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logically valid formula

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  • First-order logic — is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic (a less… …   Wikipedia

  • Gödel's completeness theorem — is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first order logic. It was first proved by Kurt Gödel in 1929. A first order formula is called logically valid if… …   Wikipedia

  • Entailment — For other uses, see Entail (disambiguation). In logic, entailment is a relation between a set of sentences (e.g.,[1] meaningfully declarative sentences or truthbearers) and a sentence. Let Γ be a set of one or more sentences; let S1 be the… …   Wikipedia

  • Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …   Wikipedia

  • Method of analytic tableaux — A graphical representation of a partially built propositional tableau In proof theory, the semantic tableau (or truth tree) is a decision procedure for sentential and related logics, and a proof procedure for formulas of first order logic. The… …   Wikipedia

  • Interpretation (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 …   Wikipedia

  • Tautology (logic) — In propositional logic, a tautology (from the Greek word ταυτολογία) is a propositional formula that is true under any possible valuation (also called a truth assignment or an interpretation) of its propositional variables. For example, the… …   Wikipedia

  • Decidability (logic) — In logic, the term decidable refers to the decision problem, the question of the existence of an effective method for determining membership in a set of formulas. Logical systems such as propositional logic are decidable if membership in their… …   Wikipedia

  • Formal interpretation — A formal interpretation [http://books.google.com/books?id=weKqT3ka5g0C pg=PA74 lpg=PA74 dq=%22Formal+interpretation%22+%22formal+language%22 source=web ots=pLN ms7Wi2 sig=P JqwdzOqLcX4nMpP64qmacnkDU hl=en#PPA74,M1 Cann Ronnie, Formal Semantics:… …   Wikipedia

  • Problem of evil — Part of a series on God General conceptions …   Wikipedia

  • Second-order logic — In logic and mathematics second order logic is an extension of first order logic, which itself is an extension of propositional logic.[1] Second order logic is in turn extended by higher order logic and type theory. First order logic uses only… …   Wikipedia

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