Related papers: Untangled: A Complete Dynamic Topological Logic

Temporal logics are widely used by the Formal Methods and AI communities. Linear Temporal Logic is a popular temporal logic and is valued for its ease of use as well as its balance between expressiveness and complexity. LTL is equivalent in…

We define when a ternary term $m$ of an algebraic language $\mathcal{L}$ is called a \textit{distributive nearlattice term} (DN-term) of a sentential logic $\mathcal{S}$. Distributive nearlattices are ternary algebras generalising Tarski…

Probabilistic Computation Tree Logic (PCTL) is a well-known modal logic which has become a standard for expressing temporal properties of finite-state Markov chains in the context of automated model checking. In this paper, we give a…

In this chapter we study modal logics of topological spaces in the combined language with the derivational modality and the difference modality. We give axiomatizations and prove completeness for the following classes: all spaces,…

Auxiliary tasks facilitate learning in situations where data is scarce or the principal task of interest is extremely complex. This idea is primarily inspired by the improved generalization capability induced by solving multiple tasks…

A natural liberalization of Datalog is used in the Distributed Knowledge Authorization Language (DKAL). We show that the expressive power of this liberal Datalog is that of existential fixed-point logic. The exposition is self-contained.

A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is…

The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and…

We prove a topological completeness theorem for the modal logic GLP containing operators $\langle\lambda\rangle$ for $\lambda \in$ Ord intended to capture progressively stronger notions of consistency in mathematical theories. We show that,…

DatalogMTL is a powerful rule-based language for temporal reasoning. Due to its high expressive power and flexible modeling capabilities, it is suitable for a wide range of applications, including tasks from industrial and financial…

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…

Standpoint linear temporal logic ($SLTL$) is a recently introduced extension of classical linear temporal logic ($LTL$) with standpoint modalities. Intuitively, these modalities allow to express that, from agent $a$'s standpoint, it is…

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,…

We consider a logic used to describe sets of configurations of distributed systems, whose network topologies can be changed at runtime, by reconfiguration programs. The logic uses inductive definitions to describe networks with an unbounded…

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…

Building on previous work by Andr\'e Platzer, we present a formal language for Stochastic Differential Dynamic Logic, and define its semantics, axioms and inference rules. Compared to the previous effort, our account of the Stochastic…

There has been renewed interest in recent years in McKinsey and Tarski's interpretation of modal logic in topological spaces and their proof that S4 is the logic of any separable dense-in-itself metric space. Here we extend this work to the…

Executing complex manipulation in cluttered environments requires satisfying coupled geometric and temporal constraints. Although Spatio-Temporal Logic (SpaTiaL) offers a principled specification framework, its use in gradient-based…

Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these…

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…