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The monadic second-order logic of graphs XII: planar graphs and planar maps
Theoretical Computer Science, 2000 We prove that we can specify by formulas of monadic second-order logic the unique planar embedding of a 3-connected planar graph. If the planar graph is not 3-connected but given with a linear order of its set of edges, we can also define a planar ...
Bruno Courcelle
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Monadic Second-Order Logics with Cardinalities
2003We delimit the boundary between decidability versus undecidability of the weak monadic second-order logic of one successor (WS1S) extended with linear cardinality constraints of the form |X1|+...+|Xr| < |Y1|+...+|Ys|, where the Xis and Yjs range over finite subsets of natural numbers.
Felix Klaedtke, Harald Rueß
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On the existence of a modal-logical basis for monadic second-order logic
Journal of Logic and Computation, 2012Kamp (PhD Thesis, University of California, LA) proved that the tense logic of the connectives Until and Since is expressively complete over the class DCLO of Dedekind complete linear orders in the sense that this logic can express exactly the same conditions over DCLO as first-order logic.
Hella, Lauri, Tulenheimo, Tero
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Theoretical Computer Science, 2008 International audienceWe consider the notion of modular decomposition for countable graphs. The modular decomposition of a graph given with an enumeration of its set of vertices, can be defined by formulas of Monadic Second-Order logic. Another result is
Bruno Courcelle
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Monadic second-order logic and hypergraph orientation
[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science, 2002It is proved that in every undirected graph or, more generally, in every undirected hypergraph of bounded rank, one can specify an orientation of the edges or hyperedges by monadic second-order formulas using quantifications on sets of edges or hyperedges.
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Measure Quantifier in Monadic Second Order Logic
2015We study the extension of Monadic Second Order logic with the “for almost all” quantifier \(\forall ^{=1}\) whose meaning is, informally, that \(\forall ^{=1}X.\phi (X)\) holds if \(\phi (X)\) holds almost surely for a randomly chosen X. We prove that the theory of \(\mathrm {MSO}+\forall ^{=1}\) is undecidable both when interpreted on \((\omega ,
Henryk Michalewski, Matteo Mio
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Interpreting second-order logic in the monadic theory of order
Journal of Symbolic Logic, 1983AbstractUnder a weak set-theoretic assumption we interpret second-order logic in the monadic theory of order.
Yuri Gurevich, Saharon Shelah
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Sequentiality, second order monadic logic and tree automata
Proceedings of Tenth Annual IEEE Symposium on Logic in Computer Science, 2002Given a term rewriting system R and a normalizable term t, a redex is needed if in any reduction sequence of t to a normal for m, this redex will be contracted. Roughly, R is sequential if there is an optimal reduction strategy in which only needed redexes are contracted. More generally, G. Huet and J.-J.
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A Monadic Second-Order Temporal Logic framework for hypergraphs
Neural Computing and ApplicationsInternational ...
Bikram Pratim Bhuyan +4 more
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Baire Category Quantifier in Monadic Second Order Logic
2015We consider Rabin's Monadic Second Order logic MSO of the full binary tree extended with Harvey Friedman's "for almost all" second-order quantifier $$\forall ^*$$ with semantics given in terms of Baire Category. In Theorem 1 we prove that the new quantifier can be eliminated $$\text {MSO}\!+\!\forall ^* \!=\! \text {MSO}$$. We then apply this result to
Michalewski, Henryk, Mio, Matteo
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