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A New One-Pass Tableau Calculus for PLTL [chapter]

Stefan Schwendimann
<span title="">1998</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;
The paper presents a one-pass tableau calculus PLTLT for the propositional linear time logic PLTL.  ...  It may thus be a suitable starting point for the development of a parallel decision method for PLTL.  ...  Conclusion We have presented a new one-pass tableau calculus for PLTL which works, as most modal calculi, on trees rather than graphs .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-69778-0_28">doi:10.1007/3-540-69778-0_28</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4lsbnbiysraxjcwk5w3nds4nxu">fatcat:4lsbnbiysraxjcwk5w3nds4nxu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190226081619/http://pdfs.semanticscholar.org/7bac/569bf9284e306bd665b76e4530138bf22267.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/7b/ac/7bac569bf9284e306bd665b76e4530138bf22267.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-69778-0_28"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Towards Certified Model Checking for PLTL Using One-Pass Tableaux

Alex Abuin, Alexander Bolotov, Unai Díaz De Cerio, Montserrat Hermo, Paqui Lucio, Michael Wagner
<span title="2019-10-15">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5notxo7dsndjfej4w6752adxc4" style="color: black;">International Symposium/Workshop on Temporal Representation and Reasoning</a> </i> &nbsp;
The paper argues that one-pass (context-based) tableau for PLTL can be efficiently used in the CMC setting, emphasising the following two advantages of this technique.  ...  The combination of the one-pass tableau and the dual sequent calculus enables us to provide not only counter-examples for unsatisfied properties, but also proofs for satisfied properties that can be checked  ...  We abbreviate the one-pass tableau method as τ ↑ pltl and its dual sequent calculus as TTC.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.time.2019.12">doi:10.4230/lipics.time.2019.12</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/time/AbuinBDHL19.html">dblp:conf/time/AbuinBDHL19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bnbnyj6xvffyrjwzbyg4wdalri">fatcat:bnbnyj6xvffyrjwzbyg4wdalri</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200219022236/https://drops.dagstuhl.de/opus/volltexte/2019/11370/pdf/LIPIcs-TIME-2019-12.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/c8/3c/c83cd9442f8cf60f669692fb440ae2414a6f1cf7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.time.2019.12"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Dual Systems of Tableaux and Sequents for PLTL

Jose Gaintzarain, Montserrat Hermo, Paqui Lucio, Marisa Navarro, Fernando Orejas
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/anq6kvwvqbegtipq5vfhvonzqq" style="color: black;">The Journal of Logic and Algebraic Programming</a> </i> &nbsp;
This tableau method TTM is directly associated to a one-sided sequent calculus called TTC.  ...  On one hand, traditional tableau systems for temporal logic (TL) generate an auxiliary graph that must be checked and (possibly) pruned in a second phase of the refutation procedure.  ...  kinds of extensions of PLTL such as the modal µ-calculus, and so on.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jlap.2009.05.001">doi:10.1016/j.jlap.2009.05.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5prtdwaag5c5jmwjbnnay3lj54">fatcat:5prtdwaag5c5jmwjbnnay3lj54</a> </span>
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Resolution-Based Model Construction for PLTL

Michel Ludwig, Ullrich Hustadt
<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;
In this paper we present a resolution-based approach for constructing models for satisfiable PLTL formulae.  ...  Our approach is based on using the standard model construction for sets of propositional clauses saturated under ordered resolution in the different time points of a temporal model.  ...  Another type of proof methods for PLTL are, for instance, tableauxbased approaches [5] and an implementation of a one-pass tableau calculus [6] exists in the Logics Workbench [7] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/time.2009.11">doi:10.1109/time.2009.11</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/time/LudwigH09.html">dblp:conf/time/LudwigH09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lawqgxinjnfklmxgdx3qh4feo4">fatcat:lawqgxinjnfklmxgdx3qh4feo4</a> </span>
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Propositional Temporal Proving with Reductions to a SAT Problem [chapter]

Richard Williams, Boris Konev
<span title="">2013</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 present a new approach to reasoning in propositional linear-time temporal logic (PLTL). The method is based on the simplified temporal resolution calculus.  ...  We describe an implementation of the method using the CAMUS system for MUS computation and present an in-depth comparison of the performance of the new solver against a clausal temporal resolution prover  ...  Conclusions and future work In this paper we have investigated a new approach to PLTL reasoning based on reductions to MUS enumeration.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-38574-2_30">doi:10.1007/978-3-642-38574-2_30</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/w3c47khtgzdt7gifkhjtmkipa4">fatcat:w3c47khtgzdt7gifkhjtmkipa4</a> </span>
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A resolution calculus for the branching-time temporal logic CTL

