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propositional logic, Boolean algebra, Heyting algebra: is false when A is true and B is false but true otherwise. may mean the same as (the symbol may also indicate the domain and codomain of a function; see table of mathematical symbols).
[1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory. [5] A Boolean function takes the form : {,} {,}, where {,} is known as the Boolean domain and is a non ...
In logic, a truth function [1] is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value(s) will always output the same truth value.
Standard part function; Set theory. Forcing (mathematics) Boolean-valued model; Kripke semantics. General frame; Predicate logic. First-order logic. Infinitary logic; Many-sorted logic; Higher-order logic. Lindström quantifier; Second-order logic; Soundness theorem; Gödel's completeness theorem. Original proof of Gödel's completeness theorem ...
In logic, a symbol that represents a function from individuals or tuples of individuals to truth values, essentially a generalization of a predicate. [234] predicate functor logic A logical system that combines elements of predicate logic with the concept of functors, allowing for a more expressive representation of properties and relations.
The two subjects of mathematical logic and set theory have belonged to mathematics since the end of the 19th century. [46] [47] Before this period, sets were not considered to be mathematical objects, and logic, although used for mathematical proofs, belonged to philosophy and was not specifically studied by mathematicians. [48]
A variety of basic concepts is used in the study and analysis of logical reasoning. Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case.
It is a comprehensive treatise on logic that discusses many basic concepts of logic and provides a systematic exposition of types of propositions and their truth conditions. [196] In Chinese philosophy, the School of Names and Mohism were particularly influential. The School of Names focused on the use of language and on paradoxes.
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