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This paper presents an ω-complete proof system for the extension of first order Interval Temporal Logic (ITL, [12, 15, 4] ) by a projection operator [16, 11] . ... An extension of the proof system which is complete for the extension of Duration Calculus (DC ,  ) by projection is also given. ... Research on the topic of this article was partially supported by a fellowship with the International Institute for Software Technology of the United Nations University and Contract No. ...doi:10.1093/logcom/14.2.215 fatcat:w72s6rzlyvgrxn3webbbmzgbxu
Regimantas Pliuskevicius (Vilnius) 2004m:03067 03B44 03B70 Gueley, Dimitar P. (4-BIRM-SC; Birmingham) A complete proof system for first-order interval temporal logic with projection. ... Logic Comput. 14 (2004), no. 2, 215-249. An extension of first-order Interval Temporal Logic (ITL) with a projection operator (denoted as ITL\\) is considered. ...
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability ... (or undecidability) results, expressiveness and proof systems. ... This work was partially supported by EPSRC research project EP/F033567. ...arXiv:1005.3199v3 fatcat:nogsv2iggvd5likbkrnmnzpsdu
Lecture Notes in Computer Science
Interval Temporal Logic (ITL) is a formalism for reasoning about time periods. ... We have developed a complete axiomatization for such a version of quantified ITL over finite domains and can show completeness by representing finite-state automata in ITL and then translating ITL formulas ... Acknowledgments The author thanks Antonio Cau and Jordan Dimitrov for suggesting improvements to the presentation. Moshe Vardi and Wolfgang Thomas also provided helpful advice. ...doi:10.1007/3-540-45022-x_19 fatcat:yymx5f4bifdtpm7wyfdxkirhli
We extrapolate the notions of decidability, axiomatizability, expressiveness, model checking, etc. for each logic analysed. We also provide a comparison of features of the temporal logics discussed. ... Over the last two decades, there has been an extensive study on logical formalisms for specifying and verifying real-time systems. ... This work was partially supported by EPSRC research project EP/F033567. ...arXiv:1005.3200v3 fatcat:xhrrcy26bzeehg7wqvjfikm26e
Petr Jirki (Prague) 96i:03012 03B45 68P15 68Q60 Li, Renwei (P-NUL-AI; Monte da Caparica); Carmo, José On completeness of a positional interval logic with equality, overlap and subinterval relations. ... Summary: “This paper presents an interval-based positional logic and proves its completeness. ...
We survey main developments, results, and open problems on interval temporal logics and duration calculi. ... We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results. ... Science and Technology Agreement, that they have received for the project: "Theory and applications of temporal logics to computer science and artificial intelligence". ...doi:10.3166/jancl.14.9-54 fatcat:svndmwuu6jex5mvhpvslv74v6m
Dutertre [DUT 95] gives two complete proof systems for first-order ÁÌÄ without chop-star for finite time. ... We present a completeness proof for Propositional Interval Temporal Logic (PITL) with finite time which avoids certain difficulties of conventional methods. ... Acknowledgements We thank the anonymous referees for their suggestions and requests for more details which helped to improve the presentation. ...doi:10.3166/jancl.14.55-104 fatcat:rfryn6mn6vhidpxpb4mik74gbe
In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems ... Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. ... Conclusions We presented a sound and complete relational proof system for HS interval temporal logic. ...doi:10.3166/jancl.16.251-277 fatcat:p2nfnh54jbcy3nuyjw54e6wxqa
We first establish the completeness of a system of axioms and proof rules for the operator relative to validity in the extension of DC by neighbourhood formulas, which express the neighbourhood values ... By establishing a relatively complete axiomatisation for the neighbourhood formulas in DC , we then achieve completeness of our system relative to basic DC . ... Introduction The Duration Calculus (DC ) was introduced in [ZHO 91] as a first order temporal logic for reasoning about real-time systems. ...doi:10.3166/jancl.14.149-180 fatcat:6soqnfuxffdvzfi5lkbdgf5yju
In this paper we analyse various temporal formalisms introduced for specification, including propositional/first-order linear temporal logics, branching temporal logics, interval temporal logics, real-time ... We give decidability, axiomatizability, expressiveness, model checking results for each logic analysed. We also provide a comparison of features of the temporal logics discussed. ... This work was partially supported by EPSRC research project EP/F033567. Some parts of this paper exists in  . ...doi:10.1007/s11704-013-2195-2 fatcat:5lyaji5wnzbyfdmbxwzbxjosku
Corsetti, A. Montanari and P. San Pietro, Embedding time granularity in a logical specification language for synchronous real-time systems, Science of Computer Programming 20 (1993) 141-171. ... Acknowledgements We thank Dino Mandrioli, Angelo Morzenti, and Elena Ratto for the useful discussions and the anonymous referees for their helpful and perceptive suggestions ... First, a formal proof of completeness for the logical system is needed if we want to use it to derive proofs of properties of specifications. ...doi:10.1016/0167-6423(93)90025-k fatcat:nkiayrtu2fczbaeppyv52ducoq
Summary: “The connection among temporal logic, first-order logic and formal language theory is well known in the context of propo- sitional temporal logic (PTL). ... In the present paper the situation is analyzed for the propositional interval temporal logic (ITL), which has been used for the specification of digital circuits. ...
Proof details in: HS: a multimodal logic with modal operators associated with Allen's interval relations. ... A difficult proof of undecidability via tiling of the Compass Logic Compass Logic [Venema'90]: a two-dimensional modal logic interpreted on products of two linear orders, with modal operators for ... PostScriptum: Terminator vs Turing Terminator: research project at Microsoft Research, Cambridge, focused on the development of automatic methods for proving program termination and general liveness properties ...doi:10.1109/time.2012.26 dblp:conf/time/Goranko12 fatcat:jh2ipoolprhjni2gnrzkrdcr3m
We show that MPNL is decidable in double exponential time and expressively complete with respect to a well-defined subfragment of the two-variable fragment FO 2 [N, =, <, s] of first-order logic for linear ... Interval temporal logics formalize reasoning about interval structures over (usually) linearly ordered domains, where time intervals are the primitive ontological entities and truth of formulae is defined ... Montanari), the Italian GNCS project Logics, automata, and games for the formal verification of complex systems (D. Bresolin, D. Della Monica, A. Montanari, G. ...doi:10.3233/978-1-60750-606-5-695 dblp:conf/ecai/BresolinMGMS10 fatcat:hjsfpppxincaxjft6wkull7bhm
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