Related papers: Semantics and Axiomatization for Stochastic Differ…
This paper introduces a new proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform substitutions make it possible…
This paper introduces a differentiable semantic reasoner, where rules are presented as a relevant set of graph transformations. These rules can be written manually or inferred by a set of facts and goals presented as a training set. While…
This article introduces a relatively complete proof calculus for differential dynamic logic (dL) that is entirely based on uniform substitution, a proof rule that substitutes a formula for a predicate symbol everywhere. Uniform…
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…
We define sound and adequate denotational and operational semantics for the stochastic lambda calculus. These two semantic approaches build on previous work that used similar techniques to reason about higher-order probabilistic programs,…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. Temporal logics have been an important research subject within this direction. Although numerous logics have…
This paper introduces a dynamic logic extension of separation logic. The assertion language of separation logic is extended with modalities for the five types of the basic instructions of separation logic: simple assignment, look-up,…
Differentiable logics (DL) have recently been proposed as a method of training neural networks to satisfy logical specifications. A DL consists of a syntax in which specifications are stated and an interpretation function that translates…
We develop a logic which enables reasoning about single steps of non-deterministic parallel Abstract State Machines (ASMs). Our logic builds upon the unifying logic introduced by Nanchen and St\"ark for reasoning about hierarchical…
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
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…
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 endow prioritised default logic (PDL) with argumentation semantics using the ASPIC+ framework for structured argumentation, and prove that the conclusions of the justified arguments are exactly the prioritised default extensions.…
Dynamic Topological Logic (DTL) is a multimodal system for reasoning about dynamical systems. It is defined semantically and, as such, most of the work done in the field has been model-theoretic. In particular, the problem of finding a…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…