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

Tobias Ganzow, Łukasz Kaiser
2010 Lecture Notes in Computer Science  
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

Patrick Cégielski, Malika More
2004 Theoretical Computer Science  
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]

Serge Autexier, Carsten Schürmann
2003 Lecture Notes in Computer Science  
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]

Wolfgang Thomas
1997 Lecture Notes in Computer Science  
) 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]

Thierry Cachat
2006 Lecture Notes in Computer Science  
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

Yoram Hirshfeld, Alex Rabinovich
2008 Information and Computation  
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

Erich Grädel
2002 Theoretical Computer Science  
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]

Thierry Cachat
2006 arXiv   pre-print
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]

Irene Stahl
1994 Lecture Notes in Computer Science  
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

Frank Morawietz, Tom Cornell
1997 Proceedings of the 35th annual meeting on Association for Computational Linguistics -  
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

Ramit Das, R. Ramanujam, Sunil Simon
2019 Electronic Proceedings in Theoretical Computer Science  
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]

Kevin Watkins, Iliano Cervesato, Frank Pfenning, David Walker
2004 Lecture Notes in Computer Science  
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

Renate A. Schmidt
2012 Journal of Applied Logic  
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

Martin Otto
1999 Theoretical Computer Science  
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]

Frank Morawietz, Tom Cornell
1997 arXiv   pre-print
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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