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The complexity of first-order and monadic second-order logic revisited

Markus Frick, Martin Grohe
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic.  ...  We establish a number of similar lower bounds for the model-checking problem for first-order logic, for example, on the class of all trees.  ...  In this paper, we prove new lower bounds on the complexity of the modelchecking problems for first-order and monadic second-order logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2004.01.007">doi:10.1016/j.apal.2004.01.007</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ujya375lw5a7vdx7njjjgur5qy">fatcat:ujya375lw5a7vdx7njjjgur5qy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810182152/http://www.labri.fr/perso/courcell/CoursMaster/FrickGrohe.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/9a/b9/9ab906d5e113eda8f6ff348cf8ce8f3149a97328.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.apal.2004.01.007"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

The complexity of first-order and monadic second-order logic revisited

M. Frick, M. Grohe
<i title="IEEE Comput. Soc"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnybbxuptncftdgxtodn5edz7m" style="color: black;">Proceedings 17th Annual IEEE Symposium on Logic in Computer Science</a> </i> &nbsp;
In this paper, we give super-exponential lower bounds for fixed-parameter tractable model-checking problems for first-order and monadic second-order logic.  ...  We establish a number of similar lower bounds for the model-checking problem for first-order logic, for example, on the class of all trees.  ...  In this paper, we prove new lower bounds on the complexity of the modelchecking problems for first-order and monadic second-order logic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2002.1029830">doi:10.1109/lics.2002.1029830</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/FrickG02.html">dblp:conf/lics/FrickG02</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/absq6vjuu5cuhojbdmluqpso2e">fatcat:absq6vjuu5cuhojbdmluqpso2e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810182152/http://www.labri.fr/perso/courcell/CoursMaster/FrickGrohe.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/9a/b9/9ab906d5e113eda8f6ff348cf8ce8f3149a97328.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2002.1029830"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

Author Index

<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
., see Soltys, M. (1-3) 277-323 Frick, M. and Grohe, M., The complexity of first-order and monadic second-order logic revisited (1-3) 3-31 Godoy, G., Tiwari, A. and Verma, R., Deciding confluence of certain  ...  , G., Foreword (1-3) 1 Simpson, A., Computational adequacy for recursive types in models of intuitionistic set theory (1-3) 207-275 Soltys, M. and Cook, S., The proof complexity of linear algebra (1-3)  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0168-0072(04)00115-0">doi:10.1016/s0168-0072(04)00115-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/uvctnxmfzzddfeuo3fyozfjm3q">fatcat:uvctnxmfzzddfeuo3fyozfjm3q</a> </span>
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Page 6799 of Mathematical Reviews Vol. , Issue 2000j [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;
Soc. 141 (1969), 1-35; MR 40 #30], it has been known that any monadic second-order property of the (labeled) binary tree with successor functions (and not the prefix ordering) is a monadic A; property.  ...  We even show that some monadic second-order definable properties of the binary tree are not definable by any Boolean combination of monadic £2 and Il, formulas.  ... 
<span class="external-identifiers"> </span>
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The challenge of many logics: a new approach to evaluating the role of ideology in Quinean commitment

Jody Azzouni
<span title="2015-01-13">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/munzfrczajgrfktmdt7fobcory" style="color: black;">Synthese</a> </i> &nbsp;
The focus here is on the influential and important arguments of George Boolos and David Lewis that second-order logic and plural quantification don't incur additional ontological commitments over and above  ...  non-first-order ideology to first-order ideology.  ...  My especial thanks for their persistence in forcing me to expand my exposition of some of the trickier maneuvers in the paper-technical and otherwise.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11229-015-0657-9">doi:10.1007/s11229-015-0657-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2xwaqg7kxngghjtruu6itqfytu">fatcat:2xwaqg7kxngghjtruu6itqfytu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171114141550/http://publisher-connector.core.ac.uk/resourcesync/data/Springer-OA/pdf/f8d/aHR0cDovL2xpbmsuc3ByaW5nZXIuY29tLzEwLjEwMDcvczExMjI5LTAxNS0wNjU3LTkucGRm.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/ac/24ac46cd551785a450cd3e5a7ff67b8da6ae2ef3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s11229-015-0657-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 7823 of Mathematical Reviews Vol. , Issue 2003j [page]

<span title="">2003</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;
Esik, The equational theory of fixed points with applications to generalized language theory (21-36); Thomas Eiter, Georg Gottlob and Thomas Schwentick, Second-order logic over strings: regular and non-regular  ...  Nielsen, A first-order one-pass CPS transfor- mation (98-113); Ernst-Erich Doberkat, The demonic product of probabilistic relations (114-128); Gianluigi Ferrari, Ugo Monta- nari and Marco Pistore, Minimizing  ... 
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Page 10270 of Mathematical Reviews Vol. , Issue 2004m [page]

<span title="">2004</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;
The language for time granularity studied here is a fragment of the monadic second order theory of k-refinable downward unbounded layered structures.  ...  The full monadic second order theory of k-refinable downward unbounded layered structures is instead nonelementarily decidable [A. Montanari, A. Peron and A.  ... 
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Monadic Decomposition [chapter]

Margus Veanes, Nikolaj Bjørner, Lev Nachmanson, Sergey Bereg
<span title="">2014</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;
Our setting is quantifierfree formulas over a decidable background theory, such as arithmetic and we here develop a semi-decision procedure for extracting a monadic decomposition of a formula when it exists  ...  We are here interested in discovering whether a formula can be rewritten into a Boolean combination of monadic predicates.  ...  We thank the anonymous reviewers for their constructive feedback that greatly helped to improve the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-08867-9_42">doi:10.1007/978-3-319-08867-9_42</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hewaxiaawbbixoyunxpe4zncvi">fatcat:hewaxiaawbbixoyunxpe4zncvi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220213004841/http://link.springer.com/content/pdf/10.1007/978-3-319-08867-9_42.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/32/52/32528d7540683181d7a509dc87090d616889a0b7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-08867-9_42"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Monadic Decomposability of Regular Relations

