David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 38 (3):277 - 296 (1979)
The main purpose of this paper is to define and study a particular variety of Montague-Scott neighborhood semantics for modal propositional logic. We call this variety the first-order neighborhood semantics because it consists of the neighborhood frames whose neighborhood operations are, in a certain sense, first-order definable. The paper consists of two parts. In Part I we begin by presenting a family of modal systems. We recall the Montague-Scott semantics and apply it to some of our systems that have hitherto be uncharacterized. Then, we define the notion of a first-order indefinite semantics, along with the more specific notion of a first-order uniform semantics, the latter containing as special cases the possible world semantics of Kripke. In Part II we prove consistency and completeness for a broad range of the systems considered, with respect to the first-order indefinite semantics, and for a selected list of systems, with respect to the first-order uniform semantics. The completeness proofs are algebraic in character and make essential use of the finite model property. A by-product of our investigations is a result relating provability in S-systems and provability in T-systems, which generalizes a known theorem relating provability in the systems S 2° and C 2.
|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
Alonzo Church (1956). Introduction to Mathematical Logic. Princeton, Princeton University Press.
M. J. Cresswell (1970). Classical intensional logics. Theoria 36 (3):347-372.
Robert Feys (1965). Modal Logics. Louvain, E. Nauwelaerts.
G. E. Hughes (1968/1972). An Introduction to Modal Logic. London,Methuen.
Saul A. Kripke (1965). Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi. In J. W. Addison, A. Tarski & L. Henkin (eds.), Journal of Symbolic Logic. North Holland. 135-135.
Citations of this work BETA
No citations found.
Similar books and articles
Steve Awodey & Erich H. Reck (2002). Completeness and Categoricity, Part II: Twentieth-Century Metalogic to Twenty-First-Century Semantics. History and Philosophy of Logic 23 (2):77-94.
Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171 - 210.
W. J. Blok & J. Rebagliato (2003). Algebraic Semantics for Deductive Systems. Studia Logica 74 (1-2):153 - 180.
Gregory Wheeler, AGM Belief Revision in Monotone Modal Logics. LPAR 2010 Short Paper Proceedings.
Horacio Arló-Costa & Eric Pacuit (2006). First-Order Classical Modal Logic. Studia Logica 84 (2):171-210.
Anna Bucalo (1994). Modalities in Linear Logic Weaker Than the Exponential “of Course”: Algebraic and Relational Semantics. [REVIEW] Journal of Logic, Language and Information 3 (3):211-232.
Steve Awodey & Erich H. Reck, Completeness and Categoricty, Part II: 20th Century Metalogic to 21st Century Semantics.
Enrico Martino (1998). Negationless Intuitionism. Journal of Philosophical Logic 27 (2):165-177.
Added to index2009-01-28
Total downloads4 ( #302,338 of 1,692,984 )
Recent downloads (6 months)1 ( #193,926 of 1,692,984 )
How can I increase my downloads?