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On Relaxing Metric Information in Linear Temporal Logic

Carlo A. Furia, Paola Spoletini
2011 2011 Eighteenth International Symposium on Temporal Representation and Reasoning  
Metric LTL formulas rely on the next operator to encode time distances, whereas qualitative LTL formulas use only the until operator.  ...  largest distances used in M (i.e., occurrences of next), but the size of Q is independent of such distances.  ...  ACKNOWLEDGEMENTS A very preliminary version of this work has been presented at the 11th Italian Conference on Theoretical Computer Science (Cremona, Italy, 28-30 September 2009); the authors thank the  ... 
doi:10.1109/time.2011.9 dblp:conf/time/FuriaS11 fatcat:4zu2b52finhufcvruk3glpwv4u

Appearance of Thermal Time [article]

Shigenori Tanaka
2020 arXiv   pre-print
This basic equation, in turn, may be regarded as characterizing the nonequilibrium dynamical process and having a solution given by the Fisher information metric.  ...  The probability distribution of the events thus provides a mutual regulation between temperature and time, which can relevantly be expressed in terms of the Fisher information metric.  ...  Acknowledgements The author would like to acknowledge the Grants-in-Aid for Scientific Research (Nos.  ... 
arXiv:2006.08932v1 fatcat:epggvssqyfgxvpetvg3lxosulq

Quantifying Conformance using the Skorokhod Metric (full version) [article]

Jyotirmoy V. Deshmukh, Rupak Majumdar, Vinayak S. Prabhu
2015 arXiv   pre-print
Specifically, we show the result for the timed linear time logic augmented with a rich class of temporal and spatial constraint predicates.  ...  In the semi-formal approach to conformance testing, the two systems are simulated on a large set of tests, and a metric, defined on pairs of real-valued, real-timed trajectories, is used to determine a  ...  If two traces are at a distance of δ, and one trace satisfies a logical specification φ, we derive the "relaxation" needed (if any) in φ so that the other trace also satisfies this relaxed logical specification  ... 
arXiv:1505.05832v1 fatcat:yv3v675u5zbphoebzdiqnd5rjy

A Truly Robust Signal Temporal Logic: Monitoring Safety Properties of Interacting Cyber-Physical Systems under Uncertain Observation

Bernd Finkbeiner, Martin Fränzle, Florian Kohn, Paul Kröger
2022 Algorithms  
Signal Temporal Logic is a linear-time temporal logic designed for classifying the time-dependent signals originating from continuous-state or hybrid-state dynamical systems according to formal specifications  ...  For the model-free as well as for the linear model-based case, we provide optimal evaluation algorithms based on affine arithmetic and SAT modulo theory, solving over linear arithmetic.  ...  Informed Consent Statement: Not applicable.  ... 
doi:10.3390/a15040126 fatcat:tntqcabxcrfirey46pca5t3uny

Quantifying Conformance Using the Skorokhod Metric [chapter]

Jyotirmoy V. Deshmukh, Rupak Majumdar, Vinayak S. Prabhu
2015 Lecture Notes in Computer Science  
We demonstrate the robustness of the metric by proving a transference theorem: trajectories close under the Skorokhod metric satisfy "close" logical properties in the timed linear time logic TLTL augmented  ...  Definition 4 (δ-relaxation of TLTL(F T ) Formulae). Let φ be a TLTL(F T ) formula in which negations appear only on the propositional symbols.  ...  Transference of Logical Properties In this section, we demonstrate a transference result for the Skorokhod metric for a version of the timed linear time logic TLTL [4] .  ... 
doi:10.1007/978-3-319-21668-3_14 fatcat:qlwcuv7fjjaoxejthtqy5uioqa

Completeness results for two-sorted metric temporal logics [chapter]

Angelo Montanari, Maarten Rijke
1995 Lecture Notes in Computer Science  
Then, we show how to obtain the metric temporal logic of linear orders by adding an ordering over displacements.  ...  In this paper we deal with completeness results for basic systems of metric temporal logic --such issues have largely been ignored in the literature.  ...  In Section 3, we characterize the class of two-sorted frames with a linearly ordered temporal domain. 2 The basic metric logic In this section we define the minimal metric temporal logic MTLo, and consider  ... 
doi:10.1007/3-540-60043-4_66 fatcat:hsr3ats2izawdhx6zjil4bn4zq

Temporal Pattern Specifications for Self-Adaptive Requirements

Ayoub Yahiaoui, Hakim Bendjenna, Philippe Roose, Lawrence Chung, Mohamed Amroune
2019 Recent Patents on Computer Science  
Its semantics are presented in terms of fuzzy logic.  ...  One case study reviews the Smart fridge in ambient assisted living and the second case study is focused on an ambulance dispatching system using a developed support tool.  ...  APPENDIX 1 PSAS Semantics in Terms of FMTL In the following, the truth value of each formula is a possibility value [0,1]. The threshold of truth can be defined according to need in [0,1].  ... 
doi:10.2174/2213275911666181019115744 fatcat:xg7ioxe4rbcgregaoxy7uwqypy

Online Motion Planning with Soft Metric Interval Temporal Logic in Unknown Dynamic Environment [article]

