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Philosophy - Logic & Philosophy of Language | Truth and Falsehood - An Inquiry into Generalized Logical Values

Truth and Falsehood

An Inquiry into Generalized Logical Values

Series: Trends in Logic, Vol. 36

Shramko, Yaroslav, Wansing, Heinrich

2012, XIV, 250 p.

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  • Surveys and unifies various philosophical and formal treatments of truth values
  • Discusses central issues such as the relation between truth values and consequence relations 
  •  Systematically develops both semantically and proof-theoretically a theory of generalized truth values as subsets of already established truth values.

The book presents a thoroughly elaborated logical theory of generalized truth values understood as subsets of some established set of (basic) truth entities. After elucidating the importance of the very notion of a truth value in logic and philosophy, the authors examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and Michael Dunn and the notion of a bilattice (a lattice of truth values with two ordering relations) constitute the basis for further generalizations. By doing so the authors elaborate the idea of a multilattice and, most notably, a trilattice of truth values – a specific algebraic structure with an 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 also determines its own entailment relation. Both semantic ans syntactic ways of formalizing these relations by constructing various logical calculi are considered.

Content Level » Research

Keywords » first-degree entailment - lattice theory - logical semantics - trilattice logics - truth values

Related subjects » Logic & Philosophy of Language - Mathematics - Theoretical Computer Science

Table of contents 

1 Truth Values 2 Truth Values and the Slingshot Argument 3 Generalized Truth Values: From FOUR2 to SIXTEEN3 4 Generalized Truth Values: SIXTEEN3 and Beyond Axiom Systems for Trilattice Logics Sequent Systems for Trilattice Logics Intuitionistic Trilattice Logics Generalized Truth Values and Many-valued Logics: Harmonious Many-valued Logics . Generalized Truth Values and Many-valued Logics: Suszko’s Thesis Further Developments References Index

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