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The complexity of propositional linear temporal logics in simple cases [chapter]

S. Demri, Ph. Schnoebelen
1998 Lecture Notes in Computer Science  
propositions, and (3) the temporal height.  ...  In this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic  ...  PLTL is the standard linear-time propositional temporal logic used in the specification and automated verification of reactive systems [MP92, Eme90] .  ... 
doi:10.1007/bfb0028549 fatcat:tv676j3etfdkva4dxkruur3axe

The Complexity of Propositional Linear Temporal Logics in Simple Cases

Stéphane Demri, Philippe Schnoebelen
2002 Information and Computation  
propositions, and (3) the temporal height.  ...  In this paper we investigate this issue and consider model checking and satisfiability for all fragments of PLTL obtainable by restricting (1) the temporal connectives allowed, (2) the number of atomic  ...  PLTL is the standard linear-time propositional temporal logic used in the specification and automated verification of reactive systems [MP92, Eme90] .  ... 
doi:10.1006/inco.2001.3094 fatcat:22u24aacr5ax5bybc2p7bavc64

Implementing Temporal Logics: Tools for Execution and Proof [chapter]

Michael Fisher
2006 Lecture Notes in Computer Science  
Summary We have overviewed a selection of tools for execution and proof within temporal logic.  ...  from within the Logic and Computation group 2 .  ...  [this shows some of the power of temporal logic as a variety of different ω-automata can be characterised in this way] A Little Complexity The decision problem for a simple propositional (discrete, linear  ... 
doi:10.1007/11750734_8 fatcat:dnerita2qfcevnmo3ah62kf24m

Real-time and Probabilistic Temporal Logics: An Overview [article]

Savas Konur
2011 arXiv   pre-print
Although numerous logics have been introduced for the formal specification of real-time and complex systems, an up to date comprehensive analysis of these logics does not exist in the literature.  ...  We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed.  ...  In certain applications simple logics are preferred to the complex ones [12] . Complex logics are generally difficult to deal with practically.  ... 
arXiv:1005.3200v3 fatcat:xhrrcy26bzeehg7wqvjfikm26e

A Survey on Temporal Logics [article]

Savas Konur
2011 arXiv   pre-print
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability  ...  In some cases, fragments of first-order temporal logics with lower computational complexity are defined through restricted extensions to propositional temporal logics [1, 100, 35, 112] .  ...  In fact, propositional temporal logics are an extension of propositional logic with temporal operators.  ... 
arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu

Chapter 12 Temporal Representation and Reasoning [chapter]

Michael Fisher
2008 Foundations of Artificial Intelligence  
Consequently, the notion of representations changing through time is vital. And so, we need a clear way of representing both our temporal basis, and the way in which entities change over time.  ...  We aim to provide the reader with an overview of many of the ways temporal phenomena can be modelled, described, reasoned about, and applied.  ...  Acknowledgements The author would like to thank a number of experts in the area who have reviewed this chapter and provided valuable insights and corrections, in particular: Anthony Galton  ... 
doi:10.1016/s1574-6526(07)03012-x fatcat:kuqoy7zvjzd5nhqkakvdn7vgs4

Linear Functional Fixed-points [chapter]

Nikolaj Bjørner, Joe Hendrix
2009 Lecture Notes in Computer Science  
In particular, for the logic of linear functional fixed-points, we develop an abstraction refinement integration of the SMT solver Z3 and a satisfiability checker for propositional lineartime temporal  ...  -We establish that FFP(E) is PSPACE-complete modulo background theories that are in PSPACE by using a reduction from FFP(E) into propositional linear-time temporal logic.  ...  For instance, Sistla and Clarke show that linear-time temporal logic using only the operators  and  is NP-complete, and so is the case if formulas are in positive normal form using  and .  ... 
doi:10.1007/978-3-642-02658-4_13 fatcat:vwotwx4yd5bgxm3pnbavozhr5i

Page 5892 of Mathematical Reviews Vol. , Issue 98I [page]

1998 Mathematical Reviews  
Summary: “We present here a linear time temporal logic which simultaneously extends LTL, the propositional temporal logic of linear time, along two dimensions.  ...  Our results show that in almost all cases the complexity of the problem is exponentially harder than that of the sequential case.  ... 