Zhiliang Li, Mingyu Cai, Shaoping Xiao, Zhen Kan
2021 arXiv   pre-print
The metric interval temporal logic (MITL) specifications are employed to deal with time-bound constraints.  ...  However, research of formal languages involving timed temporal logic is still under investigation.  ...  Metric Interval Temporal Logic much as possible.  ... 
arXiv:2110.09007v3 fatcat:c7eihdiqfbffnjl5zllzzbh5x4

Ontologies of Time: Review and Trends

Vadim Ermolayev, Sotiris Batsakis, Natalya Keberle, Olga Tatarintseva, Grigoris Antoniou
2014 International Journal of Computer Science and Applications  
Further, the temporal logics, representation languages, and ontologies available to date, have been reviewed regarding their usability aspects and the coverage of the selected temporal features.  ...  The results reveal that the reviewed ontologies of time taken together do not satisfactorily cover some important features: (i) density; (ii) relaxed linearity; (iii) scale factors; (iv) proper and periodic  ...  Acknowledgements The research leading to this paper has been done in frame of the EU FP7 Marie Curie IRSES SemData project (, grant agreement No PIRSES-GA-2013-612551.  ... 
dblp:journals/ijcsa/ErmolayevBKTA14 fatcat:y3ofxgb3yjdspgzk7xyygzbplu

Two-sorted metric temporal logics

Angelo Montanaria, Maarten de Rijkeb
1997 Theoretical Computer Science  
Then, we show how to obtain the metric temporal logic of linear orders by adding an ordering over displacements.  ...  In this paper we deal with completeness issues for basic systems of metric temporal logic -despite their relevance, such issues have been ignored or only partially addressed in the literature.  ...  We traced a sort of preferred path from the minimal metric temporal logic MT.& to the quantified metric temporal logic Q-MT& passing through the (unquantified) metric temporal logic of linear orders MTL2  ... 
doi:10.1016/s0304-3975(96)00324-6 fatcat:jtog442npvft7d773fmcjvjnjy

Vehicle Routing Problem with Metric Temporal Logic Specifications

Sertac Karaman, Emilio Frazzoli
2008 2008 47th IEEE Conference on Decision and Control  
For the resulting Vehicle Routing Problem with Metric Temporal Logic Specifications (VRPMTL), a Mixed-Integer Linear Programming (MILP) based algorithm is provided that solves the problem to optimality  ...  Instead of servicing all the customers, feasible solutions of the VRP instance are forced to satisfy a set of complex high-level tasks given as a Metric Temporal Logic (MTL) specification, which allows  ...  ACKNOWLEDGMENTS This work was supported in part by the Michigan/AFRL Collaborative Center on Control Sciences.  ... 
doi:10.1109/cdc.2008.4739366 dblp:conf/cdc/KaramanF08 fatcat:rnuhf4pfqbfcdfmzescc7k3vuu

Goal-Oriented Monitoring Adaptation: Methodology and Patterns [chapter]

Antoine Toueir, Julien Broisin, Michelle Sibilla
2014 Lecture Notes in Computer Science  
One of the advantages of adopting a methodological approach, is that monitoring reconfiguration will be conducted through a consistent adaptation logic.  ...  the Quality of Information (QoI).  ...  Those patterns refine Achieve goals of the form P ⇒ ♦Q (see Table 1 ), and written in Linear Temporal Logic (LTL) classical operators where ♦, and W mean respectively some time in the future, always in  ... 
doi:10.1007/978-3-662-43862-6_17 fatcat:kiuex2hhejhohbn4tlbfnx5cve

Interval Temporal Logics: a Journey

Dario Della Monica, Valentin Goranko, Angelo Montanari, Guido Sciavicco
2011 Bulletin of the European Association for Theoretical Computer Science  
logics as compared to point-based ones.  ...  Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in it over the past 10 years and outline some landmark results on expressiveness  ...  researchers in the area of interval temporal logics.  ... 
dblp:journals/eatcs/MonicaGMS11 fatcat:mlerxzwp6ncqzegftg3djo7dfy

Page 7115 of Mathematical Reviews Vol. , Issue 97K [page]

1997 Mathematical Reviews  
An EXPSPACE- complete temporal logic (MITL—metric interval temporal logic) is introduced.  ...  Summary: “We determine the complexity of testing whether a finite state, sequential or concurrent probabilistic program satis- fies its specification expressed in linear-time temporal logic.  ... 

Benchmarking Noise Extrapolation with OpenPulse [article]

J. W. O. Garmon, R. C. Pooser, E. F. Dumitrescu
2019 arXiv   pre-print
In order to augment digital qubit metrics, such as gate fidelity, we discuss analog error mitigability, i.e. the ability to accurately distill precise observable estimates, as a hybrid quantum-classical  ...  Our results identify regions in the space of Hamiltonian control fields and circuit-depth which are most amenable to reliable noise extrapolation, as well as shedding light on how low-level hardware characterization  ...  In this setting, additional errors accumulate due to a longer evolution and the modified noise factor increases linearly in the temporal stretch factor.  ... 
arXiv:1909.05219v1 fatcat:jpl55guv3facriubqqxnsc6vxu
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