Corpus ID: 53328983

# 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}
}
• Published 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

#### Figures and Tables from this paper

Trilattice logic: an embedding-based approach
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
Proofs, Disproofs, and Their Duals
• H. Wansing
• Computer Science
• 2010
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
• H. Wansing
• Mathematics, Computer Science
• J. Appl. Non Class. Logics
• 2008
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
• Mathematics, Computer Science
• 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
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
• N. Kamide
• 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
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 theExpand
The Power of Belnap: Sequent Systems for SIXTEEN3
• H. Wansing
• 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

#### References

SHOWING 1-10 OF 36 REFERENCES
Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood
• Mathematics, Computer Science
• J. Log. Lang. Inf.
• 2006
It is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic and another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of higher-order values is compared. Expand
Some Useful 16-Valued Logics: How a Computer Network Should Think
• Computer Science, Mathematics
• J. Philos. Log.
• 2005
The present paper argues in favor of extending first degree entailment as a useful 16-valued logic to the set 16=℘(4) (and beyond) and defines further useful16-valued logics for reasoning about truth and (non-)falsity. Expand
Partiality and Its Dual
• J. Dunn
• Mathematics, Computer Science
• Stud Logica
• 2000
This paper explores allowing truth value assignments to be undetermined or "partial" (no truth values) and overdetermined or "inconsistent" (both truth values), thus returning to an investigation ofExpand
On Retaining Classical Truths and Classical Deducibility in Many-Valued and Fuzzy Logics
This paper finds the conditions that are individually necessary and jointly sufficient for any many-valued semantics to validate exactly the classically valid formulas, while sanctioning exactly the same set of inferences as classical logic. Expand
The Trilattice of Constructive Truth Values
• Computer Science, Mathematics
• J. Log. Comput.
• 2001
It appears that these 16 truth values constitute what the authors call a trilattice — a natural mathematical structure with three partial orderings that represent respectively a increase in information, truth and constructivity. Expand
Multi-Valued Logics
This work argues that classical logic extensions share two properties: firstly, the formal addition of truth values encoding intermediate levels of validity between true and false and, secondly, the addition oftruth values encoding Intermediate levels of certainty between true or false on the one hand (complete information) and unknown (no information) on the other. Expand
Bilattices Are Nice Things
One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a fixpointExpand
Many Valued Logic
Throughout the orthodox mainsteam of the development of logic in the West, the prevailing view was that every proposition is either true or else false (although which of these is the case may wellExpand
Two's Company: “The Humbug of Many Logical Values”
• Mathematics
• 2005
The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logicalExpand
Intuitive semantics for first-degree entailments and ‘coupled trees’
Classically, an argument A therefore B is ‘valid’ (or A is said to ‘entail’ B) if and only if (iff) each situation (model) is such that either A is false or B is true. This fits well with so-calledExpand