David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 54 (3):1042-1062 (1989)
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)|
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.
Citations of this work BETA
Josep M. Font & Ventura Verdú (1991). Algebraic Logic for Classical Conjunction and Disjunction. Studia Logica 50 (3-4):391 - 419.
Similar books and articles
Frank Wolter (1997). Superintuitionistic Companions of Classical Modal Logics. Studia Logica 58 (2):229-259.
Norihiro Kamide (2002). Kripke Semantics for Modal Substructural Logics. Journal of Logic, Language and Information 11 (4):453-470.
Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II. Studia Logica 66 (3):349-384.
Guram Bezhanishvili (2001). Glivenko Type Theorems for Intuitionistic Modal Logics. Studia Logica 67 (1):89-109.
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Milan Božić & Kosta Došen (1984). Models for Normal Intuitionistic Modal Logics. Studia Logica 43 (3):217 - 245.
Kosta Došen (1985). Models for Stronger Normal Intuitionistic Modal Logics. Studia Logica 44 (1):39 - 70.
Josep Maria Font & Miquel Rius (2000). An Abstract Algebraic Logic Approach to Tetravalent Modal Logics. Journal of Symbolic Logic 65 (2):481-518.
Ramon Jansana (1995). Abstract Modal Logics. Studia Logica 55 (2):273 - 299.
Added to index2009-01-28
Total downloads6 ( #230,031 of 1,410,023 )
Recent downloads (6 months)1 ( #177,059 of 1,410,023 )
How can I increase my downloads?