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We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have…

Logic in Computer Science · Computer Science 2025-10-14 Andreas Krebs , Arne Meier , Jonni Virtema , Martin Zimmermann

In this paper we consider two different views of the model checking problems for the Linear Temporal Logic (LTL). On the one hand, we consider the universal model checking problem for LTL, where one asks that for a given system and a given…

Logic in Computer Science · Computer Science 2024-09-30 Damien Busatto-Gaston , Youssouf Oualhadj , Léo Tible , Daniele Varacca

In a seminal paper from 1985, Sistla and Clarke showed that the model-checking problem for Linear Temporal Logic (LTL) is either NP-complete or PSPACE-complete, depending on the set of temporal operators used. If, in contrast, the set of…

Logic in Computer Science · Computer Science 2016-09-08 Michael Bauland , Martin Mundhenk , Thomas Schneider , Henning Schnoor , Ilka Schnoor , Heribert Vollmer

Temporal Equilibrium Logic (TEL) is a promising framework that extends the knowledge representation and reasoning capabilities of Answer Set Programming with temporal operators in the style of LTL. To our knowledge it is the first…

Logic in Computer Science · Computer Science 2015-03-03 Laura Bozzelli , David Pearce

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…

Logic in Computer Science · Computer Science 2018-08-16 Laura Bozzelli , Aniello Murano , Adriano Peron

A framework is presented for the verification of Signal Temporal Logic (STL) specifications over continuous-time nonlinear systems under uncertainty. Based on reachability analysis, the proposed method addresses indeterminate satisfaction…

Logic in Computer Science · Computer Science 2025-11-25 Antoine Besset , Joris Tillet , Julien Alexandre dit Sandretto

We consider an extension of linear-time temporal logic (LTL) with both local and remote data constraints interpreted over a concrete domain. This extension is a natural extension of constraint LTL and the Temporal Logic of Repeating Values,…

Logic in Computer Science · Computer Science 2022-06-06 Ashwin Bhaskar

We consider here Linear Temporal Logic (LTL) formulas interpreted over \emph{finite} traces. We denote this logic by LTLf. The existing approach for LTLf satisfiability checking is based on a reduction to standard LTL satisfiability…

Logic in Computer Science · Computer Science 2014-03-10 Jianwen Li , Lijun Zhang , Geguang Pu , Moshe Y. Vardi , Jifeng He

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…

Logic in Computer Science · Computer Science 2025-02-28 Rajab Aghamov , Christel Baier , Toghrul Karimov , Rupak Majumdar , Joël Ouaknine , Jakob Piribauer , Timm Spork

We study an extension of $\mtl$ in pointwise time with rational expression guarded modality $\reg_I(\re)$ where $\re$ is a rational expression over subformulae. We study the decidability and expressiveness of this extension ($\mtl$+$\varphi…

Logic in Computer Science · Computer Science 2017-05-04 Shankara Narayanan Krishna , Khushraj Madnani , P. K. Pandya

The expressive power of interval temporal logics (ITLs) makes them one of the most natural choices in a number of application domains, ranging from the specification and verification of complex reactive systems to automated planning.…

Logic in Computer Science · Computer Science 2023-06-22 Laura Bozzelli , Alberto Molinari , Angelo Montanari , Adriano Peron , Pietro Sala

This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…

Logic in Computer Science · Computer Science 2022-05-25 Luca Geatti , Alessandro Gianola , Nicola Gigante

HyperLTL, the extension of Linear Temporal Logic by trace quantifiers, is a uniform framework for expressing information flow policies by relating multiple traces of a security-critical system. HyperLTL has been successfully applied to…

Logic in Computer Science · Computer Science 2019-12-17 Corto Mascle , Martin Zimmermann

We study the expressivity and complexity of model checking linear temporal logic with team semantics (TeamLTL). TeamLTL, despite being a purely modal logic, is capable of defining hyperproperties, i.e., properties which relate multiple…

Logic in Computer Science · Computer Science 2021-11-24 Jonni Virtema , Jana Hofmann , Bernd Finkbeiner , Juha Kontinen , Fan Yang

It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori.…

Logic in Computer Science · Computer Science 2023-06-22 Hsi-Ming Ho , Joël Ouaknine , James Worrell

Linear Temporal Logic (LTL) interpreted on finite traces is a robust specification framework popular in formal verification. However, despite the high interest in the logic in recent years, the topic of their quantitative extensions is not…

Logic in Computer Science · Computer Science 2021-01-05 Bartosz Bednarczyk , Jakub Michaliszyn

LTL synthesis -- the construction of a function to satisfy a logical specification formulated in Linear Temporal Logic -- is a 2EXPTIME-complete problem with relevant applications in controller synthesis and a myriad of artificial…

Logic in Computer Science · Computer Science 2016-11-18 Jorge A. Baier , Alberto Camacho , Christian Muise , Sheila A. McIlraith

Synthesis of models and strategies is a very important problem in software engineering. The main element here is checking the satisfiability of formulae expressing the specification of a system to be implemented. This paper puts forward a…

Logic in Computer Science · Computer Science 2020-02-11 Magdalena Kacprzak , Artur Niewiadomski , Wojciech Penczek

We present CLTLB(D), an extension of PLTLB (PLTL with both past and future operators) augmented with atomic formulae built over a constraint system D. Even for decidable constraint systems, satisfiability and Model Checking problem of such…

Logic in Computer Science · Computer Science 2010-04-21 Marcello M. Bersani , Achille Frigeri , Angelo Morzenti , Matteo Pradella , Matteo Rossi , Pierluigi San Pietro

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of…

Logic in Computer Science · Computer Science 2015-07-01 Olaf Beyersdorff , Arne Meier , Martin Mundhenk , Thomas Schneider , Michael Thomas , Heribert Vollmer