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A sentence can be viewed as expressing a proposition, something that must be true or false. The restriction of having no free variables is needed to make sure that sentences can have concrete, fixed truth values : as the free variables of a (general) formula can range over several values, the truth value of such a formula may vary.
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.
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.
A major sentence is a regular sentence; it has a subject and a predicate, e.g. "I have a ball." In this sentence, one can change the persons, e.g. "We have a ball." However, a minor sentence is an irregular type of sentence that does not contain a main clause, e.g. "Mary!", "Precisely so.", "Next Tuesday evening after it gets dark."
A closed formula, also ground formula or sentence, is a formula in which there are no free occurrences of any variable. If A is a formula of a first-order language in which the variables v 1, …, v n have free occurrences, then A preceded by ∀v 1 ⋯ ∀v n is a universal closure of A.
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 an O-proposition, only the predicate is distributed. Consider the following: "Some politicians are not corrupt". Since not all politicians are defined by this rule, the subject is undistributed. The predicate, though, is distributed because all the members of "corrupt people" will not match the group of people defined as "some politicians".
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 ...