Knowra Symbolic logic Symbolic logic Symbolic logic represents arguments with formal languages and evaluates them using explicit rules. It makes logical structure precise enough for mathematical proof and computational analysis.
Propositional logic : A formal system that analyzes combinations of propositions using connectives such as negation, conjunction, and implication. It is the simplest major symbolic system, treating whole propositions as units.
Truth table : A table listing a compound proposition's truth value for every assignment of truth values to its components. Truth tables mechanically evaluate propositional formulas and test arguments.
George Boole : An English mathematician who developed an algebraic treatment of logic in the nineteenth century. His algebra of logic helped establish the use of symbols for formal reasoning.
Mathematical logic : The mathematical study of formal systems, proof, definability, and models. Symbolic logic supplies core languages and methods for this broader mathematical field.
Aristotelian logic : A traditional system of logic centered on categorical propositions and syllogistic inference. Its subject-predicate forms contrast with modern symbolic systems' expressive languages.
First-order logic : A formal system with predicates, variables, and quantifiers for expressing relations among objects. It extends propositional logic by representing objects, properties, and quantified claims.
Interpretation (logic) : An assignment of meanings to the symbols of a formal language within a structure or domain. Interpretations give formulas a domain and meanings, making semantic truth definable.
Gottlob Frege : A German logician and philosopher who developed modern predicate logic and a formal account of arithmetic. His Begriffsschrift introduced a powerful notation for quantified logical relations.
Automated theorem proving : The use of computer programs to search for or verify formal mathematical proofs. Machine proof systems apply symbolic rules to derive and check conclusions.
Intuitionistic logic : A logic that rejects unrestricted use of the law of excluded middle and interprets proof constructively. It shows that classical symbolic rules are not the only viable formal choices.
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