Related papers: Dynamic Cantor Derivative Logic
In the present paper syntax and semantics will be presented for an expansion of ordinary n-agent QML with constant domain, non-rigid constants, rigid variables and including both functions, relations, and equality. Further, the number of…
We present a KE-tableau-based procedure for the main TBox and ABox reasoning tasks for the description logic $\mathcal{DL}\langle \mathsf{4LQS^{R,\!\times}}\rangle(\mathbf{D})$, in short $\mathcal{DL}_{\mathbf{D}}^{4,\!\times}$. The logic…
We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…
In 1988, Ivlev proposed four-valued non-deterministic semantics for modal logics in which the alethic T axiom holds good. Unfortunately, no completeness was proved. In previous work, we proved completeness for some Ivlev systems and…
In this paper, we completely solve the problem when a Cantor dynamical system $(X,f)$ can be embedded in $\mathbb{R}$ with vanishing derivative everywhere. For this purpose, we construct a refining sequence of marked clopen partitions of…
In this paper, we study a new Kripke-style semantics for classical modal logic, named as provability models. We study provability models for the propositional modal logics K, K4, S4 GL, GLP and the interpretability logic ILM. Provability…
Differentiable logics are a family of quantitative logics originated in the machine learning literature. Because of their origin, differentiable logics often come equipped with analytic properties that guarantee that they are…
This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally…
Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested…
Formal semantics and distributional semantics are distinct approaches to linguistic meaning: the former models meaning as reference via model-theoretic structures; the latter represents meaning as vectors in high-dimensional spaces shaped…
G{\"o}del's completeness theorem for classical first-order logic is one of the most basic theorems of logic. Central to any foundational course in logic, it connects the notion of valid formula to the notion of provable formula.We survey a…
Let $T$ be a complete, model complete o-minimal theory extending the theory RCF of real closed ordered fields in some appropriate language $L$. We study derivations $\delta$ on models $\mathcal{M}\models T$. We introduce the notion of a…
This is a noncommutative-geometric study of the semiclassical dynamics of finite topological D-brane systems. Starting from the formulation in terms of A -infinity categories, I show that such systems can be described by the noncommutative…
Ardakov-Wadsley defined the sheaf D-cap of $p$-adic analytic differential operators on a smooth rigid analytic variety $X$ by restricting to the case where $X$ is affinoid and the tangent sheaf admits a smooth Lie lattice. We generalize…
In this paper, we focus on discrete-time stochastic systems modelled by nonlinear stochastic difference equations and propose robust abstractions for verifying probabilistic linear temporal specifications. The current literature focuses on…
The continuous modal mu-calculus is a fragment of the modal mu-calculus, where the application of fixpoint operators is restricted to formulas whose functional interpretation is Scott-continuous, rather than merely monotone. By…
Distributed systems are critical to reliable and scalable computing; however, they are complicated in nature and prone to bugs. To modularly manage this complexity, network middleware has been traditionally built in layered stacks of…
The displacement calculus $\mathbf{D}$ is a conservative extension of the Lambek calculus $\mathbf{L1}$ (with empty antecedents allowed in sequents). $\mathbf{L1}$ can be said to be the logic of concatenation, while $\mathbf{D}$ can be said…
We study when a piecewise full group (a.k.a. topological full group) of homeomorphisms of the Cantor space $X$ can be given a non-discrete totally disconnected locally compact (t.d.l.c.) topology and give a criterion for the alternating…
Given any strong orbit equivalence class of minimal Cantor systems and any cardinal number that is finite, countable, or the continuum, we show that there exists a minimal subshift within the given class whose number of asymptotic…