Topos based semantic for constructive logic with strong negation

&
Mathematical Logic Quarterly 38 (1):509-519 (1992)
  Copy   BIBTEX

Abstract

The aim of the paper is to show that topoi are useful in the categorial analysis of the constructive logic with strong negation. In any topos ϵ we can distinguish an object Λ and its truth-arrows such that sets ϵ have a Nelson algebra structure. The object Λ is defined by the categorial counterpart of the algebraic FIDEL-VAKARELOV construction. Then it is possible to define the universal quantifier morphism which permits us to make the first order predicate calculus. The completeness theorem is proved using the Kripke-type semantic defined by THOMASON

Categories

Keywords

Reprint years

DOI

10.1002/malq.19920380146

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,219

External links

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

Through your library

My notes

Similar books and articles

Axiomatic extensions of the constructive logic with strong negation and the disjunction property.Andrzej Sendlewski - 1995 - Studia Logica 55 (3):377 - 388.
Information Completeness in Nelson Algebras of Rough Sets Induced by Quasiorders.Jouni Järvinen, Piero Pagliani & Sándor Radeleczki - 2013 - Studia Logica 101 (5):1073-1092.
On extensions of intermediate logics by strong negation.Marcus Kracht - 1998 - Journal of Philosophical Logic 27 (1):49-73.
Priestley Duality for Paraconsistent Nelson’s Logic.Sergei P. Odintsov - 2010 - Studia Logica 96 (1):65-93.
Approximation Logic and Strong Bunge Algebra.Michiro Kondo - 1995 - Notre Dame Journal of Formal Logic 36 (4):595-605.
Review: H. Rasiowa, $mathcal{N}$-Lattices and Constructive Logic with Strong Negation. [REVIEW]David Nelson - 1969 - Journal of Symbolic Logic 34 (1):118-118.
Review: A. Bialynicki-Birula, H. Rasiowa, On Constructible Falsity in the Constructive Logic with Strong Negation. [REVIEW]David Nelson - 1970 - Journal of Symbolic Logic 35 (1):138-138.
Slaney's logic F is constructive logic with strong negation.M. Spinks & R. Veroff - 2010 - Bulletin of the Section of Logic 39 (3/4):161-173.
A sequent calculus for constructive logic with strong negation as a substructural logic.George Metcalfe - 2009 - Bulletin of the Section of Logic 38 (1/2):1-7.
Constructive logic, truth and warranted assertability.Greg Restall - 2001 - Philosophical Quarterly 51 (205):474-483.

Analytics

Added to PP
2013-12-01

Downloads
14 (#934,671)

6 months
6 (#431,022)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
Topoi: The Categorial Analysis of Logic.R. I. Goldblatt - 1982 - British Journal for the Philosophy of Science 33 (1):95-97.
An Algebraic Approach to Non-Classical Logics.Anne Preller - 1977 - Journal of Symbolic Logic 42 (3):432-432.
Topoi. The Categorical Analysis of Logic.Philip J. Scott - 1982 - Journal of Symbolic Logic 47 (2):445-448.

Add more references