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Fixed-Point Logics and Solitaire Games

Dietmar Berwanger, Erich Gr�del
<span title="2004-09-13">2004</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qj6jzeossfhihfshwf7nb7lbcq" style="color: black;">Theory of Computing Systems</a> </i> &nbsp;
On finite structures (but not on infinite ones), Solitaire-LFP is equivalent to transitive closure logic. We also consider the solitaire fragment of guarded fixed-point logics.  ...  The model-checking games associated with fixed-point logics are parity games, and it is currently not known whether the strategy problem for parity games can be solved in polynomial time.  ...  We consider guarded fragments of least fixed-point logic with two notions of guardedness.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-004-1147-5">doi:10.1007/s00224-004-1147-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o7bj3ruwkzgxxdqqnsdcboehpm">fatcat:o7bj3ruwkzgxxdqqnsdcboehpm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20051103074813/http://www-mgi.informatik.rwth-aachen.de:80/Publications/pub/graedel/BeGr_tocs.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/47/fc/47fce1cac3dc7dbbcf41f94a4c9706e04e357436.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00224-004-1147-5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the Expressivity of Minimal Generic Quantification

David Baelde
<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;
We come back to the initial design of the ∇ quantifier by Miller and Tiu, which we call minimal generic quantification. In the absence of fixed points, it is equivalent to seemingly stronger designs.  ...  We build on the idea that generic quantification is not a logical connective but one that is defined, like negation in classical logics.  ...  Notably, Miller and Tiu have shown that this core support of generic quantification, combined with least and greatest fixed points in the logic LINC [17] , is enough for providing a fully declarative  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2008.12.113">doi:10.1016/j.entcs.2008.12.113</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qpsjpaoccrcxhkvhn3vvdk5wxm">fatcat:qpsjpaoccrcxhkvhn3vvdk5wxm</a> </span>
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Guards, Bounds, and Generalized Semantics

Johan van Benthem
<span title="">2005</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dhs2rsfonnhrbntyqjovx333um" style="color: black;">Journal of Logic, Language and Information</a> </i> &nbsp;
We also show how a perspective shift to general assignment models provides a new look at the fixed-point extension LFP(FO) of first-order logic, making it decidable.  ...  Next, we relate guarded syntax to earlier quantifier restriction strategies for the purpose of achieving effective axiomatizability in second-order logic -pointing at analogies with 'persistent' formulas  ...  Consider the fixed-point version LFP(FO) of full first-order logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10849-005-5786-y">doi:10.1007/s10849-005-5786-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wejrrgf2qfd6lduis4nrs73iqa">fatcat:wejrrgf2qfd6lduis4nrs73iqa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20051225010424/http://www.illc.uva.nl:80/Publications/ResearchReports/PP-2005-07.text.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/5d/23/5d23820721d6f8b24c8a5ef6ac1dc4e47fa7bfeb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10849-005-5786-y"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Beth Definability for the Guarded Fragment [chapter]

Eva Hoogland, Maarten Marx, Martin Otto
<span title="">1999</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 guarded fragment (GF) was introduced in [1] as a fragment of first order logic which combines a great expressive power with nice modal behavior.  ...  While GF has been established as a particularly well-behaved fragment of first order logic in many respects, interpolation fails in restriction to GF, [9] .  ...  And indeed, adding least and greatest fixed points to GF yields a decidable extension ( [6] ). However, as shown in [9] , the interpolation theorem of first order logic fails for GF.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-48242-3_17">doi:10.1007/3-540-48242-3_17</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mpkg77qddzgn5kwjkm2fz4lisa">fatcat:mpkg77qddzgn5kwjkm2fz4lisa</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922005819/http://festschriften.illc.uva.nl/j50/contribs/hoogland/hoogland.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/74/c0/74c0b2a164525af7e1d494f7a85def900ad5cc97.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-48242-3_17"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Crs and Guarded Logics: A Fruitful Contact [chapter]

Johan Van Benthem
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> Bolyai Society Mathematical Studies </i> &nbsp;
This chapter is about a more specialized contact: the flow of ideas between algebra and modal logic through 'guarded fragments' restricting the range of quantification over objects.  ...  Even so, the trade between algebra and logic remains interesting, even when it is not a matter of applying concrete theorems, but exporting more general ideas. The present chapter is a case in point.  ...  Perhaps most intriguingly, guards may help lower complexity in fixed-point logics, as we have seen in a number of cases. Guarding lower down?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-35025-2_13">doi:10.1007/978-3-642-35025-2_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5mgqa6ctxvetblxduy6rgup77e">fatcat:5mgqa6ctxvetblxduy6rgup77e</a> </span>
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Decidability Results for the Boundedness Problem

