. Though [Pollard and Sag 1994] assumes that an unspecified variant of the formal logic of [Carpenter 1992] will provide a formalism for HPSG, a precise formulation of the envisaged formalism is not immediately obvious, primarily because a principal tenet of [Carpenter 1992], that feature structures represent partial information, seems to conflict with a principal tenet of [Pollard and Sag 1994], that feature structures represent abstract linguistic entities. This has caused many HPSGians to be mistakenly concerned with partial-information specific notions, such as subsumption, that are appropriate for the [Carpenter 1992] logic but inappropriate for the formalism [Pollard and Sag 1994] envisages. This paper hopes to allay this concern and the confusion it engenders by substituting [King 1989] for [Carpenter 1992] as the basis of the envisaged formalism. It demonstrates that the formal logic of [King 1989] provides a formalism for HPSG that meets all [Pollard and Sag 1994] asks of the ...

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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 provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted universal role quantifications, set ration, intersection, subset and disjointhess. A sound, complete and terminating consistency checking procedure is provided to determine the consistency of any given term in the logic. It is shown that determining consistency of terms is a NP-complete problem. Subject Areas: feature logic, constraint-based gram- mars, HPSG 1

. General agreement exists about the usefulness of sets as very highlevel representations of complex data structures. Therefore it is worthwhile to introduce sets into constraint logic programming or set constraints into programming languages in general. We start with a brief overview on different notions of sets. This seems to be necessary since there are almost as many different notions in the field as there are applications such as e.g. program analysis, rapid software prototyping, unificationbased grammar formalisms. An efficient algorithm for treating membership-constraints is introduced. It is used in the implementation of an algorithm for unifying finite sets with tails -- also presented here -- which is needed in any logic programming language embedding sets. Finally it is shown how a full set language including the operators 2, = 2, ", [ can be built on membership-constraints. The text closes with a reflection on the complexity of different algorithms -- which is single expone...

this paper. The research of Pollard and Franz was supported by a grant from the National Science Foundation (IRI-8806913). (Empty Category Principle and Subjacency) and so forth. Patterns of cross-linguistic variation are accounted for by means of the parametrization of these principles. The methodological distinction between these two approaches is widely supposed to be that rules enumerate possibilities, while principles eliminate possibilities. But it is quite difficult to distinguish formally between a parametrized disjunctive principle and a collection of schematic rules only one of which can apply to a given structure. Consider, for example, the distinction between categorial grammar application schemata, basic ID rules of GPSG, and the C-structure constraints of LFG, on the one hand, and the disjunctive clauses of ¯ X Theory or the Empty Category Principle on the other. It should also be borne in mind that so-called rule-based approaches often employ not only rules but also global constraints on representations which behave similarly to principles, such as the Head Feature Convention and the Control Agreement Principle of GPSG or the Completeness and Function-Argument Biuniqueness Conditions of LFG. HPSG belongs to the "unification-based" family of linguistic theories, but differs from LFG and GPSG in that grammars are formulated entirely in terms of universal and language-specific principles expressed as constraints on feature structures, which in turn are taken to represent possible linguistic objects. As shown by Pollard and Sag (1987), constraints on feature structures can be used to do the same duty as many of the principles and rules of GPSG, LFG and GB. Unlike rule-based theories, in HPSG, immediate dominance and linear precedence conditions (traditional...

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 derives a new and surprisingly low complexity result for inference in a new form of Reiter's propositional default logic [18]. The problem studied here is the default inference problem whose fundamental importance was pointed out by Kraus, Lehmann, and Magidor [12]. We prove that "normal" default inference, in propositional logic, is a problem complete for co-NP(3), the third level of the Boolean hierarchy [4]. Our result (by changing the underlying semantics) contrasts favorably with a similar result of Gottlob [7], who proves that standard default inference is \Pi P 2 -complete. Our inference relation also obeys all of the laws for preferential consequence relations set forth by Kraus, Lehmann, and Magidor. In particular, we get the property of being able to reason by cases and the law of cautious monotony. Both of these laws fail for standard propositional default logic. The key technique for our results is the use of Scott's domain theory to integrate defaults into pa...

... 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.

One of the design considerations for HPSG is the integration of pragmatic information with grammatical and semantic information. This paper describes how the current framework might be adapted to reflect a general theory of pragmatics, and at the same time, enable more accurate accounts of pragmatic constraints on linguistic forms within HPSG. After fixing the denotations for some necessary terminology, I describe and elaborate some proposals that are incompletely sketched in the initial expositions of HPSG (Pollard and Sag 1987, 1994). I then demonstrate how two familiar pragmatic constraints on the use of lexical items (so-called extended reference, and Japanese empathy-sensitive verbs) can be represented more completely and more accurately. The paper concludes with a discussion of what is required to represent pragmatic conditions associated with particular syntactic constructions. 1 Some background This paper is about constraints on the felicitous utterance of signs. A sign is an...