A temporal semantics for Nilpotent Minimum logic

In [Ban97] a connection among rough sets (in particular, pre-rough algebras) and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95, EG01]), in which the logic of every instant is given by {\L}3: a completeness theorem will be shown. This is the prosecution of the work initiated in [AGM08] and [ABM09], in which the authors construct a temporal semantics for the many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table

Understanding Predication in Conceptual Spaces

We argue that a cognitive semantics has to take into account the possibly partial information that a cognitive agent has of the world. After discussing Gärdenfors's view of objects in conceptual spaces, we offer a number of viable treatments of partiality of information and we formalize them by means of alternative predicative logics. Our analysis shows that understanding the nature of simple predicative sentences is crucial for a cognitive semantics

Stone-type representations and dualities for varieties of bisemilattices

In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes' representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas-Dunn duality and introduce the categories of 2spaces and 2spaces$^{\star}$. The categories of 2spaces and 2spaces$^{\star}$ will play with respect to the categories of distributive bisemilattices and De Morgan bisemilattices, respectively, a role analogous to the category of Stone spaces with respect to the category of Boolean algebras. Actually, the aim of this work is to show that these categories are, in fact, dually equivalent