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B and D Are Enough to Make the Halpern–Shoham Logic Undecidable [chapter]

Jerzy Marcinkowski, Jakub Michaliszyn, Emanuel Kieroński
2010 Lecture Notes in Computer Science  
We contribute to this eort by showing (among other results), that the fragment (where only the operators begins and during are allowed) is undecidable over discrete structures.  ...  The HalpernShoham logic is a modal logic of time intervals.  ...  In their paper, Halpern and Shoham show that (satisability of formulae of ) their logic is undecidable.  ... 
doi:10.1007/978-3-642-14162-1_30 fatcat:iio2hhom7vhd3ft6dn6c6jjgci

The Last Paper on the Halpern-Shoham Interval Temporal Logic [article]

Jerzy Marcinkowski, Jakub Michaliszyn
2010 arXiv   pre-print
The Halpern-Shoham logic is a modal logic of time intervals.  ...  We contribute to this effort by showing - what we believe is quite an unexpected result - that the logic of subintervals, the fragment of the Halpern-Shoham where only the operator "during", or D, is allowed  ...  The operator O can be expressed using E and B. In their paper, Halpern and Shoham show that (satisfiability of formulae of) their logic is undecidable.  ... 
arXiv:1010.4529v1 fatcat:tdr7vzuqbbhjbnhwkjdp3f3tba

Hybridizing Interval Temporal Logics: The First Step

Przemysław Wałęga
2017 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
My main result is that the satisfiability problem in a hybridized fragment of Halpern-Shoham logic in which formulas are in a form of conjunction of Horn clauses and only box modal operators are allowed  ...  My work revolves around the latter type of methods which seem to be more human-like and more suitable for such applications as continuous process modelling.  ...  The author is supported by the Polish National Science Centre grant DEC-2011/02/A/HS1/00395.  ... 
doi:10.1609/aaai.v31i1.11108 fatcat:66vmcmyczbax3hmy56r4quy4ea

Interval Temporal Logics: a Journey

Dario Della Monica, Valentin Goranko, Angelo Montanari, Guido Sciavicco
2011 Bulletin of the European Association for Theoretical Computer Science  
The formulae of these logics are evaluated at intervals rather than points and the main effect of that semantic feature is substantially higher expressiveness and computational complexity of the interval  ...  and (un)decidability of the satisfiability problem for the family of interval logics.  ...  Sciavicco), and the Italian PRIN project Innovative and multi-disciplinary approaches for constraint and preference reasoning (D. Della Monica, A. Montanari).  ... 
dblp:journals/eatcs/MonicaGMS11 fatcat:mlerxzwp6ncqzegftg3djo7dfy

Decidable and Undecidable Fragments of Halpern and Shoham's Interval Temporal Logic: Towards a Complete Classification [chapter]

Davide Bresolin, Dario Della Monica, Valentin Goranko, Angelo Montanari, Guido Sciavicco
2008 Lecture Notes in Computer Science  
The full modal logic of Allen's relations, called HS, has been proved to be undecidable by Halpern and Shoham under very weak assumptions on the class of interval structures, and this result was discouraging  ...  This paper contributes to the characterization of the boundary between decidability and undecidability of HS fragments.  ...  Theorem 1 (Halpern and Shoham The undecidability of the satisfiability problem for HS in all the classes Theorem 1 refers to immediately follows.  ... 
doi:10.1007/978-3-540-89439-1_41 fatcat:e4jc64cttrh6pm42d4j6admzfu

Horn Fragments of the Halpern-Shoham Interval Temporal Logic

Davide Bresolin, Agi Kurucz, Emilio Muñoz-Velasco, Vladislav Ryzhikov, Guido Sciavicco, Michael Zakharyaschev
2017 ACM Transactions on Computational Logic  
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  ...  Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.  ...  Here we show that HS ✷ horn has sufficient counting power to make it undecidable (Theorem 4.5), and that even the seemingly very limited expressiveness of HS ✷ core is still enough to make it PSPACE-hard  ... 
doi:10.1145/3105909 fatcat:t3usanf765fxxhr3ximldikmy4

Decidability of Model Checking Multi-Agent Systems with Regular Expressions against Epistemic HS Specifications

Jakub Michaliszyn, Piotr Witkowski
2019 Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence  
Epistemic Halpern-Shoham logic (EHS) is an interval temporal logic defined to verify properties of Multi-Agent Systems.  ...  We achieve this by reducing the model checking problem to the satisfiability problem of Monadic Second-Order Logic on trees.  ...  Acknowledgements The first author was supported by Polish National Science Centre grant 2014/15/D/ST6/00719.  ... 
doi:10.24963/ijcai.2019/659 dblp:conf/ijcai/Michaliszyn019 fatcat:6zjlwgyq6fczhfeik3vrcgdybe

