Related papers: Generalized topological semantics for weak modal l…
We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as…
This paper assumes a robust, in general not dominated, probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of non-negative random…
By calling into question the implicit structural rules that are taken for granted in classical logic, substructural logics have brought to the fore new forms of reasoning with applications in many interdisciplinary areas of interest.…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
Understanding realistic complex systems requires confronting significant conceptual, theoretical and experimental limitations rooted in the persistence of views that originated in the mechanics of simple moving bodies. We define the…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
Canonical models are of central importance in modal logic, in particular as they witness strong completeness and hence compactness. While the canonical model construction is well understood for Kripke semantics, non-normal modal logics…
Inquisitive modal logic, InqML, is a generalisation of standard Kripke-style modal logic. In its epistemic incarnation, it extends standard epistemic logic to capture not just the information that agents have, but also the questions that…
Building general-purpose robots that operate seamlessly in any environment, with any object, and utilizing various skills to complete diverse tasks has been a long-standing goal in Artificial Intelligence. However, as a community, we have…
We develop basic homological machinery for Z-algebras in order to prove a version of local duality for Ext-finite connected Z-algebras. As an application, we compare two notions of regularity for such algebras.
The rings of linear continuous operators on the topological spaces of $\mathfrak{G}$-zero maps were described, where $\mathfrak{G}$ is a filter on a set with an involution. This applies to modules of formal series with well ordered support…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping to convey a firm grasp of three ideas: (1)…
We introduce a two-sort weighted modal logic for possibilistic reasoning with fuzzy formal contexts. The syntax of the logic includes two types of weighted modal operators corresponding to classical necessity ($\Box$) and sufficiency…
We study modules over the ring $\widetilde{\C}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\C}$-linear topology and locally convex $\widetilde{\C}$-linear topology. In this…
Foundation models have received much attention due to their effectiveness across a broad range of downstream applications. Though there is a big convergence in terms of architecture, most pretrained models are typically still developed for…
We present a modal logic based approach to the so-called endophysical quantum universe. In particular, we treat the problem of preferred bases and that of state reduction by employing an eclectic collection of methods including Baltag's…
We present closed graph and open mapping theorems for $\wt{\C}$-linear maps acting between suitable classes of topological and locally convex topological $\wt{\C}$-modules. This is done by adaptation of De Wilde's theory of webbed spaces…
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the…