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New Algorithm for Weak Monadic Second-Order Logic on Inductive Structures
[chapter]
2010
Lecture Notes in Computer Science
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We present a 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. ...
doi:10.1007/978-3-642-15205-4_29
fatcat:ijwbf4lnibh7lf3ita7ypvgm3m
Foreword
2004
Theoretical Computer Science
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Acknowledgements This research is supported by Intas Grant "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. ...
doi:10.1016/j.tcs.2004.03.021
fatcat:wlou7oaurjglrkmccdltkiwdhu
Disproving False Conjectures
[chapter]
2003
Lecture Notes in Computer Science
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This paper describes an abstraction mechanism 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. ...
doi:10.1007/978-3-540-39813-4_2
fatcat:zli3dnw5mbf2necoazhyphjyrm
Ehrenfeucht games, the composition method, and the monadic theory of ordinal words
[chapter]
1997
Lecture Notes in Computer Science
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) are indistinguishable in rst-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. ...
doi:10.1007/3-540-63246-8_8
fatcat:ywxyeoqq6baidbrcn2d6qwldsa
Tree Automata Make Ordinal Theory Easy
[chapter]
2006
Lecture Notes in Computer Science
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We give a 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. ...
doi:10.1007/11944836_27
fatcat:lhvcjbdb5ndyroma2moiollgfa
Decidable metric logics
2008
Information and Computation
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Here we identify a fragment of the 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). ...
doi:10.1016/j.ic.2008.08.004
fatcat:muiigau64na4lllnpvgteda23q
Guarded fixed point logics and the monadic theory of countable trees
2002
Theoretical Computer Science
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Based 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. ...
doi:10.1016/s0304-3975(01)00151-7
fatcat:zu6v2vkaifebtpxsgmre3ckl54
Tree Automata Make Ordinal Theory Easy
[article]
2006
arXiv
pre-print
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We give a 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. ...
arXiv:cs/0610166v1
fatcat:imb6eujq25ba5agu4hypao4lhm
On the utility of predicate invention in inductive logic programming
[chapter]
1994
Lecture Notes in Computer Science
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The task of predicate invention in ILP is to extend the hypothesis language with 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). ...
doi:10.1007/3-540-57868-4_64
fatcat:4eocmnkog5e7damzqeb3kcmv5a
Representing constraints with automata
1997
Proceedings of the 35th annual meeting on Association for Computational Linguistics -
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The solutions to constraints expressed in 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. ...
doi:10.3115/976909.979677
dblp:conf/acl/MorawietzC97
fatcat:x4zlzx3itrddfnpowfgpf7duuy
Reasoning about Social Choice and Games in Monadic Fixed-Point Logic
2019
Electronic Proceedings in Theoretical Computer Science
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2019 pre-print arXiv:1907.09100v1 fatcat:icylqgw2rrexfixtieyfveudqe
We suggest that the 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. ...
doi:10.4204/eptcs.297.8
fatcat:zkdn3zmj5zepratv72rzhn23xy
A Concurrent Logical Framework: The Propositional Fragment
[chapter]
2004
Lecture Notes in Computer Science
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The underlying type theory uses 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. ...
doi:10.1007/978-3-540-24849-1_23
fatcat:lzh5gunf7re2zbjc5yqzwwxdf4
The Ackermann approach for modal logic, correspondence theory and second-order reduction
2012
Journal of Applied Logic
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This paper introduces a substitutionrewrite approach based 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. ...
doi:10.1016/j.jal.2012.01.001
fatcat:s3bkdpqthfh6fakvrnggrc7kxy
Bisimulation-invariant PTIME and higher-dimensional μ-calculus
1999
Theoretical Computer Science
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Paradigmatic results in this area are, 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. ...
doi:10.1016/s0304-3975(98)00314-4
fatcat:klwctsikb5fhpm45567db6vn6y
Representing Constraints with Automata
[article]
1997
arXiv
pre-print
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The solutions to constraints expressed in 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. ...
arXiv:cmp-lg/9704006v2
fatcat:bh76kx3hena63eaojppaxxxehy
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