A Treatise on Many-valued LogicsA growing interest in many-valued logic has developed which to a large extent is based on applications, intended as well as already realised ones. These applications range from the field of computer science, e.g. in the areas of automated theorem proving, approximate reasoning, multi-agent systems, switching theory, and program verification, through the field of pure mathematics, e.g. in independence of consistency proofs, in generalized set theories, or in the theory of particular algebraic structures, into the fields of humanities, linguistics and philosophy. |
Contents
General Background 336 | 3 |
The Formalized Language and its Interpretations | 15 |
Logical Validity and Entailment | 29 |
Copyright | |
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Common terms and phrases
adequate axiomatization algebraic structures axiom schemata AXML basic BL-algebra characterized classical logic condition consider Corollary corresponding defined definition denoted derivation designated truth degree disjunction equivalence relation exists extended filter finitely many-valued first-order first-order logic fuzzy logic fuzzy relation fuzzy sets G-algebra GÖDEL systems H₁ H₂ hence HEYTING algebra holds true immediately inference rules isomorphic language lattice ordering left continuous t-norm LINDENBAUM algebra logical calculus logically valid LUKASIEWICZ systems many-valued logic means monoidal MV-algebras notion operations ordering ordinal sum predicate symbol Proof propositional variables prove quantifiers residuated lattice result S-interpretation S-sequent satisfies schema semantic sequence set of wffs signed formulas subset suitable Suppose systems of many-valued t-norm based t₁ truth degree constants truth degree functions truth degree set truth value unary universe of discourse Val H Val(w valuation ẞ wff H