Related papers: Conditional algebras
We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…
Probabilistic argumentation is an alternative to causal modeling with Bayesian networks. Probabilistic argumentation structures (PAS) are defined on families of compatible frames (f.c.f). This is a generalization of the usual multivariate…
We present a general formal argumentation system for dealing with the detachment of conditional obligations. Given a set of facts, constraints, and conditional obligations, we answer the question whether an unconditional obligation is…
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.
Binary relations are one of the standard ways to encode, characterise and reason about graphs. Relation algebras provide equational axioms for a large fragment of the calculus of binary relations. Although relations are standard tools in…
Universal algebra uniformly captures various algebraic structures, by expressing them as equational theories or abstract clones. The ubiquity of algebraic structures in mathematics and related fields has given rise to several variants of…
This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the…
Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
We describe a notion of categorical model for unitless fragments of (multiplicative) linear logic. The basic definition uses promonoidal categories, and we also give an equivalent elementary axiomatisation.
We study multimodal logics over universally first-order definable classes of frames. We show that even for bimodal logics, there are universal Horn formulas that define set of frames such that the satisfiability problem is undecidable, even…
We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics. In…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
In this note we study dual coalgebras of algebras over arbitrary (noetherian) commutative rings. We present and study a generalized notion of coreflexive comodules and use the results obtained for them to characterize the so called…
In this paper I consider locally finite Lie algebras of characteristic zero satisfying the condition that for every finite number of elements $x_{1}, x_{2},..., x_{k}$ of such an algebra $L$ there is finite-dimensional subalgebra $A$ which…
We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…