Monadic second-order logic, tree automata, and constraint logic programming

Morawietz, Frank

doi:10.1515/9783110806786.41

Cited by 2 publications

(4 citation statements)

References 9 publications

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“…So if we view the inductively defined relations as part of an augmented signature, this signature contains relations on sets. These allow the specification of undecidable relations; for example, Morawietz (1997) shows how to encode the PCP. If we limit ourselves to just singleton variables in any directly or indirectly recursive clause, every relation we define stays within the capacity of MSO logic, s since, if they are first order inductively definable, they are explicitly second order definable (Rogers 1994).…”

Section: Mso Logic and Constraint Logic Programmingmentioning

confidence: 99%

Representing constraints with automata

Morawietz

Cornell

1997

Proceedings of the Eighth Conference on European Chapter of the Association for Computational Linguistics -

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In this paper we describe an approach to constraint based syntactic theories in terms of finite tree automata. 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 show that this allows an efficient representation of knowledge about the content of constraints which can be used as a practical tool for grammatical theory verification. 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. The usefulness of the approach is discussed with examples from the realm of Principles-and-Parameters based parsing.

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Section: Mso Logic and Constraint Logic Programmingmentioning

confidence: 99%

Representing constraints with automata

Morawietz

Cornell

1997

Proceedings of the Eighth Conference on European Chapter of the Association for Computational Linguistics -

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“…Some obvious advantages include that we can still use our succinct and flexible constraint language, but gain (a) a more expressive language, since we now can include inductive definitions of relations, and (b) a way of guiding the compilation process by the specification of appropriate programs. In Morawietz (1997), we define a relational extension R(WS2S) of our constraint language following the Höhfeld and Smolka scheme (Höhfeld and Smolka 1988). From the scheme we get a sound and complete, but now only semi-decidable, operational interpretation of a definite clause-based derivation process.…”

Section: Mso Logic and Constraint Logic Programmingmentioning

confidence: 99%

“…In Morawietz (1997), we define a relational extension R(WS2S) of our constraint language following the Höhfeld and Smolka scheme (Höhfeld and Smolka 1988). From the scheme we get a sound and complete, but now only semi-decidable, operational interpretation of a definite clause-based derivation process.…”

Section: Mso Logic and Constraint Logic Programmingmentioning

confidence: 99%

“…So if we view the inductively defined relations as part of an augmented signature, this signature contains relations on sets. These allow the specification of undecidable relations; for example, Morawietz (1997) shows how to encode the PCP. If we limit ourselves to just singleton variables in any directly or indirectly recursive clause, every relation we define stays within the capacity of MSO logic, 8 since, if they are first order inductively definable, they are explicitly second order definable (Rogers 1994).…”

Section: Mso Logic and Constraint Logic Programmingmentioning

confidence: 99%

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Representing constraints with automata

Morawietz

Cornell

1997

Proceedings of the 35th Annual Meeting on Association for Computational Linguistics -

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In this paper we describe an approach to constraint-based syntactic theories in terms of finite tree automata. 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 show that this allows an efficient representation of knowledge about the content of constraints which can be used as a practical tool for grammatical theory verification. 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. The usefulness of the approach is discussed with examples from the realm of Principles-and-Parameters based parsing.1 All of these are generalizations to trees of results on strings and the monadic second order theory of one successor function originally due to Büchi (1960). The applications we mention here could be adapted to strings with finite-state automata replacing tree automata. In general, all the techniques which apply to tree automata are straightforward generalizations of techniques for FSAs.2 The current version of the MONA tool works only on the MSO logic of strings. There is work in progress at the University of Aarhus to extend MONA to "MONA++", for trees (Biehl et al. 1996).

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Monadic second-order logic, tree automata, and constraint logic programming

Cited by 2 publications

References 9 publications

Representing constraints with automata

Representing constraints with automata

Representing constraints with automata

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