|Abstract||The paper focuses on extending to the ﬁrst order case the semantical program for modalities ﬁrst introduced by Dana Scott and Richard Montague. We focus on the study of neighborhood frames with constant domains and we oﬀer a series of new completeness results for salient classical systems of ﬁrst order modal logic. Among other results we show that it is possible to prove strong completeness results for normal systems without the Barcan Formula (like FOL + K) in terms of neighborhood frames with constant domains. The ﬁrst order models we present permit the study of many epistemic modalities recently proposed in computer science as well as the development of adequate models for monadic operators of high probability. Models of this type are either diﬃcult of impossible to build in terms of relational Kripkean semantics. We conclude by introducing general ﬁrst order neighborhood frames and we oﬀer a general completeness result in terms of them which circumvents some well-known problems of propositional and ﬁrst order neighborhood semantics (mainly the fact that many classical modal logics are incomplete with respect to an unmodiﬁed version of neighborhood frames). We argue that the semantical program that thus arises surpasses both in expressivity and adequacy the standard Kripkean approach, even when it comes to the study of ﬁrst order normal systems.|
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|Through your library||Only published papers are available at libraries|
Similar books and articles
Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
Horacio Arlo-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
Arnold Nat (1979). First-Order Indefinite and Uniform Neighbourhood Semantics. Studia Logica 38 (3):277 - 296.
Horacio Arló Costa (2002). First Order Extensions of Classical Systems of Modal Logic; the Role of the Barcan Schemas. Studia Logica 71 (1):87-118.
Melvin Fitting (2012). Barcan Both Ways. Journal of Applied Non-Classical Logics 9 (2-3):329-344.
Melvin Fitting (2002). Interpolation for First Order S5. Journal of Symbolic Logic 67 (2):621-634.
Horacio Arló Costa (2005). Non-Adjunctive Inference and Classical Modalities. Journal of Philosophical Logic 34 (5/6):581 - 605.
Chris Fox, Shalom Lappin & Carl Pollard, First-Order, Curry-Typed Logic for Natural Language Semantics.
Gregory Wheeler, AGM Belief Revision in Monotone Modal Logics. LPAR 2010 Short Paper Proceedings.
Added to index2010-12-22
Total downloads4 ( #188,769 of 722,703 )
Recent downloads (6 months)0
How can I increase my downloads?