Abstract

We explore the nite model theory of the characterisation theorems for modal and guarded fragments of rst-order logic over transition systems and relational structures of width two. Apart from simplifying Rosen's proof of the nite model theory version of van Benthem's classical modal characterisation theorem, we employ new techniques to capture analogous characterisations of modal logic with universal and inverse modalities. The analysis rests on Gaifman's locality theorem for rst-order logic together with a natural combinatorial construction of nite, locally acyclic covers for nite transition systems. These techniques carry over to the analysis guarded bisimulation invariance: over nite relational structures of width two, the guarded fragment precisely captures those properties that are rst-order denable and invariant under guarded bisimulation. It remains open whether a full analogue of the guarded characterisation theorem of Andreka, van Benthem and Nemeti, for relational structures of width greater than two, is also valid in the sense of nite model theory. keywords: nite model theory, modal logic, guarded fragment, bisimulation, preservation and characterisation theorems 1

Citations

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