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In semantics and pragmatics, a truth condition is the condition under which a sentence is true. For example, "It is snowing in Nebraska" is true precisely when it is snowing in Nebraska. Truth conditions of a sentence do not necessarily reflect current reality. They are merely the conditions under which the statement would be true. [1]
In realizability truth values are sets of programs, which can be understood as computational evidence of validity of a formula. For example, the truth value of the statement "for every number there is a prime larger than it" is the set of all programs that take as input a number , and output a prime larger than .
It is inadequate as a criterion because it treats facts in an isolated fashion without true cohesion and integration; nevertheless it remains a necessary condition for the truth of any argument, owing to the law of noncontradiction. The value of a proof largely lies in its ability to reconcile individual facts into a coherent whole. [6]
Truth-conditional semantics is an approach to semantics of natural language that sees meaning (or at least the meaning of assertions) as being the same as, or reducible to, their truth conditions. This approach to semantics is principally associated with Donald Davidson , and attempts to carry out for the semantics of natural language what ...
The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name truth-value semantics). Game semantics or game-theoretical semantics made a resurgence mainly due to Jaakko Hintikka for logics of (finite) partially ordered quantification , which were originally investigated ...
But Tarski's approach was extended by Davidson into an approach to theories of meaning for natural languages, which involves treating "truth" as a primitive, rather than a defined, concept. (See truth-conditional semantics.) Tarski developed the theory to give an inductive definition of truth as follows. (See T-schema)
Broadly speaking, the primary motivation for research of three valued logic is to represent the truth value of a statement that cannot be represented as true or false. [8] Łukasiewicz initially developed three-valued logic for the problem of future contingents to represent the truth value of statements about the undetermined future.
"Ground truth" may be seen as a conceptual term relative to the knowledge of the truth concerning a specific question. It is the ideal expected result. [2] This is used in statistical models to prove or disprove research hypotheses. The term "ground truthing" refers to the process of gathering the proper objective (provable) data for this test.