Lan Zhang, Ullrich Hustadt, Clare Dixon
<span title="2014-03-06">2014</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3kjjbv4edjbezl2w37ipy5lo5a" style="color: black;">ACM Transactions on Computational Logic</a> </i> &nbsp;
Here we present a resolution calculus for CTL that involves the translation of formulae to a normal form and the application of a number of resolution rules.  ...  We show that the translation preserves satisfiability, the calculus is sound, complete, and terminating, and consider the complexity of the calculus.  ...  ACKNOWLEDGMENTS The authors would like to thank the anonymous referees for their helpful comments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2529993">doi:10.1145/2529993</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yfvsxyxcebdnvow2wspi2xsuma">fatcat:yfvsxyxcebdnvow2wspi2xsuma</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170815102231/http://cgi.csc.liv.ac.uk/~ullrich/publications/Zhang+Hustadt+Dixon@ToCL2014.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/24/bf/24bf97bf3163564a0eab1e4e8a1a921e51e6ab05.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2529993"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Page 3684 of Mathematical Reviews Vol. , Issue 99f [page]

<span title="">1999</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;
99f:03003 Kreitz, Deleting redundancy in proof reconstruction (262-276); Stefan Schwendimann, A new one-pass tableau calculus for PLTL (277-291); Klaus Weich, Decision procedures for intuitionistic propositional  ...  This result holds only for first-order logic without identity. The paper gives an analogous result for a logic with identity.  ... 
<span class="external-identifiers"> </span>
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An Optimal On-the-Fly Tableau-Based Decision Procedure for PDL-Satisfiability [chapter]

Rajeev Goré, Florian Widmann
<span title="">2009</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 present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (P DL) which builds a finite rooted tree with ancestor loops and passes extra information from children  ...  It is easy to implement, with potential for parallelisation, because it constructs a pseudo-model "on the fly" by exploring each tableau branch independently.  ...  Generality: Our method for P DL fits into a class of similar "one pass" methods for other fix-point logics like PLTL [17] and CTL [1] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02959-2_32">doi:10.1007/978-3-642-02959-2_32</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nq72quy365bqrnospzdg345dny">fatcat:nq72quy365bqrnospzdg345dny</a> </span>
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Ockhamist Propositional Dynamic Logic: A Natural Link between PDL and CTL* [chapter]

Philippe Balbiani, Emiliano Lorini
<span title="">2013</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;
More generally, the semantics on which OPDL is based provides a unifying framework for making the dynamic logic family and the temporal logic family converge in a single logical framework.  ...  We present a new logic called Ockhamist Propositional Dynamic Logic, OPDL, which provides a natural link between PDL and CTL * .  ...  For example the specification for the tableau method for BCTL * proposed by [23] was much simpler than the CTL * tableau that originated from it [24] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-39992-3_22">doi:10.1007/978-3-642-39992-3_22</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/km2vbcafijdpdalx3st4apun2q">fatcat:km2vbcafijdpdalx3st4apun2q</a> </span>
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Using temporal logics of knowledge for specification and verification—a case study

Clare Dixon
<span title="">2006</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/gyhc4ppmyjfm5a64dneqesv7ka" style="color: black;">Journal of Applied Logic</a> </i> &nbsp;
We show how to specify Cluedo using temporal logics of knowledge and prove statements about the knowledge of the players using a clausal resolution calculus for this logic.  ...  Temporal logics of knowledge are useful for reasoning about situations where the knowledge of an agent or component is important, and where change in this knowledge may occur over time.  ...  Reasoning for combinations of PLTL and epistemic logics above been carried out also using tableau calculi, see for example [33] for combinations for epistemic and belief logics with PLTL, and [34]  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jal.2005.08.003">doi:10.1016/j.jal.2005.08.003</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/do3n7d5gyzdbdi6e5zkdzz4jwm">fatcat:do3n7d5gyzdbdi6e5zkdzz4jwm</a> </span>
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Theorem Proving for Pointwise Metric Temporal Logic Over the Naturals via Translations

