Related papers: Derivational modal logics with the difference moda…
We present semantic correctness proofs of forward-mode Automatic Differentiation (AD) for languages with sources of partiality such as partial operations, lazy conditionals on real parameters, iteration, and term and type recursion. We…
Dynamic Topological Logic ($\mathcal{DTL}$) is a combination of $\mathcal{S}${\em 4}, under its topological interpretation, and the temporal logic $\mathcal{LTL}$ interpreted over the natural numbers. $\mathcal{DTL}$ is used to reason about…
We carry out a semantic study of the constructive modal logic CK. We provide a categorical duality linking the algebraic and birelational semantics of the logic. We then use this to prove Sahlqvist style correspondence and completeness…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…
Categorical models of the exponential modality of linear logic will often, but not always, support an operation of differentiation. When they do, we speak of a monoidal differential modality; when they do not, we have merely a monoidal…
We introduce a monotone modal analogue of the intuitionistic (normal) modal logic IK using a translation into a suitable (intuitionistic) first-order logic. We axiomatise the logic and give a semantics by means of intuitionistic…
Derivations provide a way of transporting ideas from the calculus of manifolds to algebraic settings where there is no sensible notion of limit. In this paper, we consider derivations in certain monoidal categories, called codifferential…
We investigate the computational complexity of the satisfiability problem of modal inclusion logic. We distinguish two variants of the problem: one for the strict and another one for the lax semantics. Both problems turn out to be…
In this article we analyze the notions of amenability and paradoxical decomposition from an algebraic perspective. We consider this dichotomy for locally finite extended metric spaces and for general algebras over commutative fields. In the…
In this thesis we shall present two logical systems, MP and MP, for the purpose of reasoning about knowledge and effort. These logical systems will be interpreted in a spatial context and therefore, the abstract concepts of knowledge and…
We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.
Quantified modal logic provides a natural logical language for reasoning about modal attitudes even while retaining the richness of quantification for referring to predicates over domains. But then most fragments of the logic are…
We consider modal logics of products of neighborhood frames. We define n-product of modal logics as the logic of all products of neighborhood frames of corresponding logics and find n-product of any two pretransitive Horn axiomatizable…
We consider logics derived from Euclidean spaces $\mathbb{R}^n$. Each Euclidean space carries relations consisting of those pairs that are, respectively, distance more than 1 apart, distance less than 1 apart, and distance 1 apart. Each…
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz…
In this paper, we have described a denotational model of Intuitionist Linear Logic which is also a differential category. Formulas are interpreted as Mackey-complete topological vector space and linear proofs are interpreted by bounded…
The paper is devoted to modal properties of the ternary strict betweenness relation as used in the development of various systems of geometry. We show that such a relation is non-definable in a basic similarity type with a binary operator…
The topological interpretation of modal logics provides descriptive languages and proof systems for reasoning about points of topological spaces. Recent work has been devoted to model checking of spatial logics on discrete spatial…
We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.
We study two notions of definability for classes of relational structures based on modal extensions of {\L}ukasiewicz finitely valued-logics. The main results of the paper are the equivalent of the Goldblatt - Thomason theorem for these…