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Soundness

Definition

In logic, soundness can refer to either a property of arguments or a property of formal deductive systems.

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Abstract logic Ackermann set theory Aleph number Algebraic logic Alphabet (formal languages)Argument Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Bijection Binary operation Boolean algebra Boolean algebras canonically defined Boolean function Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Compactness theorem Complement (set theory)Complete theory Completeness (logic)Computability theory Computable function Computable set Computably enumerable set Concrete category Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Converse (logic)Countable set Decidability (logic)Decision problem Deduction system Deductive reasoning Deductive system Diagram (mathematical logic)Domain of a function Effective method Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Entscheidungsproblem Enumeration Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Formula (mathematical logic)Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set General set theory Grothendieck universe Ground expression Ground formula Gödel Gödel's completeness theorem Gödel's incompleteness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditary set Higher-order logic Hilbert's axioms Hilbert-style deductive system Hilbert system History of logic History of mathematical logic Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Internet Encyclopedia of Philosophy Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Irving Copi Isomorphism John Lemmon Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Large cardinal Lemma (mathematics)Lindström's theorem List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical system Logical truth Logicism Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Mathematical logic Mathematical object Metalanguage Metalogic Metamathematics Metatheorem Minimal axioms for Boolean algebra Model complete theory Model theory Modus ponens Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NP (complexity)Naive set theory Natural deduction Natural numbers Negation New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Open formula Operation (mathematics)Ordinal analysis Ordinal number P (complexity)P versus NP problem Paradoxes of set theory Partition of a set Peano axioms Philosophy of mathematics Power set Predicate (mathematical logic)Predicate logic Predicate variable Premise Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Proof of impossibility Proof theory Proposition Propositional calculus Propositional formula Propositional variable Quantifier (logic)Quantifier rank Recursion Recursive set Relation (mathematics)Reverse mathematics Robinson arithmetic Rule of inference Russell's paradox Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic consequence Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequence Sequent calculus Set (mathematics)Set theory Signature (logic)Singleton (mathematics)Skolem Skolem arithmetic Soundness (interactive proof)Spectrum of a sentence Spectrum of a theory Square of opposition Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic Theorem Theories of truth Theory (mathematical logic)Three-valued logic Timeline of mathematical logic Transfer principle Transitive set True arithmetic Truth Truth predicate Truth table Truth value Turing machine Type (model theory)Type soundness Type theory Type–token distinction Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)Urelement Use–mention distinction Validity (logic)Variable (mathematics)Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Zermelo–Fraenkel set theory Ω-consistent theory

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