An Approach to Non-Singular Terms in Discourse

An Approach to Non-Singular Terms in Discourse Tomek Strzalkowski School of Computing Science Simon Fraser University Burnaby. B.C.. CANADA V5A IS6 Abstract A new Theory of Names and Descriptions that offers a uniform treatment for many types of non-singular concepts found in natural language discourse is presented. We introduce a layered model of the language denotational base (the universe) in which every world object Js assagned a layer (level) reflecting its relative singularity with respect tn other objects in the universe, We define the notion of relative singularity of world objects as an abstraction class of the layer- membership relation 1. Introduction Linguistic (and related) literature describes numerous forms of non-singular concept~ that can be found in discourse including inten- sional (or functional) concepts, mass concepts, generic (or general) concepts attributive concepts, abstract concepts, etc. [I], [2]. 13] [4] 16] [10] Not all of these approaches could properly capture the distinction between singular and non-singular interpretation of linguis- tic descriptions, and some were originally devised to deal with singular terms only (such as Donnellan's attributive interpretation of definite descriptions [2]). With the exception of intensional concepts, these notions have not been given satisfactory formal representations that would account for their role in natural language discourse. Perhaps the most successful approach to non-singularity thus far has been presented by Montague [4] with his formalised concept of intension. Unfortunately, the concept of intension does not capture all aspects of non-singularity and the rigid translation system into intensional logic [4] seems to loose the smportant aspect of subjectivity in inter- preting natural language discourse. Also, the enormous complexity of any non trwial system of possible worlds proved to be a bar in developing a computationally-oriented application of Montague's theory In this paper we introduce a fragment of a new, and as we believe, computationally feasible Theory of Names and Descriptions that offers a uniform treatment for many types of non-singular con- cepts found in natural language discourse. Although we limit our presentation to nominal phrase constructions, the approach can be further extended to cover other types of phrases. In our theory we present the formalised definition of non-singularity with respect to a particular discourse situation involving a discourse message, a number of individuals (parties), and their knowledge, beliefs, awareness, etc, We introduce a layered model of reality (the universe) as perceived by a discourse participant, and define the notion of relative singularity of objects in this universe as an abstraction class of the layer- membership relation Subsequently, linguistic descriptions and names are classified as singular, measurably singular, or non-singular depend- ing on what they are assumed to denote in the universe The rela- tionship between objects addressed in discourse and classified into different layers (levels) of the universe has a particular significance for resolution of certain types of cohesive links in text. We call these links remote references because they cross level boundaries, 2. Non-singular terms in language Many philosophers and logicians, see [1]-[4], [6], [10]. appreciate that the u~age of the underlined …

Content truncated to 500 words