## A Modal Perspective on the Computational Complexity of Attribute Value Grammar (1992)

Venue: | Journal of Logic, Language and Information |

Citations: | 43 - 7 self |

### BibTeX

@ARTICLE{Blackburn92amodal,

author = {Patrick Blackburn and Edith Spaan},

title = {A Modal Perspective on the Computational Complexity of Attribute Value Grammar},

journal = {Journal of Logic, Language and Information},

year = {1992},

volume = {2},

pages = {129--169}

}

### Years of Citing Articles

### OpenURL

### Abstract

Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value descriptions unify amounts to testing for modal satisfiablity. In this paper we put this observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express re-entrancy, the ability to express generalisations, and the ability to express recursive constraints. Two main techniques are used: either Kripke models with desirable properties are constructed, or modalities are used to simulate fragments of Propositional Dynamic Logic. Further possibilities for the application of modal logic in computational linguistics are noted. Attribute Value Structures (AVSs) are probably the most widely used means of representing linguistic structure in current computational linguistics, and the process of unifying...

### Citations

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Citation Context ...ed in giving a precise account of AVMs that employed disjunction or negation. The distinction wassrst introduced by Pereira and Sheiber [33], and it underpins the in uential work of Kaspar and Rounds =-=[26]-=-[41][42]. Thus the move towards full Boolean expressivity marked an important turning point in the development of Attribute Value formalisms. What do computational linguists do with AVMs? The answer i... |

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Varieties of complex algebras
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Citation Context ...al approach of this paper with other approaches to Attribute Value logic which may more familiar to the reader. Note in particular that the standard translation links our approach with that of Smolka =-=[46]-=-. Smolka was perhaps thesrst person to make explicit the connection between AVSs andsrst order models, and he has proved a number of results concerning a certainsrst order language of AVSs, namely the... |

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Citation Context ...containing nominals. In addition to the early work by Prior and Bull already mentioned, see [31], [12] and [32] for an examination of nominals in the setting of Propositional Dynamic Logic (PDL); see =-=[11-=-] and [13] for nominals in the setting of modal logic; andsnally see [4] and [5] for nominals in tense logic. The language L KR is L augmented by two new symbols, 0 and . The symbol 0 acts as a name f... |

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Citation Context ...ture in current computational linguistics, and the process of unifying descriptions of AVSs lies at the heart of many parsers. As a number of people have recently observed (see for example [28], [6], =-=[30-=-], [38] and [43]) the most common formalisms for describing AVSs are notational variants of propositional modal languages, AVSs themselves are Kripke models, and unication amounts to looking for a sat... |

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Sag 1985. Generalized Phrase structure Grammar
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Citation Context ... which AVSs are admissible. Such views are discernible in some of the earliest work in attribute value grammar, namely Lexical Function Grammar (LFG) [24]. Generalised Phrase Structure Grammar (GPSG) =-=[14]-=-, explicitly espouses such views, and its work on feature co-occurrence restrictions remains one of the best examples of the approach in action. More recently, Head Driven Phrase Structure Grammar (HP... |

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v.: 1984, Correspondence Theory, in Handbook of Philosophical Logic 2, edited by
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Citation Context ...spondence theory. This subject is the 8 systematic study and exploitation of the relationships that exist between modal languages and various classical languages; an excellent overview is provided by =-=[2]-=-. The correspondence between L, L N and L KR andsrst order logic arises as follows. Note that AVSs (that is, Kripke models) can equally well be regarded as models for a certainsrst order language, nam... |