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The papers in this collection are all devoted to single theme: logic and its applications in computational linguistics. They share many themes, goals and techniques, and any editorial classification is bound to highlight some connections at the expense of other. Nonetheless, we have found it useful to divide these papers (somewhat arbitrarily) into the following four categories: logical semantics of natural language...
We discuss the relationship between a categorial system (PPTS) based on partial proof trees (PPTs) as the building blocks of the system, resource sensitive logics and the nature of syntactic constraints. PPTS incorporates some of the key insights of lexicalized tree adjoining grammar, namely the notion of an extended domain of locality and the consequent factoring of recursion from the domain of dependencies...
If one converts surface filters into context free rules, one has to introduce new features. These features are strictly nonlexical, and their distribution is predictable from the distribution of the lexical features. Now, given a (feature based) context free grammar, we ask whether one can identify the nonlexical features. This is not possible; however, the notion of an inessential feature offers...
A basic idea of the transformational tradition is that constituents move. More recently, there has been a trend towards the view that all features are lexical features. And in recent “minimalist” grammars, structure building operations are assumed to be feature driven. A simple grammar formalism with these properties is presented here and briefly explored. Grammars in this formalism can define languages...
This paper presents a logical formalization of Tree-Adjoining Grammar (TAG). TAG deals with lexicalized trees and two operations are available: substitution and adjunction. Adjunction is generally presented as an insertion of a tree inside another, surrounding the subtree at the adjunction node. This seems to be contradictory with standard logical ability. We prove that some logic, namely a fragment...
We state and prove Roorda's interpolation theorem in the framework of proof-net theory. This allows us to transform any proofnet into some other proof-net that matches some given (phonological or prosodic) bracketing.
The aim of this essay is to show that one can give a proof-theoretical semantics to vague predicates (most of the observational predicates). The starting point is the critic of the truth-conditional analysis of vagueness in terms of degrees of truth, and the solution proposed is based of the anti-realist principle meaning is use. Therefore the problem of vague is replaced by the problem of graduality...
An adaptation of string-semantic models to the Polymorphic Lambek Calculus is studied. We note that if quantifiers range over arbitrary sets of strings, the polymorphic calculus is incomplete. The semantics is refined so that quantifiers range over sets of strings that are the interpretation of categories, and we prove a completeness result. In addition some other models are considered and there are...
Although sloppy interpretation is usually accounted for by theories of ellipsis, it often arises in non-elliptical contexts. In this paper, a theory of sloppy interpretation is provided which captures this fact. The underlying idea is that sloppy interpretation results from a semantic constraint on parallel structures and the theory is shown to predict sloppy readings for deaccented and paycheck sentences...
A desirable goal of constraint-based parsing is that the whole process should be one of pure algorithmic constraint satisfaction; the implementor should not need to specify any control information, or be aware of how the underlying system implements control. Unfortunately, most existing tools are Turing complete, and hence require additional control information by virtue of their computational power...
In this paper we introduce the data structures and process structure of an incremental parser which reflects the underspecified nature of the information encoded in the NL string. We show how this parser can deal with so called crossover phenomena in a way other systems cannot. The parser is formulated within the LDS framework and constructs parse trees with the help of a modal logic for finite trees...
Classifying linguistic objects is a widespread and important linguistic task, and computational linguistics often requires the deduction of a classificatory system from a general linguistic theory. Since hand deducing a classificatory system may consume much effort and introduce errors, a device that effectively deduces accurate classificatory systems from general linguistic theories would benefit...
Traditional, semantic, accounts of presupposition centre on truth conditional treatments relying on entailments. In contrast, our work concentrates on the investigation of presupposition as a pragmatic phenomenon which interacts with agents’ beliefs. Several accounts (e.g., [1],[2],[5],[6],[7],[8],[23]) have taken contextual factors into account. However, they run into problems caused by the consequences...
Being a complement to [9], which concerns mainly general properties of infinite, unifiable sets of arbitrary terms, this paper provides an analysis of some specific features of sets of types and their behaviour under the influence of substitutions, especially unifiers.
In the framework of labelled proof nets the task of parsing in categorial grammar can be reduced to the problem of first-order matching under theory. Here we shall show how to use the same method of labelled proof nets to reduce the task of generating to the problem of higher-order matching.
Mildly context sensitive grammar formalisms such as multi-component TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a non-semilinear language. This implies that none of the aforementioned grammar formalisms is strong enough to generate this language.
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which are not provided by such grammars. Recent approaches to weighted constraint logic grammars attempt to address this issue by adding numerical calculation schemata...
We provide a characterization of the local sets (sets of trees generated by CFGs) in terms of definability in a restricted logical language, which we contrast with a similar characterization of the recognizable sets (sets of trees accepted by finite-state tree automata). In a strong sense, the distinction between these two captures abstractly the distinction between ordinary CFGs and those in which...
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