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Decidability of the Interval Temporal Logic ABB over the Natural Numbers

Angelo Montanari, Gabriele Puppis, Pietro Sala, Guido Sciavicco, Marc Herbstritt
2010 Symposium on Theoretical Aspects of Computer Science  
In this paper, we focus our attention on the interval temporal logic of the Allen's relations "meets", "begins", and "begun by" (ABB for short), interpreted over natural numbers.  ...  Then, we prove that the satisfiability problem for ABB over natural numbers is decidable by providing a small model theorem based on an original contraction method.  ...  Guido Sciavicco has also been supported by the Spain/South Africa Integrated Action N. HS2008-0006 on: "Metric interval temporal logics: Theory and Applications".  ... 
doi:10.4230/lipics.stacs.2010.2488 dblp:conf/stacs/MontanariSS10 fatcat:t5kedcasl5ejtbxxm6wopnvqay

DECIDABILITY OF THE INTERVAL TEMPORAL LOGIC ABB OVER THE NATURAL NUMBERS

Angelo Montanari, Gabriele Puppis, Pietro Sala, Guido Sciavicco
2010 Symposium on Theoretical Aspects of Computer Science   unpublished
In this paper, we focus our attention on the interval temporal logic of the Allen's relations "meets", "begins", and "begun by" (ABB for short), interpreted over natural numbers.  ...  Then, we prove that the satisfiability problem for ABB over natural numbers is decidable by providing a small model theorem based on an original contraction method.  ...  We interpret formulas of ABB in interval temporal structures over natural numbers endowed with the relations "meets", "begins", and "begun by".  ... 
fatcat:tsrdp3jlrfcovlb63vqkot7kd4

Decidability of the interval temporal logic ABBar over the natural numbers [article]

A. Montanari, G. Puppis, P. Sala, G. Sciavicco
2010 arXiv   pre-print
In this paper, we focus our attention on the interval temporal logic of the Allen's relations "meets", "begins", and "begun by" (ABBar for short), interpreted over natural numbers.  ...  Then, we prove that the satisfiability problem for ABBar over natural numbers is decidable by providing a small model theorem based on an original contraction method.  ...  We interpret formulas of ABB in interval temporal structures over natural numbers endowed with the relations "meets", "begins", and "begun by".  ... 
arXiv:0912.3429v2 fatcat:whtdwhkmf5ch5hr35rb4dc7xsu

Interval-based Synthesis

Angelo Montanari, Pietro Sala
2014 Electronic Proceedings in Theoretical Computer Science  
over finite linear orders and natural numbers.  ...  We introduce the synthesis problem for Halpern and Shoham's modal logic of intervals extended with an equivalence relation over time points, abbreviated HSeq.  ...  for AĀBB over finite linear orders is decidable, but not primitive recursive (and undecidable over the natural numbers).  ... 
doi:10.4204/eptcs.161.11 fatcat:7wvwqxunszgobbltw5xj47vvfy

Reasoning with Time Intervals: A Logical and Computational Perspective

Guido Sciavicco
2012 ISRN Artificial Intelligence  
and outline some landmark results on expressiveness and (un)decidability of the satisfiability problem for the family of modal interval logics.  ...  Without purporting to provide a comprehensive survey of the field, we take the reader to a journey through the main developments in modal and first-order interval temporal reasoning over the past ten years  ...  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

Maximal Decidable Fragments of Halpern and Shoham's Modal Logic of Intervals [chapter]

Angelo Montanari, Gabriele Puppis, Pietro Sala
2010 Lecture Notes in Computer Science  
AĀBB properly extends interesting interval temporal logics recently investigated in the literature, such as the logic BB of Allen's "begun by/begins" relations and propositional neighborhood logic AĀ,  ...  ", and "begins" of Allen's interval algebra (AĀBB logic).  ...  Decidability of the interval temporal logic ABB over the natural numbers. tions of the Association for Computing Machinery, 26(11):832-843, 1983.  ... 
doi:10.1007/978-3-642-14162-1_29 fatcat:acok2rbcefcydbnlg6mkecyin4

ON BEGINS, MEETS AND BEFORE

DAVIDE BRESOLIN, PIETRO SALA, GUIDO SCIAVICCO
2012 International Journal of Foundations of Computer Science  
Interval temporal logics (ITLs) are logics for reasoning about temporal statements expressed over intervals, i.e., periods of time.  ...  We know from previous work that the combination ABBA is decidable only when finite domains are considered (and undecidable elsewhere), and that ABB is decidable over the natural numbers.  ...  the Italian GNCS project "Logics, Automata, and Games for the formal verification of complex systems".  ... 
doi:10.1142/s012905411240028x fatcat:gxpof6dmynebrpkan673qk75hu

Interval Temporal Logics over Strongly Discrete Linear Orders: the Complete Picture

