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A Survey on Temporal Logics [article]

Savas Konur
<span title="2011-04-25">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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  ...  This work was partially supported by EPSRC research project EP/F033567.  ...  Temporal formalisms we will analyse include propositional/first-order linear temporal logics, branching temporal logics, partial-order temporal logics and interval temporal logics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.3199v3">arXiv:1005.3199v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nogsv2iggvd5likbkrnmnzpsdu">fatcat:nogsv2iggvd5likbkrnmnzpsdu</a> </span>
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A survey on temporal logics for specifying and verifying real-time systems

Savas Konur
<span title="2013-04-01">2013</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mea4bx5mifbxdbgjmmfhl6qbhq" style="color: black;">Frontiers of Computer Science</a> </i> &nbsp;
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  ...  temporal logics and probabilistic temporal logics.  ...  This work was partially supported by EPSRC research project EP/F033567. Some parts of this paper exists in [231] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11704-013-2195-2">doi:10.1007/s11704-013-2195-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5lyaji5wnzbyfdmbxwzbxjosku">fatcat:5lyaji5wnzbyfdmbxwzbxjosku</a> </span>
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Deciding Global Partial-Order Properties

Rajeev Alur, Ken McMillan, Doron Peled
<span title="">2005</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fyhr5xuigbfmdabfoqp2f7lbum" style="color: black;">Formal methods in system design</a> </i> &nbsp;
Temporal logics that are interpreted over partial orders allow specifications relating global snapshots, and permit reduction algorithms to generate only one representative linearization of every possible  ...  Temporal logics that are interpreted over partial orders allow specifications relating global snapshots, and permit reduction algorithms to generate only one representative linearization of every possible  ...  How does one define a temporal logic over partial orders?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10703-005-4592-0">doi:10.1007/s10703-005-4592-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/cfyc7hr5ivefhel4xzs5hfzgie">fatcat:cfyc7hr5ivefhel4xzs5hfzgie</a> </span>
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Interleaving set temporal logic

Shmuel Katz, Doron Peled
<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
A new temporal logic and interpretation are suggested which have features from linear temporal logic, branching time temporal logic, and partial order temporal logic.  ...  For the common partial order derived from sequentiality in execution of each process, the logic will distinguish between nondeterminism due to the parallel execution and nondeterminism due tc !~:a!  ...  In order to show that ISTL* strictly includes linear temporal logic, we first show how to embed a li ear assertion in ISTL*.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(90)90096-z">doi:10.1016/0304-3975(90)90096-z</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ul63pju2zbdhfgd3xztjanjtyi">fatcat:ul63pju2zbdhfgd3xztjanjtyi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190325203927/https://core.ac.uk/download/pdf/82184759.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/79/30/793084b6016b72102d29af746fdcef6d2b59a73d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(90)90096-z"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Axiomatizations for Temporal Epistemic Logic with Perfect Recall over Linear Time

Szabolcs Mikulas, Mark Reynolds, Tim French
<span title="">2009</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5notxo7dsndjfej4w6752adxc4" style="color: black;">2009 16th International Symposium on Temporal Representation and Reasoning</a> </i> &nbsp;
(By uniform flows of time, we mean that time is an arbitrary linear order that is common knowledge to all agents).  ...  The axiomatizations are shown to be sound and complete in the case of arbitrary linear orders and the rationals.  ...  linear orders (the integers), dense linear orders (the rationals) and continuous linear orders (the reals).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/time.2009.18">doi:10.1109/time.2009.18</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/time/MikulasRF09.html">dblp:conf/time/MikulasRF09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z6njc4epjjhrtpeuhsakebuauq">fatcat:z6njc4epjjhrtpeuhsakebuauq</a> </span>
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Modeling concurrency with partial orders

Vaughan Pratt
<span title="">1986</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6ni4hdyv7zdtzjxnzscp53l5ry" style="color: black;">International journal of parallel programming</a> </i> &nbsp;
Concurrency has been expressed variously in terms of formal languages (typically via the shuffle operator), partial orders, and temporal logic, inter alia.  ...  The heart of the approach is a notion of partial string derived from the view of a string as a linearly ordered multiset by relaxing the linearity constraint, thereby permitting partially ordered multisets  ...  The intersection of the linearizations of a partial order is that partial order.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bf01379149">doi:10.1007/bf01379149</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iqmhi2qgffbbzcfxnucdejuvce">fatcat:iqmhi2qgffbbzcfxnucdejuvce</a> </span>
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Temporal theories of reasoning

Joeri Engelfriet, Jan Treur
<span title="">1995</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5dxceprzerhvngc2dulzkx45le" style="color: black;">Journal of Applied Non-Classical Logics</a> </i> &nbsp;
We choose to model the information states by partial models and the patterns either by linear time or branching time temporal models.  ...  The examples indicate that partial temporal logic is a powerful means of describing and formalizing complex reasoning patterns, as the dynamic aspects of reasoning systems are integrated into the static  ...  Temporal Partial Logic In this section we introduce our temporal partial logic, based on branching time structures.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/11663081.1995.10510845">doi:10.1080/11663081.1995.10510845</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7asl6gtzi5h4vglrisnynxp6a4">fatcat:7asl6gtzi5h4vglrisnynxp6a4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811073508/http://www.cs.vu.nl/~wai/Papers/JANCL95TTR.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0e/52/0e52a2c9eefefad881e75dbd909bb49e0d58df07.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/11663081.1995.10510845"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> tandfonline.com </button> </a>