Achim Blumensath, Martin Otto, Mark Weyer, Wolfgang Thomas
<span title="2014-08-15">2014</span> <i title="Logical Methods in Computer Science e.V."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c67srop7pbe3nciquoxzy3d6pm" style="color: black;">Logical Methods in Computer Science</a> </i> &nbsp;
bound for the number of iterations phi takes to reach its least fixed point, uniformly across all trees.  ...  Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the fixed-point recursion based on phi is spurious over the class of all trees in the sense that there is some uniform finite  ...  We shall see that the restriction to least fixed points that are guardedi.e., fixed points of formulae in the starred logics -is the right counterpart, in the guarded world, for monadic fixed points.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2168/lmcs-10(3:2)2014">doi:10.2168/lmcs-10(3:2)2014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tze3aigqq5c7vgajlgjfrt3vuu">fatcat:tze3aigqq5c7vgajlgjfrt3vuu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190228054917/http://pdfs.semanticscholar.org/8d3f/e5a1ba54137d143a99c49d3ce738f56108bd.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/8d/3f/8d3fe5a1ba54137d143a99c49d3ce738f56108bd.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2168/lmcs-10(3:2)2014"> <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>

Weak Mso with the Unbounding Quantifier [article]

Mikolaj Bojanczyk
<span title="2009-02-06">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The class has two equivalent descriptions: in terms of automata (a type of deterministic counter automaton), and in terms of logic (weak monadic second-order logic with a bounding quantifier).  ...  Effective translations between the logic and automata are given.  ...  For any fixed n, the following set of runs is clearly open: A value of at least n is output at least once on counter c.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0902.1042v1">arXiv:0902.1042v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3k6fhyqpavb33jki3rdiqv7c4q">fatcat:3k6fhyqpavb33jki3rdiqv7c4q</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0902.1042/0902.1042.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> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0902.1042v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The Semijoin Algebra and the Guarded Fragment

Dirk Leinders, Maarten Marx, Jerzy Tyszkiewicz, Jan Van den Bussche
<span title="">2005</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/dhs2rsfonnhrbntyqjovx333um" style="color: black;">Journal of Logic, Language and Information</a> </i> &nbsp;
We also define a fixed point extension of the semijoin algebra that corresponds to µGF.  ...  In this paper, we show that if we replace in Codd's relational algebra the product operator by the "semijoin" operator, then the resulting "semijoin algebra" is equivalent to the guarded fragment of first-order  ...  We recall the definition of guarded fixed point logic µGF [15] . For background on fixed point logics, we refer to Ebbinghaus and Flum [7] . DEFINITION 13 (µGF) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10849-005-5789-8">doi:10.1007/s10849-005-5789-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6rvhetedibhhnobjfuauujynf4">fatcat:6rvhetedibhhnobjfuauujynf4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922002902/https://uhdspace.uhasselt.be/dspace/bitstream/1942/955/1/semijoin.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/b7/3d/b73dafc26e2e30f4582277bf0f8eaa2af7820825.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10849-005-5789-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Queries with guarded negation

Vince Bárány, Balder ten Cate, Martin Otto
<span title="2012-07-01">2012</span> <i title="VLDB Endowment"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p6rqwwpkkjbcldejepcehaalby" style="color: black;">Proceedings of the VLDB Endowment</a> </i> &nbsp;
In addition, an analysis of standard benchmark workloads shows that many uses of negation in SQL in practice are guarded.  ...  Inspired by recent results in finite model theory, we consider a restricted form of negation, guarded negation.  ...  Guarded Negation Fixed Point Logic (GNFP) further extends GNFO with an operator for least fixed points of positively definable monotone operations on relations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14778/2350229.2350250">doi:10.14778/2350229.2350250</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aripunuyezfhrpdaslsci3lspu">fatcat:aripunuyezfhrpdaslsci3lspu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20121012214522/http://vldb.org/pvldb/vol5/p1328_vincebarany_vldb2012.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/3a/44/3a44e0ec730fd3021f324aa2bfa8ddd3d09d074d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.14778/2350229.2350250"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Guarded Teams: The Horizontally Guarded Case

