Journal of Symbolic Logic 54 (3):1042-1062 (1989)

Abstract
The object of this paper is to make a study of four systems of modal logic (S4, S5, and their intuitionistic analogues IM4 and IM5) with the techniques of the theory of abstract logics set up by Suszko, Bloom, Brown, Verdú and others. The abstract concepts corresponding to such systems are defined as generalizations of the logics naturally associated to their algebraic models (topological Boolean or Heyting algebras, general or semisimple). By considering new suitably defined connectives and by distinguishing between having the rule of necessitation only for theorems or as a full inference rule (which amounts to dealing with all filters or with open filters of the algebras) we are able to reduce the study of a modal (abstract) logic L to that of two nonmodal logics L - and L + associated with L. We find that L is "of IM4 type" if and only if L - and L + are both intuitionistic and have the same theorems, and logics of type S4, IM5 or S5 are obtained from those of type IM4 simply by making classical L -, L + or both. We compare this situation with that found in recent approaches to intuitionistic modal logic using birelational models or using higher-level sequent-systems. The treatment of modal systems with abstract logics is rather new, and in our way to it we find several general constructions and results which can also be applied to other modal systems weaker than those we study in detail
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2274764
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 64,178
Through your library

References found in this work BETA

Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
Algebraic Aspects of Deduction Theorems.Janusz Czelakowski - 1985 - Studia Logica 44 (4):369 - 387.
Modality and Possibility in Some Intuitionistic Modal Logics.Josep M. Font - 1986 - Notre Dame Journal of Formal Logic 27 (4):533-546.

View all 11 references / Add more references

Citations of this work BETA

Algebraic Study of Two Deductive Systems of Relevance Logic.Josep Maria Font & Gonzalo Rodríguez - 1994 - Notre Dame Journal of Formal Logic 35 (3):369-397.

View all 7 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
40 ( #270,826 of 2,454,961 )

Recent downloads (6 months)
1 ( #449,233 of 2,454,961 )

How can I increase my downloads?

Downloads

My notes