A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using these bisimulations the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property, and proving invariance and definability results.

[1]  C. Cerrato General canonical models for graded normal logics (graded modalities IV) , 1990, Stud Logica.

[2]  Maarten de Rijke,et al.  Counting Objects , 1995, J. Log. Comput..

[3]  L F Goble,et al.  Grades of modality , 1970 .

[4]  Maarten de Rijke Modal model theory , 1995 .

[5]  M. de Rijke,et al.  Bisimulations for Temporal Logic , 1997, J. Log. Lang. Inf..

[6]  Maurizio Fattorosi-Barnaba,et al.  Graded modalities. III (the completeness and compactness of S40) , 1988, Stud Logica.

[7]  Holger Schlingloff Expressive completeness of temporal logic of trees , 1992, J. Appl. Non Class. Logics.

[8]  Maurizio Fattorosi-Barnaba,et al.  Graded modalities. I , 1985, Stud Logica.

[9]  Maarten de Rijke,et al.  Simulating Without Negation , 1997, J. Log. Comput..

[10]  Kit Fine,et al.  In so many possible worlds , 1972, Notre Dame J. Formal Log..

[11]  Akira Nakamura On a Logic Based on Graded Modalities , 1993 .

[12]  Johan van Benthem,et al.  Exploring logical dynamics , 1996, Studies in logic, language and information.

[13]  Francesco Caro Graded modalities, II (canonical models) , 1988, Stud Logica.

[14]  Maarten de Rijke,et al.  Generalized quantifiers and modal logic , 1993, J. Log. Lang. Inf..

[15]  maarten marx Algebraic Relativization and Arrow Logic , 1995 .

[16]  Claudio Cerrato Decidability by filtrations for graded normal logics (graded modalities V) , 1994, Stud Logica.

[17]  Wiebe van der Hoek On the Semantics of Graded Modalities , 1992, J. Appl. Non Class. Logics.

[18]  Chen C. Chang,et al.  Model Theory: Third Edition (Dover Books On Mathematics) By C.C. Chang;H. Jerome Keisler;Mathematics , 1966 .

[19]  Francesco M. Donini,et al.  Reasoning in description logics , 1997 .