Related papers: Generalized Bosbach States
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
Divisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek's basic logic with an important significance in the study of fuzzy logic. The purpose of this paper is to investigate commutative…
We propose a novel form of classification of multipartite states, in terms of the maximum degree of non-locality they can exhibit under any choice of local observables. This uses the hierarchy of notions previously introduced by Abramsky…
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language. In particular, certain bilattices have been used to model…
Topos quantum theory provides representations of quantum states as direct generalizations of the probability distribution, namely probability valuation. In this article, we consider extensions of a known bijective correspondence between…
Many-valued models generalise the structures from classical model theory by defining truth values for a model with an arbitrary algebra. Just as algebraic varieties provide semantics for many non-classical propositional logics, models…
Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…
We describe a general approach to deriving linear-time logics for a wide variety of state-based, quantitative systems, by modelling the latter as coalgebras whose type incorporates both branching and linear behaviour. Concretely, we define…
Continuing a previous analysis originally motivated by physics, we consider representable states on quasi-local quasi *-algebras, starting with examining the possibility for a {\em compatible} family of {\em local} states to give rise to a…
We study the equational theory of the Weihrauch lattice with multiplication, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the product $\times$, and the finite…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
This paper presents State Algebra, a novel framework designed to represent and manipulate propositional logic using algebraic methods. The framework is structured as a hierarchy of three representations: Set, Coordinate, and Row…
We provide a new foundational approach to the generalization of terms up to equational theories. We interpret generalization problems in a universal-algebraic setting making a key use of projective and exact algebras in the variety…
An algebraic characterization of vacuum states in Minkowski space is given which relies on recently proposed conditions of geometric modular action and modular stability for algebras of observables associated with wedge-shaped regions. In…
This paper presents an investigation on the structure of conditional events and on the probability measures which arise naturally in this context. In particular we introduce a construction which defines a (finite) {\em Boolean algebra of…
Non-classical probability (along with its underlying logic) is a defining feature of quantum mechanics. A formulation that incorporates them, inherently and directly, would promise a unified description of seemingly different prescriptions…
This paper presents a Probabilistic State Algebra as an extension of deterministic propositional logic, providing a computational framework for constructing Markov Random Fields (MRFs) through pure linear algebra. By mapping logical states…
We define generalised Gaussian states for quantum cosmological models based on the $\mathfrak{su(1,1)}$ algebra, with particular emphasis on its realisation in group field theory for a single field mode, and study their semiclassical…
In several recent papers on entanglement in relativistic quantum systems and relativistic Bell's inequalities, relativistic Bell-type two-particle states have been constructed in analogy to non-relativistic states. These constructions do…
We study the residuated basic logic ($\mathsf{RBL}$) of residuated basic algebra in which the basic implication of Visser's basic propositional logic ($\mathsf{BPL}$) is interpreted as the right residual of a non-associative binary operator…