Related papers: Kripke Contexts, Double Boolean Algebras with Oper…
The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal…
It is well-known fact that there exists 1-1 correspondence between so-called double (or flou) sets and intuitionistic sets (also known as orthopairs). At first glance, these two concepts seem to be irreconcilable. However, one must remember…
The notion of prop models the operations with multiple inputs and multiple outpus, acting on some algebraic structures like the bialgebras or the Lie bialgebras. In this paper, we generalize the Koszul duality theory of associative algebras…
Polymodal provability logic GLP is incomplete w.r.t. Kripke frames. It is known to be complete w.r.t. topological semantics, where the diamond modalities correspond to topological derivative operations. However, the topologies needed for…
We give Hennessy-Milner classes for intuitionistic, dual-intuitionistic and bi-intuitionistic logic interpreted in intuitionistic Kripke models, and generalise these results to modal (dual- and bi-)intuitionistic logics. Our main technical…
As the foundation of current natural language processing methods, pre-trained language model has achieved excellent performance. However, the black-box structure of the deep neural network in pre-trained language models seriously limits the…
We consider the operation of sum on Kripke frames, where a family of frames-summands is indexed by elements of another frame. In many cases, the modal logic of sums inherits the finite model property and decidability from the modal logic of…
In "Centre of Core Regular Double Stone Algebra" (CRDSA), many useful results are shown that begin to indicate the nearly Boolean nature of CRDSA which we focus on here. We define the node set lattice through the well known binary…
The fundamental algebraic concepts of quantum mechanics, as expressed by many authors, are reviewed and translated into the framework of the relatively new non-distributive system of Boolean fractions (also called conditional events or…
We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of…
Systems for language understanding have become remarkably strong at overcoming linguistic imperfections in tasks involving phrase matching or simple reasoning. Yet, their accuracy drops dramatically as the number of reasoning steps…
Up-directed rough sets are introduced and studied by the present author in earlier papers. This is extended by her in two different granular directions in this research, with a surprising algebraic semantics. The granules are based on ideas…
Knowledge and Action Bases (KABs) have been recently proposed as a formal framework to capture the dynamics of systems which manipulate Description Logic (DL) Knowledge Bases (KBs) through action execution. In this work, we enrich the KAB…
Standard abstract model checking relies on abstract Kripke structures which approximate concrete models by gluing together indistinguishable states, namely by a partition of the concrete state space. Strong preservation for a specification…
The concepts of rough and definite objects are relatively more determinate than those of granules and granulation in general rough set theory (RST) [1]. Representation of rough objects can however depend on the dialectical relation between…
We revisit Dieter Spreen's notion of a representation associated to a numbered basis equipped with a strong inclusion relation. We show that by relaxing his requirements, we obtain different classically considered representations as…
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
We define the notion of a model of higher-order modal logic in an arbitrary elementary topos $\mathcal{E}$. In contrast to the well-known interpretation of (non-modal) higher-order logic, the type of propositions is not interpreted by the…