# Harmonious Many-Valued Propositional Logics and the Logic of Computer Networks

@inproceedings{Wansing2008HarmoniousMP, title={Harmonious Many-Valued Propositional Logics and the Logic of Computer Networks}, author={Heinrich Wansing and Yaroslav Shramko}, year={2008} }

In this paper we reconsider the notion of an n-valued propositional logic. In many-valued logic, sometimes a distinction is made not only between designated and undesignated (not designated) truth values, but between designated, undesignated, and antidesignated truth values. But even if the set of truth values is, in fact, tripartitioned, usually only a single semantic consequence relation is defined that preserves the possession of a designated value from the premises to the conclusions of an… Expand

#### 11 Citations

Trilattice logic: an embedding-based approach

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- J. Log. Comput.
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An alternative new proof of the cut-elimination and completeness theorem for such a trilattice logic is obtained using two embedding theorems and the Craig interpolation and Maksimova separation theoresms are proved using the same embeddingTheorems. Expand

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An inferentialist semantics in terms of proofs, disproofs, and their duals is developed for bi-intuitionistic logic with strong negation. Expand

Constructive negation, implication, and co-implication

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- J. Appl. Non Class. Logics
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A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented. Expand

Suszko’s Thesis, Inferential Many-valuedness, and the Notion of a Logical System

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- Stud Logica
- 2008

Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. Expand

Bi-facial Truth: a Case for Generalized Truth Values

- Mathematics, Computer Science
- Stud Logica
- 2013

We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework.… Expand

Completeness and cut-elimination theorems for trilattice logics

- Mathematics, Computer Science
- Ann. Pure Appl. Log.
- 2011

A sequent calculus L 16 for Odintsov’s Hilbert-style axiomatization L B of a logic related to the trilattice S I X T E E N 3 of generalized truth values is introduced and a simple semantics for L 16 is proved using Maehara's decomposition method that simultaneously derives the cut-elimination theorem for L 15. Expand

Representation of interlaced trilattices

- Computer Science
- J. Appl. Log.
- 2013

The aim of the present work is to develop a first purely algebraic study of trilattices, focusing in particular on the problem of representing certain subclasses of trILattices as special products of bilattices. Expand

Embedding-Based Methods for Trilattice Logic

- Mathematics, Computer Science
- 2013 IEEE 43rd International Symposium on Multiple-Valued Logic
- 2013

An alternative new proof of the cut-elimination and completeness theorems for such a trilattice logic is obtained using two embedding theoresms. Expand

What is a Genuine Intuitionistic Notion of Falsity

- Mathematics
- 2013

I highlight the importance of the notion of falsity for a semantical consideration of intuitionistic logic. One can find two principal (and non-equivalent) versions of such a notion in the… Expand

The Power of Belnap: Sequent Systems for SIXTEEN3

- Mathematics, Computer Science
- J. Philos. Log.
- 2010

Cut-free, sound and complete sequent calculi for truth entailment and falsity entailment in $\textit{SIXTEEN}_3$ are presented. Expand

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