Davide Bresolin, Dario Della Monica, Angelo Montanari, Pietro Sala, Guido Sciavicco
2012 Electronic Proceedings in Theoretical Computer Science  
The number of decidable fragments over natural numbers raises up to 47: three undecidable fragments become decidable with a non-primitive recursive complexity.  ...  In this paper, we identify all fragments of Halpern and Shoham's interval temporal logic HS with a decidable satisfiability problem over the class of strongly discrete linear orders.  ...  Introduction Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly (or partially) ordered domains.  ... 
doi:10.4204/eptcs.96.12 fatcat:5s4cyf6zx5hafavf6nxeo73c5i

On the Complexity of Fragments of the Modal Logic of Allen's Relations over Dense Structures [chapter]

Davide Bresolin, Dario Della Monica, Angelo Montanari, Pietro Sala, Guido Sciavicco
2015 Lecture Notes in Computer Science  
Interval temporal logics provide a natural framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities.  ...  In this paper, we consider all fragments of Halpern and Shoham's interval temporal logic HS with a decidable satisfiability problem over the class of all dense linear orders, and we provide a complete  ...  The distinctive features of interval temporal logics turn out to be useful in these domains.  ... 
doi:10.1007/978-3-319-15579-1_40 fatcat:7vp7a2m3lvddbmutsm5d43bzxe

Begin, After, and Later: a Maximal Decidable Interval Temporal Logic

Davide Bresolin, Pietro Sala, Guido Sciavicco
2010 Electronic Proceedings in Theoretical Computer Science  
Interval temporal logics (ITLs) are logics for reasoning about temporal statements expressed over intervals, i.e., periods of time.  ...  We know from previous works that the combination ABBbarAbar is decidable only when finite domains are considered (and undecidable elsewhere), and that ABBbar is decidable over the natural numbers.  ...  Introduction Interval temporal logics (ITLs) are logics for reasoning about temporal statements expressed over intervals instead of points.  ... 
doi:10.4204/eptcs.25.10 fatcat:fhkxwxtwqvc5tktmzsh7i3xe2q

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.  ...  This is surprising as this logic is decidable over dense orders and its reflexive variant is known to be decidable over discrete structures.  ...  A number of decidability results concerning variants of this logic has been published.  ... 
arXiv:1010.4529v1 fatcat:tdr7vzuqbbhjbnhwkjdp3f3tba

Two-sorted Point-Interval Temporal Logics

Philippe Balbiani, Valentin Goranko, Guido Sciavicco
2011 Electronical Notes in Theoretical Computer Science  
We analyze their expressiveness, comparative to interval-based logics, and the complexity of their satisfiability problems.  ...  There are two natural and well-studied approaches to temporal ontology and reasoning: point-based and interval-based.  ...  Acknowledgement Guido Sciavicco was partially supported by the Spanish MEC project TIN2009-14372-C03-01, and the Spanish fellowship 'Ramon y Cajal' RYC-2011-07821.  ... 
doi:10.1016/j.entcs.2011.10.004 fatcat:djkkub25pvbivlplmtto7yo7sq

Model Checking Epistemic Halpern-Shoham Logic Extended with Regular Expressions [article]

Alessio Lomuscio, Jakub Michaliszyn
2015 arXiv   pre-print
The Epistemic Halpern-Shoham logic (EHS) is a temporal-epistemic logic that combines the interval operators of the Halpern-Shoham logic with epistemic modalities.  ...  We compare the expressive power of EHSre with standard temporal logics.  ...  The second author was generously supported by Polish National Science Center based on the decision number DEC-2011/03/N/ST6/00415. This research was supported by the EPSRC under grant EP/I00520X.  ... 
arXiv:1509.00608v1 fatcat:cq2au6iuyzdnjl57njwh7jj7dm

Model Checking Systems Against Epistemic Specifications

Alessio R. Lomuscio
2014 Electronic Proceedings in Theoretical Computer Science  
We introduce EHS + , a novel temporal-epistemic logic defined on temporal intervals characterised by regular expressions.  ...  We investigate the complexity of verifying multi-agent systems against EHS + specifications for a number of fragments of EHS + with results ranging from PSPACE-completeness to non-elementary time.  ...  This research was funded by the EPSRC under grant EP/I00520X. The second author acknowledges support from the Polish National Science Center, grant 2014/15/D/ST6/00719.  ... 
doi:10.4204/eptcs.146.0.3 fatcat:56n3cvwokfe4hjswl2al3ta2p4

Optimizing away joins on data streams

Lukasz Golab, Theodore Johnson, Nick Koudas, Divesh Srivastava, David Toman
2008 Proceedings of the 2nd international workshop on Scalable stream processing system - SSPS '08  
The basis of the optimization is a powerful but decidable theory in which constraints over data streams can be formulated.  ...  ., client requests and server responses) using temporal join conditions (e.g., within 5 seconds), followed by computation of aggregates (e.g., COUNT) over temporal windows (e.g., every 5 minutes).  ...  number of SYNs, SYN-ACKs and FINs in each 5-minute interval.  ... 
doi:10.1145/1379272.1379282 dblp:conf/edbt/GolabJKST08 fatcat:l5cbhifcjrhc3f4wkbpbebud5e
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