Related papers: Connexive implications in Substructural Logics

The paper is essentially a continuation of B.Plotkin, G.Zhitomirski, "Some logical invariants of algebras and logical relations between algebras", St.Peterburg Math. J., {19:5}, (2008) 859 -- 879, whose main notion is that of…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

We describe a general construction of finiteness spaces which subsumes the interpretations of all positive connectors of linear logic. We then show how to apply this construction to prove the existence of least fixpoints for particular…

It is well-known that relatively pseudocomplemented lattices can serve as an algebraic semantics of intuitionistic logic. To extend the concept of relative pseudocomplementation to non-distributive lattices, the first author introduced…

In the latest developments in the theory of skew lattices, distributivity has been one of the main topics of study. The largest classes of examples of such algebras are distributive. Unlike what happens in lattices, the properties of…

This work was intended to be an attempt to introduce the meta-language for working with multiple-conclusion inference rules that admit asserted propositions along with the rejected propositions. The presence of rejected propositions, and…

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…

A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…

It is a well-known fact that although the poset of open sets of a topological space is a Heyting algebra, its Heyting implication is not necessarily stable under the inverse image of continuous functions and hence is not a geometric…

In this paper we study projective algebras in varieties of (bounded) commutative integral residuated lattices from an algebraic (as opposed to categorical) point of view. In particular we use a well-established construction in residuated…

We study finite dimensional almost and quasi-effective prolongations of nilpotent Z-graded Lie algebras, especially focusing on those having a decomposable reductive structural subalgebra. Our assumptions generalize effectiveness and…

We show analogues of the classical Krein-Milman theorem for several ordered algebraic structures, especially in a semilattice (non-linear) framework. In that case, subsemilattices are seen as convex subsets, and for our proofs we use…

In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…

We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, that is, the equational theory of commutative residuated Kleene lattices (action lattices), and infinitary commutative action logic,…

We define and axiomatize three new logics based on the connexive logic $\mathsf{C}$, the modal logic $\mathsf{CnK}$ and the conditional logics $\mathsf{CnCK}$ and $\mathsf{CnCK}_R$. These logics display strong connexivity properties and are…

In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…

We extend classical work by Janusz Czelakowski on the closure properties of the class of matrix models of entailment relations - nowadays more commonly called multiple-conclusion logics - to the setting of non-deterministic matrices…

We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…

We examine the interplay between projectivity (in the sense that was introduced by S.~Ghilardi) and uniform post-interpolant for the classical and intuitionistic propositional logic. More precisely, we explore whether a projective…

The class of all $\ast$-continuous Kleene algebras, whose description includes an infinitary condition on the iteration operator, plays an important role in computer science. The complexity of reasoning in such algebras - ranging from the…