We consider the family of logics from NExt which are determined by linear frames with reflexive and symmetric relation of accessibility. The condition of linearity in such frames was first defined in the paper [9]. We prove that the cardinality of the logics under consideration is uncountably infinite.

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

We define a special family of Brouwerian logics determined by linearly ordered frames. Then we prove that all logics of this family have the finite model property and are Kripke complete.

It is well known that the non-orthogonality relation between the (pure) states of a quantum system is reflexive and symmetric, and the modal logic $$\mathbf {KTB}$$ is sound and complete with respect to the class of sets each equipped with a reflexive and symmetric binary relation. In this paper, we consider two properties of the non-orthogonality relation: Separation and Superposition. We find sound and complete modal axiomatizations for the classes of sets each equipped with a reflexive and symmetric relation that (...) satisfies each one of these two properties and both, respectively. We also show that the modal logics involved are decidable. (shrink)

In this paper we construct a continuum of logics, extensions of the modal logic T2 = KTB ⊕ □2p → □3p, which are non-compact and hence Kripke incomplete.