A First Study of the Horn Fragment of the Modal Logic of Time Intervals

Davide Bresolin, Emilio Muñoz-Velasco, Guido Sciavicco
2014 Italian Conference on Computational Logic  
The most influential propositional interval-based logic is probably Halpern's and Shoham Modal Logic of Time Intervals, a.k.a. HS.  ...  Here, we approach this problem by considering the Horn fragment of HS and proving that the satisfiability problem remains undecidable, at least for discrete linear orders.  ...  Hence, we can assume w.l.o.g. that all configurations have the same length and that they are long enough to contain the relevant part of the tape. hAiu ^[U ](u ! (hAiu ^[B]?))  ... 
dblp:conf/cilc/BresolinMS14 fatcat:dup7235cmjadpif3a7mql4tsjm

Modal Logics of Topological Relations

Carsten Lutz, Frank Wolter, Yde Venema
2006 Logical Methods in Computer Science  
As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham.  ...  The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological  ...  Acknowledgement The authors wish to acknowledge helpful comments from two anonymous referees.  ... 
doi:10.2168/lmcs-2(2:5)2006 fatcat:pvfw5gxoffcllendypyk6dahna

Reasoning with Time Intervals: A Logical and Computational Perspective

Guido Sciavicco
2012 ISRN Artificial Intelligence  
point of view, to Allen (1983) from the algebraic and first-order one, and to Halpern and Shoham (1991) from the modal logic one.  ...  and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of modal interval logics.  ...  Acknowledgments The author would like to thank the editorial board of the International Scholarly Research Network for this invitation to publish a spotlight paper and the Spanish MEC Projects TIN2009-  ... 
doi:10.5402/2012/616087 fatcat:dnfestytkfcilcjpfuq7aqmplq

Representing and reasoning with events from natural language [chapter]

Miguel Leith, Jim Cunningham
1997 Lecture Notes in Computer Science  
Following on from the work of Moens and Steedman and the later work of Kent, we have identi ed a fragment of an interval tense logic of Halpern and Shoham that is expressive enough to represent the temporal  ...  Linguistic categories such as progressives, perfectives, tense and temporal adverbials are at the heart of our ability to describe events in natural language.  ...  Operators of HS That Are of Immediate Use to Us It has been shown by Halpern and Shoham in 3] that the validity problem in HS logic is undecidable in all but the simplest classes of frames such as nite  ... 
doi:10.1007/bfb0035638 fatcat:f6kxruvxa5azbiybdjmz24bdii

Hybrid Metric Propositional Neighborhood Logics with Interval Length Binders

Dario Della Monica, Valentin Goranko, Guido Sciavicco
2011 Electronical Notes in Theoretical Computer Science  
We investigate the question of how much hybrid machinery can be added to the interval neighbourhood logic PNL and its metric extension MPNL without losing the decidability of their satisfiability problem  ...  and further references to it.  ...  In [16] , Halpern and Shoham introduced a multi-modal logic, hereafter called HS, involving modal operators corresponding to all Allen's interval relations and showed that such a logic is undecidable  ... 
doi:10.1016/j.entcs.2011.06.009 fatcat:imdcxtvcrjfr5dusv52faaekfq

Undecidability of the Logic of Overlap Relation over Discrete Linear Orderings

Davide Bresolin, Dario Della Monica, Valentin Goranko, Angelo Montanari, Guido Sciavicco
2010 Electronical Notes in Theoretical Computer Science  
That, in particular, holds for most fragments of Halpern and Shoham's interval modal logic HS.  ...  The validity/satisfiability problem for most propositional interval temporal logics is (highly) undecidable, under very weak assumptions on the class of interval structures in which they are interpreted  ...  The first major step in this direction was taken by Halpern and Shoham themselves in their original paper, where they show that undecidability results for HS hold even if one restricts the logic to its  ... 
doi:10.1016/j.entcs.2010.04.006 fatcat:cpdnt7iuwjf4ngnyd4lfhez4hy

A Multi-Valued Simplified Halpern–Shoham–Moszkowski Logic for Gradable Verifiability in Reasoning about Digital Circuits

Krystian Jobczyk
2021 Electronics  
In 1991, Halpern and Shoham proposed a new temporal system (HS) to describe external relations between intervals.  ...  Moszkowski introduced a first interval-interpreted temporal logic system, the so-called Interval Temporal Logic (ITL), as a system suitable to express mutual relations inside intervals for reasonings about  ...  Acknowledgments: The author would like to thank Antoni for his permanent encouragement to write and think like an engineer.  ... 
doi:10.3390/electronics10151817 fatcat:mucpzlhlvnewdc3blvulrju5vu

Model Checking Systems Against Epistemic Specifications

Alessio R. Lomuscio
2014 Electronic Proceedings in Theoretical Computer Science  
To do so we introduce a further temporal-epistemic logic, called EHS RE , in which regular expressions are used within propositions, and give a polynomial time reduction of the model checking problem from  ...  EHS RE to EHS + .  ...  Acknowledgments The authors would like to thank Angelo Montanari whose comments on (Lomuscio and Michaliszyn 2014) led to the present investigation.  ... 
doi:10.4204/eptcs.146.0.3 fatcat:56n3cvwokfe4hjswl2al3ta2p4
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