Fuzzy Halpern and Shoham’s interval temporal logics

 

Abstract

The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.

Citation

Please, cite this work as:

[Con+23] W. Conradie, D. Della Monica, E. Mu~noz-Velasco, et al. “Fuzzy Halpern and Shoham’s interval temporal logics”. In: Fuzzy Sets and Systems 456 (2023). Logic (214 p.), pp. 107-124. ISSN: 0165-0114. DOI: https://doi.org/10.1016/j.fss.2022.05.014. URL: https://www.sciencedirect.com/science/article/pii/S0165011422002068.

NoteBibTeX

@Article{CONRADIE2023107,
     title = {Fuzzy Halpern and Shoham’s interval temporal logics},
     journal = {Fuzzy Sets and Systems},
     volume = {456},
     pages = {107-124},
     year = {2023},
     note = {Logic (214 p.)},
     issn = {0165-0114},
     doi = {https://doi.org/10.1016/j.fss.2022.05.014},
     url = {https://www.sciencedirect.com/science/article/pii/S0165011422002068},
     author = {Willem Conradie and Dario {Della Monica} and Emilio Mu{~n}oz-Velasco and Guido Sciavicco and Ionel Eduard Stan},
     keywords = {Fuzzy interval temporal logic, Satisfiability, Expressive power, Finite model checking},
     abstract = {The most representative interval temporal logic, called HS, was introduced by Halpern and Shoham in the nineties. Recently, HS has been proposed as a suitable formalism for modern artificial intelligence applications; however, when dealing with real-life data one is not always able to express temporal relations and propositional labels in a definite, crisp way. In this paper, following the seminal ideas of Fitting and Zadeh, we present a fuzzy generalization of HS, called FHS, that partially solves such problems of expressive power. We study FHS from both a theoretical and an application standpoint: first, we discuss its syntax, semantics, expressive power, and satisfiability problem; then, we define and solve the time series FHS finite model checking problem, to serve as the basis of future applications.},
}

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Fuzzy Halpern and Shoham’s interval temporal logics

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Papers citing this work

The following is a non-exhaustive list of papers that cite this work:

[1] F. Petry. “Intuitionistic Fuzzy Sets for Spatial and Temporal Data Intervals”. In: Information 15.4 (Apr. 2024), p. 240. ISSN: 2078-2489. DOI: 10.3390/info15040240. URL: http://dx.doi.org/10.3390/info15040240.

[2] Y. Salhi and M. Sioutis. “On prime scenarios in qualitative spatial and temporal reasoning”. In: Information and Computation 300 (Oct. 2024), p. 105198. ISSN: 0890-5401. DOI: 10.1016/j.ic.2024.105198. URL: http://dx.doi.org/10.1016/j.ic.2024.105198.