Free and Projective Bimodal Symmetric Gödel Algebras

Studia Logica 104 (1):115-143 (2016)
  Copy   BIBTEX

Abstract

Gödel logic is the extension of intuitionistic logic by the linearity axiom. Symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives. Symmetric Gödel logic is the extension of symmetric intuitionistic logic. The proof-intuitionistic calculus, the language of which is an enrichment of the language of intuitionistic logic by modal operator was investigated by Kuznetsov and Muravitsky. Bimodal symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives and two modal operators. Bimodal symmetric Gödel logic is embedded into an extension of Gödel–Löb logic, the language of which contains disjunction, conjunction, negation and two modal operators. The variety of bimodal symmetric Gödel algebras, that represent the algebraic counterparts of bimodal symmetric Gödel logic, is investigated. Description of free algebras and characterization of projective algebras in the variety of bimodal symmetric Gödel algebras is given. All finitely generated projective bimodal symmetric Gödel algebras are infinite, while finitely generated projective symmetric Gödel algebras are finite

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,991

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Free Spectra of Linear Equivalential Algebras.Katarzyna Slomczyńska - 2005 - Journal of Symbolic Logic 70 (4):1341 - 1358.
Free Algebras for Gödel-Löb Provability Logic.Sam J. van Gool - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10. CSLI Publications. pp. 217-233.
On a four-valued modal logic with deductive implication.Marcelo E. Coniglio & Martín Figallo - 2014 - Bulletin of the Section of Logic 43 (1/2):1-18.
A Note on the Godel-Gentzen Translation.Hajime Ishihara - 2000 - Mathematical Logic Quarterly 46 (1):135-138.
Decision methods for linearly ordered Heyting algebras.Sara Negri & Roy Dyckhoff - 2006 - Archive for Mathematical Logic 45 (4):411-422.

Analytics

Added to PP
2015-09-23

Downloads
22 (#731,954)

6 months
5 (#710,905)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Modal logic.Alexander Chagrov - 1997 - New York: Oxford University Press. Edited by Michael Zakharyaschev.
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.

View all 10 references / Add more references