Doubt Fuzzy BOI-ideal of BOI-algebra

The aim of this paper is to introduce the notion of doubt fuzzy BOI-ideal of BOI-algebra and to study their properties. The homomorphic image and the inverse image of a doubt fuzzy BOI-ideal isstudied well. The Cartesian product of doubt fuzzy BOI-ideal is introduced and discussed

An Abstract Approach to Consequence Relations

We generalise the Blok-J\'onsson account of structural consequence relations, later developed by Galatos, Tsinakis and other authors, in such a way as to naturally accommodate multiset consequence. While Blok and J\'onsson admit, in place of sheer formulas, a wider range of syntactic units to be manipulated in deductions (including sequents or equations), these objects are invariably aggregated via set-theoretical union. Our approach is more general in that non-idempotent forms of premiss and conclusion aggregation, including multiset sum and fuzzy set union, are considered. In their abstract form, thus, deductive relations are defined as additional compatible preorderings over certain partially ordered monoids. We investigate these relations using categorical methods, and provide analogues of the main results obtained in the general theory of consequence relations. Then we focus on the driving example of multiset deductive relations, providing variations of the methods of matrix semantics and Hilbert systems in Abstract Algebraic Logic

Convolution, Separation and Concurrency

A notion of convolution is presented in the context of formal power series together with lifting constructions characterising algebras of such series, which usually are quantales. A number of examples underpin the universality of these constructions, the most prominent ones being separation logics, where convolution is separating conjunction in an assertion quantale; interval logics, where convolution is the chop operation; and stream interval functions, where convolution is used for analysing the trajectories of dynamical or real-time systems. A Hoare logic is constructed in a generic fashion on the power series quantale, which applies to each of these examples. In many cases, commutative notions of convolution have natural interpretations as concurrency operations.Comment: 39 page

On algebraic supergroups, coadjoint orbits and their deformations

In this paper we study algebraic supergroups and their coadjoint orbits as affine algebraic supervarieties. We find an algebraic deformation quantization of them that can be related to the fuzzy spaces of non commutative geometry.Comment: 37 pages, AMS-LaTe

Cubic BOI-ideal of BOI-algebra

In this paper, the notion of cubic BOI-ideal of BOI-algebra is introduced. Some characterization of cubic BOI-ideal of BOI-algebra is given. Several theorems are presented in this regard. Thehomomorphic image and inverse image of cubic BOI-ideal are studied