Notre Dame Journal of Formal Logic 35 (1):116-129 (1994)
|Abstract||Once the Kripke semantics for normal modal logics were introduced, a whole family of modal logics other than the Lewis systems S1 to S5 were discovered. These logics were obtained by changing the semantics in natural ways. The same can be said of the Kripke-style semantics for relevant logics: a whole range of logics other than the standard systems R, E and T were unearthed once a semantics was given (cf. Priest and Sylvan , Restall , and Routley et al. ). In a similar way, weakening the structural rules of the Gentzen formulation of classical logic gives rise to other ‘substructural’ logics such as linear logic (as in Girard ). This process of ‘strategic weakening’ is becoming popular today, with the discovery of applications of these logics to areas such as linguistics and the theory of computation (cf. van Benthem ). Until now no-one has (to my knowledge) examined what the process of weakening does to the Kripke-style semantics of intuitionistic logic. This paper remedies the deficiency, introducing the family of subintuitionistic logics. These systems have some appealing features. Unlike other substructural logics such as linear logic (which lack distribution of extensional disjunction over conjunction) they have a very natural Kripke-style worlds semantics. Also, the difficulties with regard to modelling quantification in these systems may be able to shed some light on the difficulties in naturally modelling quantification in relevant logics, as it must be admitted that the semantics currently available for quantified relevant logics are rather baroque (cf. Fine ). But most importantly, delving in the undergrowth of logics such as intuitionistic logic gives us a ‘feel’ for how such systems are put together, and what job is being done by each aspect of the modelling conditions in..|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
Nobu-Yuki Suzuki (1993). Some Results on the Kripke Sheaf Semantics for Super-Intuitionistic Predicate Logics. Studia Logica 52 (1):73 - 94.
Juliana Bueno-Soler (2010). Two Semantical Approaches to Paraconsistent Modalities. Logica Universalis 4 (1).
Luca Viganò (2000). Labelled Non-Classical Logics. Kluwer Academic Publishers.
Ewa Orlowska (1992). Relational Proof System for Relevant Logics. Journal of Symbolic Logic 57 (4):1425-1440.
Nobu -Yuki Suzuki (1990). Kripke Bundles for Intermediate Predicate Logics and Kripke Frames for Intuitionistic Modal Logics. Studia Logica 49 (3):289 - 306.
Greg Restall (1998). Displaying and Deciding Substructural Logics 1: Logics with Contraposition. Journal of Philosophical Logic 27 (2):179-216.
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Norihiro Kamide (2002). Kripke Semantics for Modal Substructural Logics. Journal of Logic, Language and Information 11 (4):453-470.
Added to index2009-01-28
Total downloads8 ( #123,036 of 549,068 )
Recent downloads (6 months)1 ( #63,185 of 549,068 )
How can I increase my downloads?