research-article

Horn Fragments of the Halpern-Shoham Interval Temporal Logic

Authors:

Davide Bresolin,

Emilio Muñoz-Velasco,

Vladislav Ryzhikov,

Guido Sciavicco,

Michael ZakharyaschevAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 18, Issue 3

Article No.: 22, Pages 1 - 39

https://doi.org/10.1145/3105909

Published: 11 August 2017 Publication History

Abstract

We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.

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Wałęga PZawidzki MHaase CMarquis PSon TKern-Isberner G(2023)Computing all facts entailed by an LTL specificationProceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning10.24963/kr.2023/66(679-689)Online publication date: 2-Sep-2023
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Index Terms

Horn Fragments of the Halpern-Shoham Interval Temporal Logic
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
2. Theory of computation

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cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 18, Issue 3

July 2017

273 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3130378

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

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Publication History

Published: 11 August 2017

Accepted: 01 April 2017

Revised: 01 March 2017

Received: 01 May 2016

Published in TOCL Volume 18, Issue 3

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“iTract: Islands of Tractability in Ontology-Based Data Access”
INDAM-GNCS project 2017 “Logics and Automata for Interval Model Checking”
EPSRC UK project
Spanish project

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Pagliarini GScaboro SSerra GSciavicco GStan I(2024)Neural-symbolic temporal decision trees for multivariate time series classificationInformation and Computation10.1016/j.ic.2024.105209(105209)Online publication date: Aug-2024
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Wałęga PZawidzki MHaase CMarquis PSon TKern-Isberner G(2023)Computing all facts entailed by an LTL specificationProceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning10.24963/kr.2023/66(679-689)Online publication date: 2-Sep-2023
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https://doi.org/10.1080/22797254.2023.2262738
Conradie WDella Monica DMuñoz-Velasco ESciavicco GStan I(2023)Fuzzy Halpern and Shoham's interval temporal logicsFuzzy Sets and Systems10.1016/j.fss.2022.05.014456(107-124)Online publication date: Mar-2023
https://doi.org/10.1016/j.fss.2022.05.014
Wałęga P(2023)Computational complexity of hybrid interval temporal logicsAnnals of Pure and Applied Logic10.1016/j.apal.2022.103165174:1(103165)Online publication date: Jan-2023
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Brandt SKalayci ERyzhikov VXiao GZakharyaschev M(2019)Querying log data with metric temporal logicJournal of Artificial Intelligence Research10.1613/jair.1.1122962:1(829-877)Online publication date: 17-Apr-2019
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Wałęga P(2019)Hybrid fragments of Halpern–Shoham logic and their expressive powerTheoretical Computer Science10.1016/j.tcs.2019.01.014Online publication date: Jan-2019
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Muñoz-Velasco EPelegrín MSala PSciavicco GStan I(2019)On coarser interval temporal logicsArtificial Intelligence10.1016/j.artint.2018.09.001266(1-26)Online publication date: Jan-2019
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