Affiliations: CONICET and Departamento de Matemáticas, Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000- Tandil, Argentina. scelani@exa.unicen.edu.ar | Departament de Lógica História i Filosofia de la Ciéncia, Facultat de Filosofia, Universitat de Barcelona (UB), Montalegre 6, 08001 Barcelona, Spain. jansana@ub.edu
Note: [] Address for correspondence: Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto 399, 7000- Tandil, Argentina The research conducting to the paper has been possible thanks to the Marie Curie Actions-International Research Staff Exchange Scheme (IRSES) MaToMUVI-FP7-PEOPLE-2009-IRSES from the European Union. The research of the first author has also been partially supported by CONICET (Argentina) grant PIP 112-200801-02543.
Note: [] The research of the first author has also been partially supported by CONICET (Argentina) grant PIP 112-200801-02543. The research of the second author has been also partially supported by grants 2009SGR-1433 of the AGAUR of the Generalitat de Catalunya and by grant MTM2008-01139 of the Spanish Ministerio de Ciencia e Innovacion, which includes eu feder funds.
Abstract: The minimum system of Positive Modal Logic SK+ is the (∧, ∨, □, ◊, ⊥, $\top$)-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 the model theory for classical normal modal 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.
