David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Bulletin of Symbolic Logic 9 (3):387-405 (2003)
We provide a canonical construction of conformal covers for finite hypergraphs and present two immediate applications to the finite model theory of relational structures. In the setting of relational structures, conformal covers serve to construct guarded bisimilar companion structures that avoid all incidental Gaifman cliques-thus serving as a partial analogue in finite model theory for the usually infinite guarded unravellings. In hypergraph theoretic terms, we show that every finite hypergraph admits a bisimilar cover by a finite conformal hypergraph. In terms of relational structures, we show that every finite relational structure admits a guarded bisimilar cover by a finite structure whose Gaifman cliques are guarded. One of our applications answers an open question about a clique constrained strengthening of the extension property for partial automorphisms (EPPA) of Hrushovski, Herwig and Lascar. A second application provides an alternative proof of the finite model property (FMP) for the clique guarded fragment of first-order logic CGF, by reducing (finite) satisfiability in CGF to (finite) satisfiability in the guarded fragment, GF
|Keywords||finite model theory extension property for partial isomorphisms guarded logics finite model property|
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Citations of this work BETA
Ian Hodkinson (2006). Complexity of Monodic Guarded Fragments Over Linear and Real Time. Annals of Pure and Applied Logic 138 (1):94-125.
Martin Otto (2004). Modal and Guarded Characterisation Theorems Over Finite Transition Systems. Annals of Pure and Applied Logic 130 (1-3):173-205.
Martin Otto (2013). Expressive Completeness Through Logically Tractable Models. Annals of Pure and Applied Logic 164 (12):1418-1453.
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