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1 2012

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A Note on the Model Theory for PositiveModal Logic

Celani S., Jansana R.

Fundamenta Informaticae

2012

Vol. 114, nr 1

31-54

The minimum system of Positive Modal Logic SK+ is the (...)-fragment of the minimum normal modal logic K with local consequence. In this paper we develop some of the model theory for SK+ along the yet standard lines of themodel theory for classical normalmodal logic. We define the notion of positive bisimulation between two models, and we study the notions of m-saturated models and replete models. We investigate the positive maximal Hennessy-Milner classes. Finally, we present a Keisler-Shelah type theorem for positive bisimulations, a characterization of the first-order formulas invariant for positive bisimulations, and two definability theorems by positive modal sequents for classes of pointed models.