Robust Alternating-Time Temporal Logic

Aniello Murano; Daniel Neider; Martin Zimmermann

Home/Archive/arXiv

arXiv · 2307.10885

Robust Alternating-Time Temporal Logic

Aniello Murano·Daniel Neider·Martin Zimmermann

View original source ↗Read source document ↗Export metadata ↓

Abstract

In multi-agent system design, a crucial aspect is to ensure robustness, meaning that for a coalition of agents A, small violations of adversarial assumptions only lead to small violations of A's goals. In this paper we introduce a logical framework for robust strategic reasoning about multi-agent systems. Specifically, inspired by recent works on robust temporal logics, we introduce and study rATL and rATL*, logics that extend the well-known Alternating-time Temporal Logic ATL and ATL* by means of an opportune multi-valued semantics for the strategy quantifiers and temporal operators. We study the model-checking and satisfiability problems for rATL and rATL* and show that dealing with robustness comes at no additional computational cost. Indeed, we show that these problems are PTime-complete and ExpTime-complete for rATL, respectively, while both are 2ExpTime-complete for rATL*.

Explore related subjects

cs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Aniello Murano, Daniel Neider, Martin Zimmermann. 2023-07-20. Robust Alternating-Time Temporal Logic. https://arxiv.org/abs/2307.10885

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

TREBL -- A Relative Complete Temporal Event-B Logic. Part I: Theory

The verification of liveness conditions is an important aspect of state-based rigorous methods. This article addresses the extension of the logic of Event-B to a powerful logic, in which properties of traces of an Event-B machine can be expressed. However, all formulae of this logic are still interpreted over states of an Event-B machine rather than traces. The logic exploits that for an Event-B machine $M$ a state $S$ determines all traces of $M$ starting in $S$. We identify a fragment called TREBL of this logic, in which all liveness conditions of interest can be expressed, and define a set of sound derivation rules for the fragment. We further show relative completeness of these derivation rules in the sense that for every valid entailment of a formula $φ$ one can find a derivation, provided the machine $M$ is sufficiently refined. The decisive property is that certain variant terms must be definable in the refined machine. We show that such refinements always exist. Throughout the article several examples from the field of security are used to illustrate the theory.

cs.LO↗

arXiv2026

Scenes: A Meta-Logical Algebra for Mutable State

Modelling of mutable state spaces and precisely describing how variables are manipulated in a program is a fundamental problem in compositional verification. Though we can make use of the embedded abstract syntax of a program for such analysis, this runs contrary to the shallow-embedding approach, and hampers efficient proof automation. On the other hand, lenses and prisms provide an elegant algebraic foundation for modelling state, which provide sufficient structure to provide meta-logical program analysis, but without requiring a deep embedding. Nevertheless lenses, as complex algebraic objects, cannot easily be combined, complemented, or collected in sets. In this paper we contribute an accompanying algebraic structure called the scene, which allows us to characterise the set of variables, or coordinates, in a state space. Scenes intuitively correspond to sets of lenses, but like lenses they are purely semantic algebraic objects. We demonstrate that scenes provide us with sufficient structure to characterise the lens-based meta-logical properties, like independence and equivalence. Moreover, we introduce the notion of a scene space, analogous to a vector space, which allows us to recover a set-like algebraic structure. Finally, we show how scenes allow us to characterise the free and bound variables of expressions and programs, without any need for syntax, and demonstrate their use for reasoning about programs by deriving reasoning principles for the parallel composition operator.

cs.LO↗

arXiv2026

Completeness of Kozen's Axiomatization for the Modal mu-Calculus: A Simple Proof

The modal mu-calculus, introduced by Dexter Kozen, is an extension of modal logic with fixpoint operators. Its axiomatization, Koz, was introduced at the same time and is an extension of the minimal modal logic K with the so-called Park fixpoint induction principle. It took more than a decade for the completeness of Koz to be proven, finally achieved by Igor Walukiewicz. However, his proof is fairly involved. In this article, we present an improved proof for the completeness of Koz which, although similar to the original, is simpler and easier to understand. Keywords: The modal mu-calculus, completeness, omega-automata.

cs.LO↗