In formal theories of truth, a truth predicate is a fundamental concept based on the sentences of a formal language as interpreted logically. That is,...

meaning of a predicate is exactly a function from the domain of objects to the truth values "true" and "false". In the semantics of logic, predicates are interpreted...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy...

in common the claim that assertions of predicate truth of a statement do not attribute a property called "truth" to such a statement. Gottlob Frege was...

Gödel used in his incompleteness theorems. Roughly, this states that a truth-predicate satisfying Convention T for the sentences of a given language cannot...

ideas about truth are often confused with the quite distinct notions of "logic and inquiry", "judging what is true", and "truth predicates". In one classical...

subject and a predicate, connected by a copula. For example, the statement "all humans are mortal" has the subject "all humans", the predicate "mortal", and...

functional predicate, or function symbol, is a logical symbol that may be applied to an object term to produce another object term. Functional predicates are...

occurrences of the truth predicate in natural language. In particular, Schema T treats only "freestanding" uses of the predicate—cases when it is applied...

truth values true and false. Because the first-order interpretations described here are defined in set theory, they do not associate each predicate symbol...

words add an additional parameter to the construction of an accurate truth predicate. Among the philosophers who grappled with this problem is Alfred Tarski...

In logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic in which all relation symbols[clarification...

contain the truth predicate, and defining a truth predicate over just that segment: this action adds new sentences to the language, and truth is in turn...

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity...

In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not...

or syntactic expression. In formal semantic theories of truth, a truth predicate is a predicate on the sentences of a formal language, interpreted for...

the truth predicate. Some sentences are stable in their evaluations, such as the truth-teller sentence, The truth-teller is true. Assuming the truth-teller...

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which...

words add an additional parameter to the construction of an accurate truth predicate. Among the philosophers who grappled with this problem is Alfred Tarski...

analysis of the truth of the liar sentence. It is not possible to replace "not provable" with "false" in a Gödel sentence because the predicate "Q is the Gödel...

we can read a definite answer, 'Yes' or 'No,' to the question, 'Is the predicate value true?'." 1952 (1952): Kleene includes a discussion of the unsolvability...

{\displaystyle T^{*},} but that doesn't define truth for the stronger system However, this formula only defines a truth predicate for formulas in the original language...

standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations...

logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic...

as x and y attached to predicate letters such as Px and xRy, having instead individual constants a, b, ..attached to predicate letters are propositional...

first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or quantifiers. However, all the machinery of propositional...

the language; in the case of predicate logic more logical axioms than that are required, in order to prove logical truths that are not tautologies in the...

as expressing some truth, but in contrast to the notion of a scientific law, which is experimental, the justification of the truth of a theorem is purely...

\exists x\,\mathrm {Cube} (x)} However, we cannot do the same with the predicate. That is, the following expression: ∃ P P ( b ) {\displaystyle \exists...

unsatisfiable). The definition of tautology can be extended to sentences in predicate logic, which may contain quantifiers—a feature absent from sentences of...