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On homomorphic images and the free distributive lattice extension of a distributive nearlattice

Celani S., Calomino I.

Reports on Mathematical Logic

2016

Vol. 51

57--73

In this paper we will introduce N-Vietoris families and prove that homomorphic images of distributive nearlattices are dually characterized by N-Vietoris families. We also show a topological approach of the existence of the free distributive lattice extension of a distributive nearlattice.

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.

Modal Tarski algebras

Celani S.

Reports on Mathematical Logic

2005

Nr 39

113-126

In this paper we shall study the representation theory for Tarski algebras with a modal operator. In particular, we shall give a representation for finite Tarski algebras and finite Tarski algebras with a modal operator by means of the so-called Tarski sets and Tarski relational sets, respectively. We will also consider some varieties of Tarski modal algebras.

A note on classical modal relevant algebras

Celani S.

Reports on Mathematical Logic

1998

No. 32

35-52

In this paper we define three classes of classical modal relevant algebras (CR-algebras), and study they representation theory. We also investigate sufficient conditions that make the class be the same. We finish the work characterizing the simple and subdirectly irreducible algebras for a particular variety of CR-algebras.