Ullrich Hustadt, Ana Ozaki, Clare Dixon
<span title="2020-02-19">2020</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2ewief65xnegfh2slwulpgsnba" style="color: black;">Journal of automated reasoning</a> </i> &nbsp;
In particular, we present two approaches for translating from MTL to LTL which preserve the ExpSpace complexity of the satisfiability problem for MTL.  ...  Our translations allow us to utilise LTL solvers to solve satisfiability and we empirically compare the translations, showing in which cases one performs better than the other.  ...  The tree method is again based on Schwendimann's one-pass tableau calculus, the graph method is based on a one-pass and-or tree tableau calculus [26] resulting in a time complexity optimal decision procedure  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10817-020-09541-4">doi:10.1007/s10817-020-09541-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pqz4xkmztbcapm2gm32bq2kzrq">fatcat:pqz4xkmztbcapm2gm32bq2kzrq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200509134315/https://link.springer.com/content/pdf/10.1007/s10817-020-09541-4.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/05/1b/051b93d663929d39bfcddd00ef655288c617f63e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10817-020-09541-4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

An On-the-fly Tableau-based Decision Procedure for PDL-satisfiability

Pietro Abate, Rajeev Goré, Florian Widmann
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
Ease of generating proofs: our tableau calculus can be turned into a cut-free Gentzen-style calculus with "cyclic proofs".  ...  We present a tableau-based algorithm for deciding satisfiability for propositional dynamic logic (PDL) which builds a finite rooted tree with ancestor cycles and which passes extra information from children  ...  Generality: Our method for PDL fits into a class of similar "one pass" methods for other fix-point logics like PLTL [18] and CTL [1] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2009.02.036">doi:10.1016/j.entcs.2009.02.036</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jfvhzqk4kvgcvite7tl5ul4o5y">fatcat:jfvhzqk4kvgcvite7tl5ul4o5y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705103627/http://twb.rsise.anu.edu.au/files/abate-gore-widmann-pdl-m4m07.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/0b/e4/0be4bbbec5edeaff099bcb4157e90decae3d949f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2009.02.036"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

First-Order LTL Model Checking Using MDGs [chapter]

Fang Wang, Sofiène Tahar, Otmane Ait Mohamed
<span title="">2004</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;
In this paper, we describeafi rst-order linear time temporal logic (LTL) model checkerb ased on multiway decision graphs (MDG).  ...  We developed afi rst-order temporal language, L MDG * ,w hiche xpresses asubset of many-sorted first-order LTLand extends an earlier language, L MDG ,d efined for an MDG based abstractC TL model checking  ...  Although these procedures are based on the same tableau construction method, Wring improveso no thersb ya pplying rewriting on theP LTLf ormula and simplifying the result GBA.  ... 
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Theorem Proving for Metric Temporal Logic over the Naturals [chapter]

Ullrich Hustadt, Ana Ozaki, Clare Dixon
<span title="">2017</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In particular, we present two approaches for translating from MTL to LTL which preserve the ExpSpace complexity of the satisfiability problem for MTL.  ...  In each of these approaches we consider the case where the mapping between states and time points is given by (1) a strict monotonic function and by (2) a non-strict monotonic function (which allows multiple  ...  With the pltl [21] system we have used the graph method which is based on a one-pass and-or tree tableau calculus [13] and is time complexity optimal for LTL.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-63046-5_20">doi:10.1007/978-3-319-63046-5_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iahhcdxyhbhhlmtjltdy3j2bba">fatcat:iahhcdxyhbhhlmtjltdy3j2bba</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190304180116/http://pdfs.semanticscholar.org/ca04/cde35a4c22be7f51cae82256c9ad0ef5f619.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/ca/04/ca04cde35a4c22be7f51cae82256c9ad0ef5f619.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-63046-5_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

An axiomatization of full Computation Tree Logic

M. Reynolds
<span title="">2001</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4l7nckgxmbcgvj5vxsioq6qwyq" style="color: black;">Journal of Symbolic Logic (JSL)</a> </i> &nbsp;
We give a sound and complete axiomatization for the full computation tree logic. CTL*, of R-generable models. This solves a long standing open problem in branching time temporal logic.  ...  We can also mention that an automaton is used to deal with infinite paths in a tableau refutation in [Walukiewicz, 1995] in the proof of completeness for an axiom system for the modal ul-calculus.  ...  For each t E T we shall write [t] for the --class Note that as (T, <, _) is floored, with [Xo] as the floor, for every s E S there is a fullpath starting at [Xo] and passing through s. 14.2.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829134039/http://researchrepository.murdoch.edu.au/id/eprint/12272/1/axiomatization_of_full_computation_tree_logic.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/9e/08/9e083657c5ec0a2de0ef441538f3eb9d62bc5f99.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2695091"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>
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