Related papers: The flattening operator in team-based logics
In previous work we established a multilinear duality and factorisation theory for norm inequalities for pointwise weighted geometric means of positive linear operators defined on normed lattices. In this paper we extend the reach of the…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
We formally investigate immediate and mediate grounding operators from an inferential perspective. We discuss the differences in behaviour displayed by several grounding operators and consider a general distinction between grounding and…
We augment LP with a strong conditional operator, to yield a logic we call "strong LP," or LP=>. The resulting logic can speak of consistency in more discriminating ways, but introduces new possibilities for trivializing paradoxes.
To construct more homogeneous operators, B. Bagchi and G. Misra in \cite{d} introduced the operator $\left(\begin{smallmatrix} T_0 & T_0-T_1 \\ 0 & T_1\\ \end{smallmatrix}\right)$ and proved that when $T_0$ and $T_1$ are homogeneous…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
We prove expressive completeness results for convex propositional and modal team logics, where a logic is convex if, for each formula, if it is true in two teams $t$ and $u$ and $t\subseteq s\subseteq u$, then it is also true in $s$. We…
State machine formalisms equipped with hierarchy and parallelism allow to compactly model complex system behaviours. Such models can then be transformed into executable code or inputs for model-based testing and verification techniques.…
In order to enrich dynamic semantic theories with a `pragmatic' capacity, we combine dynamic and nonmonotonic (preferential) logics in a modal logic setting. We extend a fragment of Van Benthem and De Rijke's dynamic modal logic with…
We establish linear convergence of relocated fixed-point iterations as introduced by Atenas et al. (2025) assuming the algorithmic operator satisfies a linear error bound. In particular, this framework applies to the setting where the…
The most recent wave of applications of logic to operator algebras is a young and rapidly developing field. This is a snapshot of the current state of the art.
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce the connective implication to be everywhere defined and satisfying (left) adjointness with the connective…
The foundational character of certain algebraic structures as Boolean algebras and Heyting algebras is rooted in their potential to model classical and constructive logic, respectively. In this paper we discuss the contributions of…
Recent developments in machine learning have introduced models that approach human performance at the cost of increased architectural complexity. Efforts to make the rationales behind the models' predictions transparent have inspired an…
This paper presents a few additions to commutant lifting theory. An operator interpolation problem is introduced and shown to be equivalent to the relaxed commutant lifting problem. Using this connection a description of all solutions of…
We re-cast in a more combinatorial and computational form the foldings approach of John Stallings and pursue a detailed study of the subgroup structure of free groups. In particular, we introduce the notions of an "algebraic" and a "free"…
Hamiltonian operators are used in the theory of integrable partial differential equations to prove the existence of infinite sequences of commuting symmetries or integrals. In this paper it is illustrated the new Reduce package \cde for…
This survey aims to give a brief introduction to operator theory in the Hardy space over the bidisc $H^2(\mathbb D^2)$. As an important component of multivariable operator theory, the theory in $H^2(\mathbb D^2)$ focuses primarily on two…
As an abstraction and generalization of the integral operator in analysis, integral operators (known as Rota-Baxter operators of weight zero) on associative algebras and Lie algebras have played an important role in mathematics and physics.…