Truth and Falsehood: An Inquiry into Generalized Logical ValuesSpringer Science & Business Media, 15 set 2011 - 250 pagine The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of (basic) truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. |
Sommario
1 | |
2 Truth Values and the Slingshot Argument | 19 |
From FOUR2 to SIXTEEN3 | 41 |
SIXTEEN3 and Beyond | 63 |
5 Axiom Systems for Trilattice Logics | 93 |
6 Sequent Systems for Trilattice Logics | 113 |
7 Intuitionistic Trilattice Logics | 143 |
Altre edizioni - Visualizza tutto
Truth and Falsehood: An Inquiry into Generalized Logical Values Yaroslav Shramko,Heinrich Wansing Anteprima non disponibile - 2013 |
Truth and Falsehood: An Inquiry into Generalized Logical Values Yaroslav Shramko,Heinrich Wansing Anteprima non disponibile - 2011 |
Parole e frasi comuni
AA/B admissible in cut-free AðxÞ algebraic values antidesignated values axiom systems axiomatized Biff bilattice Chap connectives consequence relation consider constructive cut-elimination theorem cut-free ð Þ Deduction Theorem Definition denote designated values disambiguations disjunction entailment relation expression extended falsity entailment falsity order FOUR2 Frege implies induction hypothesis inference rules interpretation introduced intuitionistic intuitionistic logic Kripke frame language lattice Lbase Lemma logical system logical values Łukasiewicz Malinowski many-valued logic matrix modal modus ponens Moreover negation non-empty set non-Fregean logic notion obtain Odintsov operations paraconsistent logic partial orders predicate premises proof systems propositional logic propositional variable provable q-matrix respect Sect sequent calculus set of formulas set of truth slingshot argument Springer Science+Business Media structure subset Tarskian Theorem three-valued trilattice logics true sentences truth and falsity truth entailment truth order truth values valuation function valuation system