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In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
propositional logic first-order predicate logic, first-order logic, predicate logic, argument, input value, output formal system, logical system, logistic system, logical calculus, logic formal logic, mathematical logic, symbolic logic elementary logic
An interpretation is an assignment of meaning to the symbols of a formal language.Many formal languages used in mathematics, logic, and theoretical computer science are defined in solely syntactic terms, and as such do not have any meaning until they are given some interpretation.
In formal languages, truth functions are represented by unambiguous symbols.This allows logical statements to not be understood in an ambiguous way. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives.
A logic that extends first-order logic to allow for more nuanced expressions of quantifier scope and dependence, particularly in contexts of game-theoretical semantics. independent Referring to a pair of propositions that are not contrary , subcontrary , contradictory , logically equivalent , or implied one by the other (either the first by the ...
Mathematical logic, also called 'logistic', 'symbolic logic', the 'algebra of logic', and, more recently, simply 'formal logic', is the set of logical theories elaborated in the course of the nineteenth century with the aid of an artificial notation and a rigorously deductive method. [5]
In symbolic logic, the universal quantifier symbol (a turned "A" in a sans-serif font, Unicode U+2200) is used to indicate universal quantification. It was first used in this way by Gerhard Gentzen in 1935, by analogy with Giuseppe Peano's (turned E) notation for existential quantification and the later use of Peano's notation by Bertrand Russell.
WFF is part of an esoteric pun used in the name of the academic game "WFF 'N PROOF: The Game of Modern Logic", by Layman Allen, [21] developed while he was at Yale Law School (he was later a professor at the University of Michigan). The suite of games is designed to teach the principles of symbolic logic to children (in Polish notation). [22]