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

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 ...

This paper is about the good side of modal logic, the bad side of modal logic, and how hybrid logic takes the good and xes the bad. In essence, modal logic is a simple formalism for working with relational structures (or multigraphs) . But modal logic has no mechanism for referring to or reasoning about the individual nodes in such structures, and this lessens its eectiveness as a representation formalism. In their simplest form, hybrid logics are upgraded modal logics in which reference to individual nodes is possible. But hybrid logic is a rather unusual modal upgrade. It pushes one simple idea as far as it will go: represent all information as formulas. This turns out to be the key needed to draw together a surprisingly diverse range of work (for example, feature logic, description logic and labelled deduction) . Moreover, it displays a number of knowledge representation issues in a new light, notably the importance of sorting. Keywords: Labelled deduction, description logic, f...

Unification-based grammar formalisms have become the predominant paradigm in natural language processing (NLP) and computational linguistics (CL). Their success stems from the fact that they can be seen as high-level declarative programming languages for linguists, which allow them to express linguistic knowledge in a monotonic fashion. Moreover, such formalisms can be given a precise, set-theoretical semantics. This paper presents TDL, a typed feature-based language and inference system, which is specifically designed to support highly lexicalized grammar theories like HPSG, FUG, or CUG. TDL allows the user to define (possibly recursive) hierarchically-ordered types, consisting of type constraints and feature constraints over the boolean connectives , , and :. TDL distinguishes between avm types (open-world reasoning), sort types (closed-world reasoning), built-in types and atoms, and allows the declaration of partitions and incompatible types. Working with partially as ...

The desirability of Horn clauses in logical deductive systems has long been recognized. The reasons are at least threefold. Firstly, while inference algorithms for full logics of any reasonable extent are typically intractable, for systems restricted to Horn clauses the picture is much better. (For example, in ordinary propositional logic, while the full satisfiability problem is NP-complete, a linear-time algorithm exists for Horn clauses.) Secondly, the knowledge-representation capabilities of Horn clauses, while weaker than those of the full logic, remain remarkably rich; indeed, far richer than that of simple conjunctive logic alone. Thirdly, Horn clauses define the maximal subset of a full logic which has the property of admitting generic models, which roughly means that for any set of Horn clauses, there is a least model of the clauses in that set. It is the purpose of this paper to initiate an investigation of Horn clause logic for an extended class of feature structures. After laying the groundwork for this context, we provide two key results. In the first, we show how the property of admitting

In this paper we consider the problem of incorporating mechanisms for expressing abstractions and generalisations into constraint-based formalisms for linguistic description. Much recent work has been done on the denotational semantics of these languages, rather less on their suitability for the task of producing realistically large linguistic descriptions (their "phenomenological" semantics) and on the desiderata for their empirical computational behaviour (their operational semantics). In essence, an adequate formalism should have the properties both of a good programming language and of a support for theory construction.

We use Scott's domain theory and methods from Reiter's default logic to suggest some ways of modelling default constraints in feature logic. We show how default feature rules, derived from default constraints, can be used to give ways to augment strict feature structures with default information.

Many theories of grammar and styles of grammar specification have stemmed from mathematical logic, computer science, and computational linguistics, and have been used for describing natural languages. By a series of constructions, we relate categorial, attribute and logic grammars via (axiomatic) labelled deductive systems, and extend this relation to accommodate unification-based grammars and so-called Montague Grammar. The axioms of a labelled deductive system can also be used to constrain the proof search by automatically generating an LR parser from them; we describe the implementation of such a parser-generator. Furthermore, we show how a modification of the LR parsing algorithm, plus the (meta-level) information contained in the axioms, can be used to parse a grammar specification which is based on procedural rather than combinatorial properties of the language. 1 Introduction Many theories of grammar have been proposed in theoretical linguistics, computational linguistics, com...

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical. We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with just transitive and inverse roles is still in PSpace.We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decis...

I 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-eintrancy, the ability to express generalisations, and the ability to express recursive constraints. Two mail techniques axe 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 repre_ senting linguistic structure 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