We show that given a finite, transitive and reflexive Kripke model 〈W,4, J·K〉 and w ∈ W , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bisimulation is definable in the s...

Products were introduced in the 1970s as a natural type of combined modal logics. They arise in different areas of pure and applied logics — spatial reasoning, multi-agent systems, quantified modal and intuitionistic logics etc. The theory of products was systematized and essentially developed first in the paper [GS98] and then in the book [GKWZ03], but during the past 10 years new important re...

fictional names have been one of the most important and serious topics in the contemporary philosophy of language and metaphysics.several questions such as “do fictional names refer to any objects?” “are fictional characters existent objects?” have resulted in a considerable literature of philosophy. in this essay, we will follow two objectives. first we will describe and elaborate the ideas ...

We present Kripke semantics for some substructural logics with weakening, known as logics with BCK implication. This work is a continuation of the work of Allwein and Dunn on Kripke semantics for Linear Logic, which in turn rested on Dunn’s Gaggle Theory and on Urquhart’s Representation Theory for nondistributive lattices. The basic idea in the representation theory is to use maximally disjoint...

For any ordinal Λ, we can define a polymodal logic GLPΛ, with a modality [ξ] for each ξ < Λ. These represent provability predicates of increasing strength. Although GLPΛ has no non-trivial Kripke frames, Ignatiev showed that indeed one can construct a universal Kripke frame for the variable-free fragment with natural number modalities, denoted GLPω. In this paper we show how to extend these con...

In this paper we present duplication-free tableau calculi for three propositional intermediate interpolable logics, namely the logic characterized by rooted Kripke models with depth two at most, the logic characterized by rooted Kripke models with two final elements at most and depth two at most and the logic characterized by rooted Kripke models with a final element at most (also known as Jank...

Kripke semantics plays a fundamental role for modal logics where it often provides modular semantics allowing a clear treatment of various logics related by the addition of axioms or connectives. Kripke semantics is also the “natural semantics” for classical modal logic in the sense that it is given by the representation theory for modal algebras. The algebraic structure corresponding to a trad...

We compare Kripke models and a simpliied notion of Interpreted Systems as semantic structures for reasoning about knowledge. It is intuitively clear that interpreted systems represent a special class of Kripke models; the goal of this paper is to make this intuition formal, and to clarify the relationship between the two semantic structures. Our method is to deene a map from the class of system...