A Declarative Semantics for CLP with Qualification and Proximity

Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause annotations based on uncertain truth values, qualification values as a generalization of uncertain truth values, and unification based on proximity relations. On the other hand, the CLP scheme has established itself as a powerful extension of LP that supports efficient computation over specialized domains while keeping a clean declarative semantics. In this paper we propose a new scheme SQCLP designed as an extension of CLP that supports qualification values and proximity relations. We show that several previous proposals can be viewed as particular cases of the new scheme, obtained by partial instantiation. We present a declarative semantics for SQCLP that is based on observables, providing fixpoint and proof-theoretical characterizations of least program models as well as an implementation-independent notion of goal solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10

Principles and Implementation of Deductive Parsing

We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as to implement the corresponding parser. The method generalizes easily to parsers for augmented phrase structure formalisms, such as definite-clause grammars and other logic grammar formalisms, and has been used for rapid prototyping of parsing algorithms for a variety of formalisms including variants of tree-adjoining grammars, categorial grammars, and lexicalized context-free grammars.Comment: 69 pages, includes full Prolog cod

On subsumption and semiunification in feature algebras

AbstractWe consider a generalization of term subsumption, or matching, to a class of mathematical structures which we call feature algebras. We show how these generalize both first-order terms and the feature structures used in computational linguistics. The notion of term subsumption generalizes to a natural notion of algebra homomorphism. In the setting of feature algebras, unification, corresponds naturally to solving constraints involving equalities between strings of unary function symbols, and semiunification also allows inequalities representing subsumption constraints. Our generalization allows us to show that the semiunification problem for finite feature algebras is undecidable. This implies that the corresponding problem for rational trees (cyclic terms) is also undecidable

A feature-based syntax/semantics interface

Syntax/Semantics interfaces using unification-based or feature-based formalisms are increasingly common in the existing computational linguistics literature. The primary reason for attempting to specify a syntax/semantics interface in feature structures is that it harmonizes so well with the way in which syntax is now normally described; this close harmony means that syntactic and semantic processing (and indeed other processing, see below) can be as tightly coupled as one wishes - indeed, there need not be any fundamental distinction between them at all. In this paper, we first point out several advantages of the unification-based view of the syntax/semantics interface over standard views. These include (i) a more flexible relation to nonsyntactic constraints on semantics; (ii) a characterization of semantic ambiguity, which in turn provides a framework in which to describe disambiguation, and (iii) the opportunity to underspecify meanings in a way difficult to reconcile with other views. The last point is illustrated with an application to the notorious scope ambiguity problem

Representing grammar, meaning and knowledge

Among the expertises relevant for successful natural language understanding are grammar, meaning and background knowledge, all of which must be represented in order to decode messages from text (or speech). The present paper is a sketch of one cooperation of grammar and meaning representations -- with some remarks about knowledge representation -- which allows that the representations involved be heterogeneous even while cooperating closely. The modules cooperate in what might be called a PLURALIST fashion, with few assumptions about the representations involved. In point of fact, the proposal is compatible with state-of-the-art representations from all three areas. The paper proceeeds from the nearly universal assumption that the grammar formalism is feature-based and insufficiently expressive for use in meaning representation. It then demonstrates how feature formalisms may be employed as a semantic metalanguage in order that semantic constraints may be expressed in a single formalism with grammatical constraints. This allows a tight coupling of syntax and semantics, the incorporation of nonsyntactic constraints (e.g., from knowledge representation) and the opportunity to underspecify meanings in novel ways -- including, e.g., ways which distinguish ambiguity and underspecification (vagueness). We retain scepticism vis-à-vis more ASSIMILATIONIST proposals for the interaction of these -- i.e., proposals which foresee common formalisms for grammar, meaning and knowledge representation. While such proposals rightfully claim to allow for closer integration, they fail to account for the motivations which distinguish formalisms - elaborate expressive strength in the case of semantic representations, monotonic (and preferably decidable) computation in the case of grammar formalisms, and the characterization of taxonomic reasoning in the case of knowledge representation

Higher Order Unification Revisited: Complete Sets of Transformations

In this paper, we reexamine the problem of general higher-order unification and develop an approach based on the method of transformations on systems of terms which has its roots in Herbrand\u27s thesis, and which was developed by Martelli and Montanari in the context of first-order unification. This method provides an abstract and mathematically elegant means of analyzing the invariant properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information. Our major contribution is three-fold. First, we have extended the Herbrand- Martelli-Montanari method of transformations on systems to higher-order unification and pre-unification; second, we have used this formalism to provide a more direct proof of the completeness of a method for higher-order unification than has previously been available; and, finally, we have shown the completeness of the strategy of eager variable elimination. In addition, this analysis provides another justification of the design of Huet\u27s procedure, and shows how its basic principles work in a more general setting. Finally, it is hoped that this presentation might form a good introduction to higher-order unification for those readers unfamiliar with the field