In this paper we introduce a modal lan- guage L T for imposing constraints on trees, and an extension LT(L r) for imposing con- straints on trees decorated with feature structures. The motivation for introducing these languages is to provide tools for formalising grammatical frameworks perspicuously, and the paper illustrates this by showing how the leading ideas of arsa can be captured in LT(Lr).

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...

Feature logics form a class of specialized logics which have proven especially useful in classifying and constraining the linguistic objects known as feature structures. Linguistically, these structures have their origin in the work of the Prague school of linguistics, followed by the work of Chomsky and Halle in The Sound Pattern of English [16]. Feature structures have been reinvented several times by computer scientists: in the theory of data structures, where they are known as record structures, in artificial intelligence, where they are known as frame or slot-value structures, in the theory of data bases, where they are called "complex objects", and in computati

This paper is formal and quite difficult for readers untrained in modal logic; I have no illusions about this and I apologize in advance if I fail to make things as clear and simple as I should. I do believe, however, that much of the complexity in this paper is unavoidable and anything that is simpler will be so at the cost of precision. Almost everything will be defined here, so that the discussion will on the whole be self-contained. But this is really not to say much when it come to mathematical topics. The reader who is seriously interested should perhaps read an introductory book on modal logic and the lucid survey article [ Bull and Segerberg, 1984 ] to get enough background. I can also recommend [ Blackburn, 1993 ] as an introduction into modal logic in connection with avms. It is impossible to go through all technical proofs in great detail; this would be tantamount to writing a book on this topic. But, I hope, the line of argumentation can be understood even without a proper understanding of the technical points. For the message is of wider importance. If I am right, then modal logic, where it fails, fails necessarily Is there a genuine modal perspective on feature structures? 3 -- and no other framework I know of will not under these circumstances. Secondly, it provides enough technical apparatus to allow to prove significant results. To those who remain unimpressed I can only appeal to their sense of beauty and naturalness. Among the persons who have quite generally helped to shape my views on syntax and logic I wish to thank explicitly those who have contributed to the present paper. These are Mark Ellison and two anonymous referees, who had the questionable pleasure of reading an earlier version of this paper. Moreover, the results on modal feature logic...

This paper discusses an approach to feature logic called the structural approach. The method consists in first viewing feature structures as models (or relational structures) in the standard model theoretic sense, and then going on to consider various languages that can be interpeted on these structures and the way these languages are interrelated. It will be shown that the structural approach offers...

Montague's famous characterization of the homomorphic relation between syntax and semantics naturally gives way in computational applications to constraint-based formulations. This was originally motivated by the close harmony it provides with syntax, which is universally processed in a constraint-based fashion. Employing the same processing discipline in syntax and semantics allows that their processing (and indeed other processing) can be as tightly coupled as one wishes -- indeed, there needn't be any fundamental distinction between them at all. In this paper, we point out several advantages of the constraint-based view of semantics processing over standard views. These include (i) the opportunity to incorporate nonsyntactic constraints on semantics, such as those arising from phonology and context; (ii) the opportunity to formulate principles which generalize over syntax and semantics, such as those found in head-driven phrase structure grammar; (iii) a characterization of semantic ...

A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism--to express syntactic theories purely in terms of the properties of the class of structures they license. By focusing on the structural properties of languages rather than on mechanisms for generating or checking structures that exhibit those properties, this model-theoretic approach can offer simpler and significantly clearer expression of theories and can potentially provide a uniform formalization, allowing disparate theories to be compared on the basis of those properties. We discuss L,p, a monadic second-order logical framework for such an approach to syn- tax that has the distinctive virtue of being superficially expressive--supporting direct statement of most linguistically significant syntactic properties -- but having well-defined strong generative capacity -- languages are definable in L,p iff they are strongly context-free. We draw examples from the realms of GPSG and GB.

Abstract. Increasingly, inheritance hierarchies are being used to reduce redundancy in natural language processing lexicons. Systems that utilize inheritance hierarchies need to be able to insert words under the optimal set of classes in these hierarchies. In this paper, we formalize this problem for feature-based default inheritance hierarchies. Since the problem turns out to be NP-complete, we present an approximation algorithm for it. We show that this algorithm is efficient and that it performs well with respect to a number of standard problems for default inheritance. A prototype implementation has been tested on lexical hierarchies and it has produced encouraging results. The work presented here is also relevant to other types of default hierarchies. Abstract. In zunehmendem Masse werden Erbschaftshierarchien zur kompakten Beschreibung von Worteigenschaften in Sprachverarbeitungslexica verwendet. Systeme, die Erbschaftshierarchien benützen, müssen Worte in die optimale Klasse (oder Menge von Klassen) der Hierarchien einfügen können. Dieser Beitrag formalisiert das Problem für merkmalsbasierte default-Hierarchien. Da das Problem NP-vollständig ist, wird hier ein Approximationsalgorithmus vorgeschlagen. Es wird gezeigt, daß der Algorithmus effizient ist und daß er in Hinsicht auf einige Standardprobleme der default-Hierarchien gut funktioniert. Eine Prototypimplementierung zeigt gute Resultate an einigen Hierarchien, die für Lexica der Computerlinguistik geschrieben wurden. Diese Forschung kann auch für andere Arten von default-Hierarchien angewendet werden. 1

... this paper is easy to read. Far from it. Truth is a profound and subtle matter, and a woolly characterisation of truth offers merely a utility that is severely curtailed and a comprehensibility that is largely illusory. My characterisation is anything but woolly. It is rigorous enough to avoid omission, imprecision and contradiction. But such rigour demands much not only of the author but also of the reader. This paper is not light bedtime reading.

We develop an extensible description logic for stating the content of optimalitytheoretic constraints in phonology, and specify a class of structures for interpreting it. The aim is a transparent formalisation of OT. We show how to state a wide range of constraints, including markedness, input–output faithfulness and base–reduplicant faithfulness. However, output–output correspondence and ‘intercandidate’ sympathy are revealed to be problematic: it is unclear that any reasonable class of structures can reconstruct their proponents’ intentions. But our contribution is positive. Proponents of both output–output correspondence and sympathy have offered alternatives that fit into the general OT picture. We show how to state these in a reasonable extension of our formalism. The problematic constraint types were developed to deal with opaque phenomena. We hope to shed new light on the debate about how to handle opacity, by subjecting some common responses to it within OT to critical investigation.