is a philosopher ...
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