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
Ezio Di Nucci
Jack Alan Reynolds
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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.
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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.
George Weaver & Jeffrey Welaish (1986). Back and Forth Constructions in Modal Logic: An Interpolation Theorem for a Family of Modal Logics. Journal of Symbolic Logic 51 (4):969-980.
C. C. Chang & H. J. Keisler (1976). Model Theory. Journal of Symbolic Logic 41 (3):697-699.
G. Weaver (1978). Compactness theorems for finitely-many-valued logics. Studia Logica 37:413.
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