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Logical consequence

Definition

Logical consequence is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements. A valid logical argument is one in which the conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the following questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises? All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth.

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Zalta Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Emil Leon Post Empirical evidence Empty set Encyclopedia of Mathematics Entail (disambiguation)Enumeration Epistemic modality Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry European Mathematical Society Evidentiality Exclusive or Exhaustivity Existential closure Existential quantification Expression (mathematics)Extension (semantics)Extension by definitions Extension by new constant and function names Extensionality False (logic)Faultless disagreement Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Focus (linguistics)Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal semantics (natural language)Formal system Formalism (philosophy of mathematics)Formation rule Foundations of geometry Foundations of mathematics Free choice inference Free logic Free variables and bound variables Function (mathematics)Function application Functional predicate Fuzzy set General set theory Generalized quantifier Generative grammar Geoffrey Hunter (logician)German language Givenness Glue semantics Greg Restall Grothendieck universe Ground expression Ground formula Gödel Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Homogeneity (linguistics)Horseshoe (symbol)Hurford disjunction IMPLY gate If and only if Image (mathematics)Inaccessible cardinal Inalienable possession Independence (mathematical logic)Index of logic articles Indexicality Indiana Philosophy Ontology Project Inductive reasoning Inference Inference rule Inferentialism Infinite-valued logic Infinite set Informal logic Information theory Inhabited set Injective function Inquisitive semantics Intended interpretation Intension Intensional logic Internet Encyclopedia of Philosophy Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Intersective modifier Intuitionist Inverter (logic gate)Isomorphism J. 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theorem Many-valued logic Map (mathematics)Maria Luisa Dalla Chiara Material conditional Material nonimplication Mathematical logic Mathematical object Meaning postulate Mereology Metalanguage Metalogic Metamathematics Michael Dummett Michael Friedman (philosopher)Minimal axioms for Boolean algebra Mirativity Modal logic Modal subordination Modality (semantics)Model complete theory Model theory Monad (functional programming)Monadic predicate calculus Monadic second-order logic Monotonicity of entailment Montague grammar Morse–Kelley set theory NAND gate NIMPLY gate NOR gate NP (complexity)Naive set theory Name Natural deduction Necessity and sufficiency Negation New Foundations Non-Euclidean geometry Non-classical logic Non-logical symbol Non-monotonic logic Non-standard model Non-standard model of arithmetic OR gate Opaque context Open formula Operation (mathematics)Ordinal analysis Ordinal number Outline of logic Oxford University Press P (complexity)P versus NP problem Paradox Paradoxes of set theory Partition of a set Peano axioms Peirce's law Performative utterance PhilPapers Philosophical analysis Philosophical logic Philosophy of language Philosophy of logic Philosophy of mathematics Plural quantification Polarity item Polish language Possible world Power set Pragmatics Predicate (mathematical logic)Predicate logic Predicate variable Premise Presupposition Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Principle of compositionality Privative adjective Probabilistic logic Probability Proof of impossibility Proof theory Proposition Propositional attitudes Propositional calculus Propositional formula Propositional variable Quantificational variability effect Quantifier (logic)Quantifier raising Quantifier rank Quantization (linguistics)Question under discussion Reason Recursion Recursive set Reference Relation (mathematics)Responsive predicate Reverse mathematics Rising declarative Robinson arithmetic Rule of inference Russell's paradox Satisfiability Saturated model Scalar implicature Schema (logic)Schröder–Bernstein theorem Scope (formal semantics)Second-order arithmetic Second-order logic Segmented discourse representation theory Self-verifying theories Semantic parsing Semantic theory of truth Semantics (logic)Semantics of logic Sentence (mathematical logic)Sequent calculus Set (mathematics)Set theory Sheffer stroke Signature (logic)Singleton (mathematics)Situation semantics Skolem arithmetic Sloppy identity Sole sufficient operator Soundness Spectrum of a sentence Spectrum of a theory Speech act Square of opposition Squiggle operator Stanford Encyclopedia of Philosophy Statement (logic)Stewart Shapiro Strawson entailment Strength (mathematical logic)Strict conditional String (formal languages)Structure (mathematical logic)Subsective modifier Subset Substitution (logic)Substructure (mathematics)Subtrigging Supertask Supervaluationism Surjective function Syllogism Symbol (formal)Syntax (logic)Syntax–semantics interface T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautological consequence Tautology (logic)Tee (symbol)Telicity Temperature paradox Tense–aspect–mood Term (logic)Term logic Theorem Theories of truth Theory (mathematical logic)Theory of justification Therefore sign Three-valued logic Tilde Timeline of mathematical logic Transfer principle Transitive set Triple bar True (logic)True arithmetic Truth Truth-conditional semantics Truth predicate Truth table Truth value Turing machine Turned A Turnstile (symbol)Type (model theory)Type shifter Type theory Type theory with records Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal grinder Universal quantification Universal set Universe (mathematics)Up tack Urelement Vagueness Validity (logic)Variable (mathematics)Vel (symbol)Venn diagram Veridicality Vincent F. Hendricks Von Neumann universe Von Neumann–Bernays–Gödel set theory W.V. Quine Wedge (symbol)Well-formed formula Willard Van Orman Quine XNOR gate XOR gate Zermelo–Fraenkel set theory

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