Syntactic features and synonymy relations: A unified treatment of some proofs of the compactness and interpolation theorems
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Studia Logica 53 (2):325 - 342 (1994)
This paper introduces the notion of syntactic feature to provide a unified treatment of earlier model theoretic proofs of both the compactness and interpolation theorems for a variety of two valued logics including sentential logic, first order logic, and a family of modal sentential logic includingM,B,S 4 andS 5. The compactness papers focused on providing a proof of the consequence formulation which exhibited the appropriate finite subset. A unified presentation of these proofs is given by isolating their essential feature and presenting it as an abstract principle about syntactic features. The interpolation papers focused on exhibiting the interpolant. A unified presentation of these proofs is given by isolating their essential feature and presenting it as a second abstract principle about syntactic features. This second principle reduces the problem of exhibiting the interpolant to that of establishing the existence of a family of syntactic features satisfying certain conditions. The existence of such features is established for a variety of logics (including those mentioned above) by purely combinatorial arguments.
|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
George Weaver (1982). A Note on the Interpolation Theorem in First Order Logic. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (14-18):215-218.
George Weaver (1978). Compactness Theorems for Finitely-Many-Valued Sentenial Logics. Studia Logica 37 (4):413 - 416.
Citations of this work BETA
No citations found.
Similar books and articles
John W. Dawson Jr (2006). Why Do Mathematicians Re-Prove Theorems? Philosophia Mathematica 14 (3):269-286.
Jan Krajíček (1997). Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic. Journal of Symbolic Logic 62 (2):457-486.
Alexander Paseau (2011). Proofs of the Compactness Theorem. History and Philosophy of Logic 31 (1):73-98.
Patrick Blackburn & Maarten Marx (2003). Constructive Interpolation in Hybrid Logic. Journal of Symbolic Logic 68 (2):463-480.
Branden Fitelson & Larry Wos (2001). Finding Missing Proofs with Automated Reasoning. Studia Logica 68 (3):329-356.
Jan Krajíček (1995). Bounded Arithmetic, Propositional Logic, and Complexity Theory. Cambridge University Press.
Sara Negri (2005). Proof Analysis in Modal Logic. Journal of Philosophical Logic 34 (5/6):507 - 544.
George Tourlakis (2010). On the Proof-Theory of Two Formalisations of Modal First-Order Logic. Studia Logica 96 (3):349-373.
Walter A. Carnielli (1987). Systematization of Finite Many-Valued Logics Through the Method of Tableaux. Journal of Symbolic Logic 52 (2):473-493.
Grzegorz Malinowski & Marek Michalczyk (1982). That SCI has the Interpolation Property. Studia Logica 41 (4):375 - 380.
Added to index2009-01-28
Total downloads9 ( #173,163 of 1,413,268 )
Recent downloads (6 months)1 ( #154,925 of 1,413,268 )
How can I increase my downloads?