We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces. §

The present paper adopts as its point of departure the claim by Te Winkel (1866) and Verkuyl (2008) that mental temporal representations are built on the basis of three binary oppositions: Present/Past, Synchronous/Posterior and Imperfect/Perfect. Te Winkel took the second opposition in terms of the absence or presence of a temporal auxiliary zullen ‘will’. However, in a binary system Future lo...

An ontologically transparent semantics for justifications that interprets justifications as sets of formulas they justify has been recently presented by Artemov. However, this semantics of modular models has only been studied for the case of the basic justification logic J, corresponding to the modal logic K. It has been left open how to extend and relate modular models to the already existing ...

Evaluating complex propositions requires evaluating truthvalues and assigning modal operators. Previous research suggested that evaluating truth-values may be the key to assigning modal operators. This study placed 111 third and fifth grade children in one of three training conditions: no training, training truth-value assignment, and training truthvalue and modal operator assignment. The resul...

A distributed system, possibly asynchronous, is said to have perfect recall if at all times each processor's state includes a record of all its previous states. The completeness of a propositional modal logic of knowledge and time with respect to such systems is established. The logic includes modal operators for knowledge, and the temporal operators \next" and \until."

In this paper I argue against the commonly received view that Kripke’s formal Possible World Semantics (PWS) reflects the adoption of a metaphysical interpretation of the modal operators. I consider in detail Kripke’s three main innovations vis-à-vis Carnap’s PWS: a new view of the worlds, variable domains of quantification, and the adoption of a universal notion of validity. I argue that all t...

(where an a f f i r m a t i v e sentential operator is informally characterized as one for which a p r i n c i p l e of d i s t r i b u t i o n over conjunction is not o b v i o u s l y implausible). Examples of such operators include the familiar modal operators ~ and 0, and also various epistemic and doxastic operators. I want to consider certain principles that may be held to govern certain ...

We provide a detailed analysis of very weak fragments of modal logic. Our fragments lack connectives that introduce nondeterminism and they feature restrictions on the modal operators, which may lead to substantial reductions in complexity. Our main result is a general game-based characterization of the expressive power of our fragments over the class of finite structures.

Nonmonotonic logic is a well developed research area gathering the logical formalisms that handle commonsense reasoning. One of the central issue in the area is to establish a notion of nonmonotonic provability, which is usually characterized via some modal logic. In MST93] a clear paradigm has been proposed that classiies modal monotonic logics , augmented with the \negation by fail-ure" to pr...

In this note we investigate modal logics of submaximal and nodec spaces when the modal diamond is interpreted as the closure operator of a topological space. We axiomatize the modal logic of nodec spaces. We show that the modal logic of submaximal spaces is a proper extension of the modal logic of nodec spaces, axiomatize it, and prove that it coincides with the modal logics of door spaces and ...