David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 61 (4):1057-1120 (1996)
This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L D I etc. Once the logics are `weaved', further `interaction' axioms can be geometrically motivated and added, and then systematically studied. The methodology is general and is applied to modal and intuitionistic logics as well as to general algebraic logics. We obtain general results on bulk, in the sense that we develop standard combining techniques and refinements which can be applied to any family of initial logics to obtain further combined logics. The main results of this paper is a construction for combining arbitrary, (possibly not normal) modal or intermediate logics, each complete for a class of (not necessarily frame) Kripke models. We show transfer of recursive axiomatisability, decidability and finite model property. Some results on combining logics (normal modal extensions of K) have recently been introduced by Kracht and Wolter, Goranko and Passy and by Fine and Schurz as well as a multitude of special combined systems existing in the literature of the past 20-30 years. We hope our methodology will help organise the field systematically
|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
J. Rasga, A. Sernadas & C. Sernadas (2013). Importing Logics: Soundness and Completeness Preservation. [REVIEW] Studia Logica 101 (1):117-155.
Similar books and articles
Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part I. Studia Logica 65 (3):323-353.
Nobu -Yuki Suzuki (1990). Kripke Bundles for Intermediate Predicate Logics and Kripke Frames for Intuitionistic Modal Logics. Studia Logica 49 (3):289 - 306.
Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II. Studia Logica 66 (3):349-384.
Nobu-Yuki Suzuki (1989). An Algebraic Approach to Intuitionistic Modal Logics in Connection with Intermediate Predicate Logics. Studia Logica 48 (2):141 - 155.
Kosta Došen (1985). Models for Stronger Normal Intuitionistic Modal Logics. Studia Logica 44 (1):39 - 70.
Norihiro Kamide (2002). Kripke Semantics for Modal Substructural Logics. Journal of Logic, Language and Information 11 (4):453-470.
Greg Restall (1994). Subintuitionistic Logics. Notre Dame Journal of Formal Logic 35 (1):116-129.
Marcus Kracht & Frank Wolter (1997). Simulation and Transfer Results in Modal Logic – a Survey. Studia Logica 59 (2):149-177.
Added to index2009-01-28
Total downloads9 ( #163,661 of 1,100,144 )
Recent downloads (6 months)4 ( #90,386 of 1,100,144 )
How can I increase my downloads?