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New Algorithm for Weak Monadic Second-Order Logic on Inductive Structures
[chapter]

2010
*
Lecture Notes in Computer Science
*

We present a

doi:10.1007/978-3-642-15205-4_29
fatcat:ijwbf4lnibh7lf3ita7ypvgm3m
*new**algorithm**for*model-checking*weak**monadic**second*-*order**logic**on**inductive**structures*, a class of*structures*of bounded clique width. ... In addition to the*algorithm*, we give a*new*proof of decidability of*weak*MSO*on**inductive**structures*which follows Shelah's composition method. ...*Inductive**Structures*We investigate*weak**monadic**second*-*order**logic**on**inductive**structures*. ...##
###
Foreword

2004
*
Theoretical Computer Science
*

Acknowledgements This research is supported by Intas Grant "

doi:10.1016/j.tcs.2004.03.021
fatcat:wlou7oaurjglrkmccdltkiwdhu
*Weak*Arithmetics" 001-447. Guest ... Karine Shahbazyan and Yuri Shoukourian study recognizability and deÿnability*for*Existential*Monadic**Second**Order*(EMSO)*logic**for*homogeneous ow event*structures*. ... They enjoy very nice properties and extend languages accepted by ÿnite automata or deÿned by*monadic**second*-*order*sentences, linked to Presburger arithmetic. ...##
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Disproving False Conjectures
[chapter]

2003
*
Lecture Notes in Computer Science
*

This paper describes an abstraction mechanism

doi:10.1007/978-3-540-39813-4_2
fatcat:zli3dnw5mbf2necoazhyphjyrm
*for*first-*order**logic*over an arbitrary but fixed term algebra to*second*-*order**monadic**logic*with 0 successor functions. ... The decidability of*second*-*order**monadic**logic*together with our notion of abstraction yields an elegant criterion that characterizes a subclass of unprovable conjectures. ... Although MONA implements only a decision procedure*for**weak**second*-*order**monadic**logic*, it is still useful since it is conservative over full*second*-*order**monadic**logic*without successor functions. ...##
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Ehrenfeucht games, the composition method, and the monadic theory of ordinal words
[chapter]

1997
*
Lecture Notes in Computer Science
*

) are indistinguishable in rst-

doi:10.1007/3-540-63246-8_8
fatcat:ywxyeoqq6baidbrcn2d6qwldsa
*order**logic*and*weak**monadic**second*-*order**logic*. ... After some preparations, we present three results: First, we (re)prove in a*new*form the \composition theorem" of Sh75, Gu79]*on**monadic*theories of concatenated*orderings*. ... 10 Acknowledgment I thank Yuri Gurevich*for*fruitful discussions which gave a good motivation and encouragement to write this paper. ...##
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Tree Automata Make Ordinal Theory Easy
[chapter]

2006
*
Lecture Notes in Computer Science
*

We give a

doi:10.1007/11944836_27
fatcat:lhvcjbdb5ndyroma2moiollgfa
*new*simple proof of the decidability of the First*Order*Theory of (ω ω i , +) and the*Monadic**Second**Order*Theory of (ω i , <), improving the complexity in both cases. ... Dagstuhl Seminar Proceedings 07441*Algorithmic*-*Logical*Theory of Infinite*Structures*... and to the participants of Dagstuhl-Seminar "*Algorithmic*-*Logical*Theory of Infinite*Structures*"*for*interesting discussions. ...##
###
Decidable metric logics

2008
*
Information and Computation
*

Here we identify a fragment of the

doi:10.1016/j.ic.2008.08.004
fatcat:muiigau64na4lllnpvgteda23q
*second**order**monadic**logic*of*order*with the " + 1" function, that expresses all the Pnueli modalities and much more. ... We suggest that this*monadic**logic*can be the framework in which temporal*logics*can be safely defined, with the guarantee that their satisfiability problem is decidable. ... Here are some examples of*logics*that have a composition theorem: (1) The*second**order**monadic**logic*of*order*, SMLO. (2) The*weak**monadic**logic*of*order*(*weak*SMLO). ...##
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Guarded fixed point logics and the monadic theory of countable trees

2002
*
Theoretical Computer Science
*

Based

doi:10.1016/s0304-3975(01)00151-7
fatcat:zu6v2vkaifebtpxsgmre3ckl54
*on*the tree model property, we show that the satisÿability problem*for*guarded ÿxed point formulae can be reduced to the*monadic*theory of countable trees (S! ... That proof relies*on*alternating automata*on*trees and*on*a forgetful determinacy theorem*for*games*on*graphs with unbounded branching. ... S We now describe a translation from CGF into*monadic**second*-*order**logic**on*countable trees. ...##
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Tree Automata Make Ordinal Theory Easy
[article]

