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Referential semantics: duality and applications

100%

Jansana R. , Palmigiano A.

Reports on Mathematical Logic

2006

tom Nr 41,spec. iss.

63-93

In this paper, Wojcicki's characterization of selfex- tensional logics as those logics that are endowed with a complete local referential semantics is extended to a fully edged duality between atlas-models (i.e. generalized matrix models) and refer- ential models of an arbitrary selfextensional logic S. This duality serves as a general template where a wide range of Stone- and Priestley-style dualities related with concrete logics can t. The rst application of this duality is a characterization of the fully selfextensional logics among the selfextensional ones. Fully selfex- tensional logics form a subclass of particularly well-behaved selfex- tensional logics, and only recently [1] this inclusion was shown to be proper. In this paper, fully selfextensional logics are character- ized as those selfextensional logics S whose algebraic counterpart Alg(S) { seen as a category { is dually equivalent to the reduced referential models of S. This implies that if S is fully selfexten- sional, then every algebra in Alg(S) is isomorphic to an algebra of sets.

A Note on the Model Theory for PositiveModal Logic

100%

Celani S. , Jansana R.

tom 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.

Note of the full generalized models of the extensions of a logic

80%

Albuquerque H. , Font J. M. , Jansana R.

Reports on Mathematical Logic

2017

tom Vol. 52

57--68

In this short note we show that the full generalized models of any extension of a logic can be determined from the full generalized models of the base logic in a simple way. The result is a consequence of two central theorems of the theory of full generalized models of sentential logics. As applications we investigate when the full generalized models of an extension can also be full generalized models of the base logic, and we prove that each Suszko lter of a logic determines a Suszko lter of each of its extensions, also in a simple way.