Pablo Barceló, Chih-Duo Hong, Xuan-Bach Le, Anthony W. Lin, Reino Niskanen, Michael Wagner
<span title="2019-07-08">2019</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pf6v2q6ji5h7birkbrtpdc2uhy" style="color: black;">International Colloquium on Automata, Languages and Programming</a> </i> &nbsp;
Monadic decomposibility -the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas -is a powerful tool for devising a decision  ...  Our main contribution is to fully settle the complexity of this decision problem by developing new techniques employing infinite Ramsey theory. The complexity for DFA (resp.  ...  Acknowledgements We thank Leonid Libkin for the useful discussion.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.103">doi:10.4230/lipics.icalp.2019.103</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/icalp/BarceloHLLN19.html">dblp:conf/icalp/BarceloHLLN19</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/exrlvgpuznbsjd7mszt3d3enra">fatcat:exrlvgpuznbsjd7mszt3d3enra</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220311011429/https://drops.dagstuhl.de/opus/volltexte/2019/10679/pdf/LIPIcs-ICALP-2019-103.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/46/1e/461e3c9fe7770e92bc0501d059e063cd8e1b9080.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.icalp.2019.103"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Page 3953 of Mathematical Reviews Vol. , Issue 92g [page]

<span title="">1992</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;
of graph languages definable in monadic second-order logic.  ...  Summary: “The class of monadic second-order definable graph languages is the smallest class containing certain elementary graph languages and closed under the Boolean set operations and under projections  ... 
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XML query-update independence analysis revisited

Muhammad Junedi, Pierre Genevàs, Nabil Layaïda
<span title="">2012</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/u26auwu2brhvtiqthfvoza3naq" style="color: black;">Proceedings of the 2012 ACM symposium on Document engineering - DocEng &#39;12</a> </i> &nbsp;
The essence of our approach and results resides in the use of an appropriate logic, to which queries and updates are both succinctly translated.  ...  Those transformations usually involve lots of XPath queries and may not need to be entirely re-executed following an update of the input document.  ...  Mondaic second order logic is equal in expressiveness to µ-logic [9] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2361354.2361375">doi:10.1145/2361354.2361375</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/doceng/JunediGL12.html">dblp:conf/doceng/JunediGL12</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ybqqt7bylng2tfvjwsctzvzgfy">fatcat:ybqqt7bylng2tfvjwsctzvzgfy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130108062257/http://hal.archives-ouvertes.fr/docs/00/73/46/68/PDF/DocEng2012-Junedi.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/e6/3e/e63eba1b62a3673d010f04a3152ff372f6a0d2aa.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2361354.2361375"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

The Ackermann approach for modal logic, correspondence theory and second-order reduction

Renate A. Schmidt
<span title="">2012</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;
sheds light on the kinds of axioms that are equivalent to first-order correspondence properties and can be used to obtain complete axiomatizations for modal logics.  ...  The approach allows us to define and characterize two new classes of formulae, which are elementary and canonical, and subsume the class of Sahlqvist formulae and the class of monadic inductive formulae  ...  The work was supported by UK EPSRC projects EP/D056152/1 and EP/F014570/1.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jal.2012.01.001">doi:10.1016/j.jal.2012.01.001</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/s3bkdpqthfh6fakvrnggrc7kxy">fatcat:s3bkdpqthfh6fakvrnggrc7kxy</a> </span>
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First-Order Queries on Finite Abelian Groups

Simone Bova, Barnaby Martin, Marc Herbstritt
<span title="2015-09-04">2015</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;
We prove that model checking first-order sentences on finite abelian groups is fixed-parameter tractable, when parameterized by the size of the sentence.  ...  We study the computational problem of checking whether a logical sentence is true in a finite abelian group.  ...  The authors thank Carlo Toffalori for a clarification on Baur-Monk theorem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.csl.2015.41">doi:10.4230/lipics.csl.2015.41</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/csl/BovaM15.html">dblp:conf/csl/BovaM15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e5g36yilhzbqbjrhu3jhzzdivy">fatcat:e5g36yilhzbqbjrhu3jhzzdivy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180512051829/http://drops.dagstuhl.de/opus/volltexte/2015/5406/pdf/3.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/d7/0f/d70f8ccd1006c9fedbee1b6e27b789d0811875f6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.csl.2015.41"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

ASNP: A Tame Fragment of Existential Second-Order Logic [chapter]

Manuel Bodirsky, Simon Knäuer, Florian Starke
<span title="">2020</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;
Amalgamation SNP (ASNP) is a fragment of existential second-order logic that strictly contains binary connected MMSNP of Feder and Vardi and binary connected guarded monotone SNP of Bienvenu, ten Cate,  ...  We show that ASNP has a complexity dichotomy if and only if the infinitedomain dichotomy conjecture holds for constraint satisfaction problems for first-order reducts of binary finitely bounded homogeneous  ...  Fig. 1 . 1 Fragments of existential second-order logic and complexity dichotomies.  ... 
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First-Order vs. Second-Order Encodings for LTLf-to-Automata Translation [article]

Shufang Zhu, Geguang Pu, Moshe Y. Vardi
<span title="2019-01-18">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Recent works used a first-order encoding of LTLf formulas to translate LTLf to First Order Logic (FOL), which is then fed to MONA to get the symbolic DFA.  ...  To that end, we propose a formalization of symbolic DFA in second-order logic, thus developing a novel connection between BDDs and MSO.  ...  First-order logic dominates second-order logic for LTL f -to-automata translation.  ... 
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