Games, Automata, Logics and Formal Verification (GandALF 2014) – Preface

Adriano Peron, Carla Piazza
2017 Information and Computation  
The collection of papers in this issue covers a variety of topics in game theory (graph games, pushdown modular games), logics (Propositional dependence logics, Propositional Dynamic Logic, First-order  ...  verification of complex systems.  ...  The paper Complexity of Validity for Propositional Dependence Logics, by Jonni Virtema, studies the complexity of the validity problems of propositional dependence logic, modal dependence logic, and extended  ... 
doi:10.1016/j.ic.2016.07.005 fatcat:4oiouzxwcfh2vfuktawrvodnmu

Taming the Complexity of Temporal Epistemic Reasoning [chapter]

Clare Dixon, Michael Fisher, Boris Konev
2009 Lecture Notes in Computer Science  
Temporal logic of knowledge is a combination of temporal and epistemic logic that has been shown to be very useful in areas such as distributed systems, security, and multi-agent systems.  ...  However, the complexity of the logic can be prohibitive.  ...  Acknowledgements The work of Fisher was partially supported by EPSRC grant EP/F033567 ("Verifying Interoperability Requirements in Pervasive Systems") and the work of Dixon was partially supported by EPSRC  ... 
doi:10.1007/978-3-642-04222-5_12 fatcat:lvsuat77wvhpxlekdv6vk7lopq

Page 263 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
263 68Q Theory of computing increasingly complicated, examples are discussed. In all cases reasonably simple proofs can be given.  ...  In the general part we give a complete proof system for first-order temporal logic with detailed proofs of useful theorems. This logic enables reasoning about gen- eral time sequences.  ... 

Reichenbach, Prior and hybrid tense logic

Patrick Blackburn, Klaus Frovin Jørgensen
2015 Synthese  
We do so by combining the central insights of Prior and Reichenbach in the framework of hybrid tense logic.  ...  That Prior was the inventor of tense logic is well known; that he was also the inventor of hybrid logic is not. Nonetheless, hybrid logic plays a clear (if somewhat restricted) role in Prior's best  ...  Tense, Temporal Reference and Tense Logic, Journal of Semantics 11: 83-101. Blackburn, P. (2006). Arthur Prior and Hybrid Logic, Synthese 150: 329-372.  ... 
doi:10.1007/s11229-015-0920-0 fatcat:3bekiznlcjcpvden6clcpujbh4

Temporal versus first-order logic to query temporal databases

Serge Abiteboul, Laurent Herr, Jan Van den Bussche
1996 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '96  
One may alternatively use an implicit access to time and express queries in temporal logic. I t is known that these two approaches yield the same expressive p o wer in the propositional case.  ...  We prove here that there are rst-order logic queries on the timestamp representation that are not expressible in (extended) temporal logic.  ...  Acknowledgments We thank Luc Segou n for pointing out the relation to communication complexity, and Victor Vianu for raising the ts-fo k issue.  ... 
doi:10.1145/237661.237674 dblp:conf/pods/AbiteboulHB96 fatcat:vczt4g7j2fbiffb42jw32qoqmy

A Proof of Stavi's Theorem [article]

Alexander Rabinovich
2017 arXiv   pre-print
Kamp's theorem established the expressive equivalence of the temporal logic with Until and Since and the First-Order Monadic Logic of Order (FOMLO) over the Dedekind-complete time flows.  ...  We present a simple proof of Stavi's theorem.  ...  Preliminaries In this section we recall the definitions of linear orders, the first-order monadic logic of order, the temporal logics and state Kamp's and Stavi's theorems. 2.1.  ... 
arXiv:1711.03876v1 fatcat:ozfsyy32dvgzdd2xiarkl5nvyi

Stutter-Invariant Languages, ω-Automata, and Temporal Logic [chapter]

Kousha Etessami
1999 Lecture Notes in Computer Science  
We will observe a simple variant of linear time propositional temporal logic (LTL) for expressing exactly the stutter-invariant ω-regular languages.  ...  Temporal logic and ω-automata are two of the common frameworks for specifying properties of reactive systems in modern verification tools.  ...  Conclusions We have provided a simple temporal logic, SI-EQLTL, for expressing the stutterinvariant ω-regular languages.  ... 
doi:10.1007/3-540-48683-6_22 fatcat:erymptso6zfcvbkip5blmzszly
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