Erich Grädel, Martin Otto, Michael Wagner
<span title="2020-01-10">2020</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/kjskj3qctjdkbigtx4fkcqiyii" style="color: black;">Annual Conference for Computer Science Logic</a> </i> &nbsp;
In fact there are two strains of guardedness for teams. Horizontal guardedness requires the individual assignments of the team to be guarded in the usual sense of guarded logics.  ...  In this paper we investigate the horizontally guarded case. We study horizontally guarded logics for teams and appropriate notions of guarded team bisimulation.  ...  is equivalent to the set of sentences of form ∀x(Xx →ψ(X,x)), where ψ(X,x) is a formula in the posGFP-fragment of least fixed-point logic, in which X occurs only positively [10] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.csl.2020.22">doi:10.4230/lipics.csl.2020.22</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/csl/Gradel020.html">dblp:conf/csl/Gradel020</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7t5ep7p2yracbiykkuxyflq2ge">fatcat:7t5ep7p2yracbiykkuxyflq2ge</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201210132746/https://drops.dagstuhl.de/opus/volltexte/2020/11665/pdf/LIPIcs-CSL-2020-22.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/4f/9d/4f9d292ae8fce0b4ec4685d8dfcd806ea19284c7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.csl.2020.22"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Fixed Points In The Ambient Logic

Silvano Dal Zilio
<span title="2009-01-01">2009</span> <i title="Zenodo"> Zenodo </i> &nbsp;
We present an extension of the ambient logic with fixed points operators in the style of the mu-calculus.  ...  Some differences exist, though, like the use of the logical operator, 0, which can be interpreted as the equivalent of a "time-stop" modality, and the presence of quantification over names, ∃n.φ.  ...  An interesting property of this new characterization of the modalities used in [3] , is that it becomes possible to prove some theorems (of the ambient logic), which where proved directly previously,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.345838">doi:10.5281/zenodo.345838</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uprqof2hhffpzhcppd5f4fobyu">fatcat:uprqof2hhffpzhcppd5f4fobyu</a> </span>
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Coinductive Uniform Proofs [article]

Ekaterina Komendantskaya, Yue Li
<span title="2019-03-18">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Coinduction occurs in two guises in Horn clause logic: in proofs of circular properties and relations, and in proofs involving construction of infinite data.  ...  We propose a general proof-theoretic framework for handling both kinds of coinduction arising in Horn clause logic.  ...  We call a ∈ L the least fixed point of f , denoted lfp ( f ), if a is a fixed point of f , and for all fixed points a ′ of f , a ≤ a ′ .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.07371v1">arXiv:1903.07371v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wbq75w5wd5dfxefhevozlz7frm">fatcat:wbq75w5wd5dfxefhevozlz7frm</a> </span>
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A Step Up in Expressiveness of Decidable Fixpoint Logics

Michael Benedikt, Pierre Bourhis, Michael Vanden Boom
<span title="">2016</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnybbxuptncftdgxtodn5edz7m" style="color: black;">Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS &#39;16</a> </i> &nbsp;
While guardedness has been applied fruitfully in the setting of first-order logic, the ability to add fixpoints while retaining decidability has been very limited.  ...  Guardedness restrictions are one of the principal means to obtain decidable logics -operators such as negation are restricted so that the free variables are contained in an atom.  ...  variables and fixed points as guards is disallowed in µGF.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2933575.2933592">doi:10.1145/2933575.2933592</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/BenediktBB16.html">dblp:conf/lics/BenediktBB16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/iofilouplngydidnz42r5dkpt4">fatcat:iofilouplngydidnz42r5dkpt4</a> </span>
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Page 2176 of Mathematical Reviews Vol. , Issue 2000c [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;
in the model class associated to every pro- gram there is a least model that can be seen as the semantics of the program, which may be built upwards as the least fixed point of a continuous immediate  ...  Summary (translated from the Russian): “The WF-semantics of ‘normal’ logic programs is described on the basis of the alter- nating fixed point concept. Our description is informal.  ... 
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A Unifying Model Checking Approach for Safety Properties of Parameterized Systems [chapter]

Monika Maidl
<span title="">2001</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 known decidable subclasses, token rings and broadcast systems, fall in our subclass, while the main novel feature is that global guards (in form of unnested quantification over index variables) are  ...  The fixed point approach for verifying that S satisfies EF q uses the fact that the set of states satisfying EF q is the least fixed point of the functional: F (X) = {s | s |= q} ∪ wp.S.X. 2 We carry  ...  out the fixpoint computation on predicates, i.e. we compute a state predicate which characterises the least fixed point of F , starting with the empty predicate false.  ... 
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