Temporal theories of reasoning

Joeri Engelfriet, Jan Treur
<span title="">1995</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5dxceprzerhvngc2dulzkx45le" style="color: black;">Journal of Applied Non-Classical Logics</a> </i> &nbsp;
We choose to model the information states by partial models and the patterns either by linear time or branching time temporal models.  ...  The examples indicate that partial temporal logic is a powerful means of describing and formalizing complex reasoning patterns, as the dynamic aspects of reasoning systems are integrated into the static  ...  Temporal Partial Logic In this section we introduce our temporal partial logic, based on branching time structures.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/11663081.1995.10510858">doi:10.1080/11663081.1995.10510858</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yx2b2gdh6ffw7dz7mvvzd3lnt4">fatcat:yx2b2gdh6ffw7dz7mvvzd3lnt4</a> </span>
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Page 5557 of Mathematical Reviews Vol. , Issue 94j [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
To this end, we extend the well-known notion of (first-order) hyperdoctrine to include partial maps.  ...  temporal logic.  ... 
<span class="external-identifiers"> </span>
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Page 640 of Mathematical Reviews Vol. , Issue 2000a [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Several temporal logics for par- tial order executions have been shown to be undecidable without the locality assumption [op. cit.].  ...  It al- lows the assessment of a generic kind of temporal operators that cannot be used to make assertions about partially ordered exe- cutions.  ... 
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Page 5547 of Mathematical Reviews Vol. , Issue 95i [page]

<span title="">1995</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
An aim is to use Petri nets to give an understanding of linear logic and give some appraisal of the value of linear logic as a specification logic for Petri nets.  ...  The necessary background information on binary decision diagrams, temporal logic, and model checking has been included in order to make the exposition as self-contained as possible.” Contents: 1.  ... 
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Tense logic and time

Johan van Benthem
<span title="">1984</span> <i title="Duke University Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/un57kpou5jawnm7yjqoeumbno4" style="color: black;">Notre Dame Journal of Formal Logic</a> </i> &nbsp;
Can fundamental temporal postulates be logically derived for these, e.g., linear order? We possess a wealth of temporal ideas and intuitions, and logic should help us in organizing and relating these.  ...  But, in a systematic logical study of temporal ontology, this first act already embodies various choices to be investigated systematically: choices of temporal individuals, relations, and postulates.  ...  Linearity, and indeed already connectedness, exclude relativistic temporal structures as mentioned earlier. Do we want logic to make physically restrictive choices as to the nature of time?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1305/ndjfl/1093870515">doi:10.1305/ndjfl/1093870515</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n3iwqjttabfn7e5byrneohwtoi">fatcat:n3iwqjttabfn7e5byrneohwtoi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20110322032745/http://fenrong.net:80/projects/translation/papers/tenselogicandtime.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/c6/76/c6767f898a341fabc0d40fb4854ad2224828f7fd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1305/ndjfl/1093870515"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Page 1441 of Mathematical Reviews Vol. , Issue 2000b [page]

<span title="">2000</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
to this property of programs.” 2000b:68144 68Q60 03B44 03B70 Bhat, Girish; Peled, Doron (1-BELL; Murray Hill, NJ) Adding partial orders to linear temporal logic.  ...  The temporal logic BPLTL (branching past linear temporal logic) is introduced. A sound and relatively complete proof system for the logic over program transitions is given. M. A.  ... 
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Page 6694 of Mathematical Reviews Vol. , Issue 94k [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
We extend its applicability to the properties of a temporal logic with a possibility operator. The al- gorithm is based on linear programming.  ...  ‘Changes to’ is one operator of a temporal proof calculus which combines Petri nets with a UNITY-like temporal logic.  ... 
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Querying TSQL2 databases with temporal logic [chapter]

Michael H. Böhlen, Jan Chomicki, Richard T. Snodgrass, David Toman
<span title="">1996</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We demonstrate that temporal logic is equal in expressive power to a syntactically defined subset of TSQL2.  ...  The translation from temporal logic to TSQLZ developed here enables a user to write high-level queries which can be evaluated against a spaceefficient representation of the database.  ...  In all cases, one produces the characteristics in essentially the same way: by encoding the linear order in temporal logic. Moreover are added to the formula.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0014161">doi:10.1007/bfb0014161</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wl7ifei6qbccnk4icgcm7krqly">fatcat:wl7ifei6qbccnk4icgcm7krqly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809152828/https://www2.cs.arizona.edu/~rts/pubs/EDBT96.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0f/37/0f379ecbf6b73f35875309707dee450a49e825ec.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0014161"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>
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