Related papers: Relational Lattice Foundation for Algebraic Logic
We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…
This article provides an algebraic study of intermediate inquisitive and dependence logics. While these logics are usually investigated using team semantics, here we introduce an alternative algebraic semantics and we prove it is complete…
In this paper, we investigate the algebras of consequence operators and finite consequence operators on a fixed language. Significant new collections of consequence operators are defined and shown to be complete and distributive…
We show that the matrix query language $\mathsf{MATLANG}$ corresponds to a natural fragment of the positive relational algebra on $K$-relations. The fragment is defined by introducing a composition operator and restricting $K$-relation…
Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of…
Recall first the algebraic treatment of flows or tensions in a transportation network $N$, i.e. a connected antisymmetric 1-graph $G(X, U)$. Assume that, unusually, we take the values of flows (resp. tensions) in $\mathbb{C}$. So the…
The article associates two fundamental lattice constructions with each regular unital real ordered Banach space (function system). These are used to establish certain results in the theory of operator algebras, specifically relating the…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
We translate effectively our earlier quantum constructions to the classical language and using Yang-Baxterisation of the Faddeev-Reshetikhin-Takhtajan algebra are able to construct Lax operators and associated $r$-matrices of classical…
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of…
We compute the lattice operations for the (pairwise) stable set in many-to-many matching markets when only path-independence on agents' choice functions is imposed. To do this, we first show that the sets of firm-quasi-stable and…
While argument mining has achieved significant success in classifying argumentative relations between statements (support, attack, and neutral), we have a limited computational understanding of logical mechanisms that constitute those…
Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is…
Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental…
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2…
This paper introduces U-relations, a succinct and purely relational representation system for uncertain databases. U-relations support attribute-level uncertainty using vertical partitioning. If we consider positive relational algebra…
This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice,…
The general aim of this article is to study the negation fragment of classical logic within the framework of contemporary (Abstract) Algebraic Logic. More precisely, we shall find the three classes of algebras that are canonically…
A binary relation defined on a poset is a weakening relation if the partial order acts as a both-sided compositional identity. This is motivated by the weakening rule in sequent calculi and closely related to models of relevance logic. For…
We propose a functional description of rewriting systems on topological vector spaces. We introduce the topological confluence property as an approximation of the confluence property. Using a representation of linear topological rewriting…