2006
*
arXiv
*
pre-print

We give a

arXiv:cs/0610166v1
fatcat:imb6eujq25ba5agu4hypao4lhm
*new*simple proof of the decidability of the First*Order*Theory of (omega^omega^i,+) and the*Monadic**Second**Order*Theory of (omega^i,<), improving the complexity in both cases. ... Our*algorithm*is based*on*tree automata and a*new*representation of (sets of) ordinals by (infinite) trees. ... and Stéphane Demri*for*pointing out some useful references and to the referees. ...##
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On the utility of predicate invention in inductive logic programming
[chapter]

1994
*
Lecture Notes in Computer Science
*

The task of predicate invention in ILP is to extend the hypothesis language with

doi:10.1007/3-540-57868-4_64
fatcat:4eocmnkog5e7damzqeb3kcmv5a
*new*predicates in case that the vocabulary given initially is insufficient*for*the learning task. ... However, whether predicate invention really helps to make learning succeed in the extended language depends*on*the bias that is currently employed. ... Acknowledgements This work has been supported by the European Community ESPRIT BRA 6020 ILP (*Inductive**Logic*Programming). ...##
###
Representing constraints with automata

1997
*
Proceedings of the 35th annual meeting on Association for Computational Linguistics -
*

The solutions to constraints expressed in

doi:10.3115/976909.979677
dblp:conf/acl/MorawietzC97
fatcat:x4zlzx3itrddfnpowfgpf7duuy
*weak**monadic**second**order*(MSO)*logic*are represented by tree automata recognizing the assignments which make the formulas true. ... We achieve this by using the intertranslatability of formulae of MSO*logic*and tree automata and the embedding of MSO*logic*into a constraint*logic*programming scheme. ... We wish especially to thank Uwe MSnnich and Jim Rogers*for*discussions and advice. Needless to say, any errors and infelicities which remain are ours alone. ...##
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Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

2019
*
Electronic Proceedings in Theoretical Computer Science
*

We suggest that the

doi:10.4204/eptcs.297.8
fatcat:zkdn3zmj5zepratv72rzhn23xy
*monadic*fixed-point*logic*with counting, an extension of*monadic*first-*order**logic**on*graphs with fixed-point and counting quantifiers, is a natural specification language*on*improvement ... The*logic*has an efficient model checking*algorithm*(in the size of the improvement graph). ... We thank the reviewers*for*their insightful comments. We thank Anup Basil Mathew*for*discussions*on*improvement dynamics. Sunil Simon was partially supported by grant MTR/ 2018/ 001244. ...##
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A Concurrent Logical Framework: The Propositional Fragment
[chapter]

2004
*
Lecture Notes in Computer Science
*

The underlying type theory uses

doi:10.1007/978-3-540-24849-1_23
fatcat:lzh5gunf7re2zbjc5yqzwwxdf4
*monadic*types to segregate values from computations. ... This separation leads to a tractable notion of definitional equality that identifies computations differing only in the*order*of execution of independent steps. ... The exploration of*monads*in*logic*programming by Bekkers and Tarau [7] concentrates*on*the use of*monads**for*data*structures*and all-solution predicate. ...##
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The Ackermann approach for modal logic, correspondence theory and second-order reduction

2012
*
Journal of Applied Logic
*

This paper introduces a substitutionrewrite approach based

doi:10.1016/j.jal.2012.01.001
fatcat:s3bkdpqthfh6fakvrnggrc7kxy
*on*Ackermann's Lemma to*second*-*order*quantifier elimination in modal*logic*. ... 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*. ... Acknowledgements The work has benefited from discussions with Andrzej Szałas*for*which I am grateful. I also thank the anonymous reviewer*for*useful comments. ...##
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Bisimulation-invariant PTIME and higher-dimensional μ-calculus

1999
*
Theoretical Computer Science
*

Paradigmatic results in this area are,

doi:10.1016/s0304-3975(98)00314-4
fatcat:klwctsikb5fhpm45567db6vn6y
*for*instance, Fagin's Theorem (the NP-recognizable properties of finite*structures*are exactly those that can be formalized in existential*second*-*order**logic*), the ... Biichi-Elgot-Trakhtenbrot Theorem (the automaton-recognizable properties of finite words are those that are definable in*monadic**second*-*order**logic*), or the Immerman-Vardi Theorem (the PTIME properties ...*second*-*order**logic*. ...##
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Representing Constraints with Automata
[article]

1997
*
arXiv
*
pre-print

The solutions to constraints expressed in

arXiv:cmp-lg/9704006v2
fatcat:bh76kx3hena63eaojppaxxxehy
*weak**monadic**second**order*(MSO)*logic*are represented by tree automata recognizing the assignments which make the formulas true. ... We achieve this by using the intertranslatability of formulas of MSO*logic*and tree automata and the embedding of MSO*logic*into a constraint*logic*programming scheme. ... We wish especially to thank Uwe Mönnich and Jim Rogers*for*discussions and advice. Needless to say, any errors and infelicities which remain are ours alone. ...
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