From many-valued consequence to many-valued connectives

Synthese:1-38 (forthcoming)

Authors
Paul Egré
École Normale Supérieure
Abstract
Given a consequence relation in many-valued logic, what connectives can be defined? For instance, does there always exist a conditional operator internalizing the consequence relation, and which form should it take? In this paper, we pose this question in a multi-premise multi-conclusion setting for the class of so-called intersective mixed consequence relations, which extends the class of Tarskian relations. Using computer-aided methods, we answer extensively for 3-valued and 4-valued logics, focusing not only on conditional operators, but also on what we call Gentzen-regular connectives. For arbitrary N-valued logics, we state necessary and sufficient conditions for the existence of such connectives in a multi-premise multi-conclusion setting. The results show that mixed consequence relations admit all classical connectives, and among them pure consequence relations are those that admit no other Gentzen-regular connectives. Conditionals can also be found for a broader class of intersective mixed consequence relations, but with the exclusion of order-theoretic consequence relations.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1007/s11229-019-02344-0
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 43,914
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Axiomatization of Semigroup Consequences.Wolfgang Rautenberg - 1989 - Archive for Mathematical Logic 29 (2):111-123.
Two-Valued Weak Kleene Logics.Bruno da Ré & Damian Szmuc - 2019 - Manuscrito 42 (1):1-43.
Aggregation and Idempotence.Lloyd Humberstone - 2013 - Review of Symbolic Logic 6 (4):680-708.
A Characteristic Model For Some Tabular Many-Valued Logics.Marion Mircheva - 1986 - Bulletin of the Section of Logic 15 (4):159-161.
Triadic Logic.Robert Lane - 2001 - The Commens Encyclopedia: The Digital Encyclopedia of Peirce Studies.

Analytics

Added to PP index
2019-09-15

Total views
3 ( #1,179,724 of 2,266,272 )

Recent downloads (6 months)
3 ( #439,992 of 2,266,272 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature