Abstract In the vein of recent work that provides non-normal modal interpretations of various topological operators, this paper proposes a modal logic for a spatial isolation operator. Focusing initially on neighbourhood systems, we prove several characterization results, demonstrating the adequacy of the interpretation and highlighting certain semantic insensitivities that result from the relative expressive weakness of the isolation operator. We then transition to the topological setting, proving a topological characterization result.

In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for = and ∈. Although, these variations coincide with the standard interpretation in Boolean-valued constructions, nonetheless they extend the scope of validity of ZF to new algebra-valued models. This paper presents, for the first time, non-trivial paraconsistent models of full ZF. Moreover, due to the validity of Leibniz's law in these structures, we will show how to construct proper models of set theory by quotienting these algebra-valued models with respect to equality, modulo the filter of the designated truth-values.

Abstract We show how to force, with finite conditions, the forcing axiom PFA(T), a relativization of PFA to proper forcing notions preserving a given Suslin tree T. The proof uses a Neeman style iteration with generalized side conditions consisting of models of two types, and a preservation theorem for such iterations. The consistency of this axiom was previously known using a standard countable support iteration and a preservation theorem due to Miyamoto.

The aim of this article is to improve our understanding of user-centered design (UCD) adoption and provide accordingly useful advice to the UCD community. UCD adoption was investigated through a Web survey. The results show that the early involvement of UCD practitioners in the product life cycle is more frequent compared to 10 years ago. It is also true that the methods and the techniques employed have shifted their focus from summative evaluation to rapid development cycles and from quantitative to qualitative evaluation methods. Based on the survey, there are several organizational factors UCD practitioners and their management should consider. UCD should be part of the business strategy and supported by higher management. Usability goals must be set through competitive analysis and practitioners should be rewarded if goals are reached or exceeded. For bespoke systems, usability goals should be explicitly discussed with the customer. Special attention should be paid to communication inside and outside the company so as to clarify the outcomes and benefits of the UCD approach.