Related papers: Boolean Algebras and Logic
We present a logic for reasoning about graded inequalities which generalizes the ordinary inequational logic used in universal algebra. The logic deals with atomic predicate formulas of the form of inequalities between terms and formalizes…
The paper presents algebraic and logical developments. From the algebraic viewpoint, we introduce Monadic Equational Systems as an abstract enriched notion of equational presentation. From the logical viewpoint, we provide Equational…
Leibniz algebras are certain generalization of Lie algebras. It is natural to generalize concepts in Lie algebras to Leibniz algebras and investigate whether the corresponding results still hold. In this paper we introduce the notion of…
In this exposition-type note we present detailed proofs of certain assertions concerning several algebraic properties of the cone and cylinder algebras. These include a determination of the maximal ideals, the solution of the B\'ezout…
This paper is inspired by 1892 paper of Johnson, where he has given an axiomatization for the variety of Boolean algebras (equivalently, for classical propositional calculus). The fact that the axioms of Johnson include the associative law,…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
We prove that order convergence on a Boolean algebra turns it into a compact convergence space if and only if this Boolean algebra is complete and atomic. We also show that on an Archimedean vector lattice, order intervals are compact with…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
We give a self-contained exposition of some mathematical aspects of the Mueller-Stokes formalism. In the first part we review some basic notions of linear algebra and establish a proper notation. In the second part we introduce the…
We investigate the representation and complete representation classes for algebras of partial functions with the signature of relative complement and domain restriction. We provide and prove the correctness of a finite equational…
We investigate the equational theory of Kleene algebra terms with variable complements -- (language) complement where it applies only to variables -- w.r.t. languages. While the equational theory w.r.t. languages coincides with the language…
Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they…
Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…
We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…
The paper introduces the notion of state for involutive bisemilattices, a variety which plays the role of algebraic counterpart of paraconsistent weak Kleene logic and whose elements are represented as Plonka sum of Boolean algebras. We…
Propositional logic serves as a fundamental cornerstone in mathematical logic. This paper delves into a semiring characterization of propositional logic, employing the Gr\"oebner-Shirshov basis theory to furnish an algebraic framework for…
The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
Strongly continuous one-parameter representations on C*-algebras and their extension to the multiplier algebra are investigated. We give also a proof of the Stone theorem on Hilbert C*-modules and look into some related problems.
The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…