Semantics Based on Conceptual Spaces

I have proposed conceptual spaces as appropriate tools for modeling the semantics of natural language (Gardenfors, 2000). A conceptual space is defined by a number of qualitative dimensions. Examples of perception-based qualitative dimensions are temperature, weight, brightness, and pitch, as well as the three ordinary spatial dimensions of height, width, and depth. The dimensions represent perceived similarity: The closer two points are within a space, the more similar they are judged to be. In the next section, I present a number of further dimensions that are involved in communicative processes.

I argue that properties can be represented as convex regions of conceptual spaces. For example, the color red is a convex region of the three-dimensional color space. A concept can thus be defined as a bundle of properties combined with information about how the properties are correlated (for a more precise definition see Gardenfors, 2000, p. 105). The concept of an apple, for instance, has properties corresponding to regions of color space, shape space, taste space, nutrition space, and other spaces (see Gardenfors, 2000, pp. 102-103, for a more detailed account of this example).

The distinction between properties and concepts is useful for analyzing the cognitive role of different word classes. In Gardenfors (2000), I proposed that properties are typically expressed by adjectives, which describe a convex region of some domain such as color, shape, or size. Correspondingly, concepts representing a complex of properties from a number of domains are typically expressed by nouns. Gardenfors and Warglien (2012) extended this analysis to verbs on the basis of the models of actions and events outlined in the section on Action domain, below.

Because the notion of a domain is central to my analysis, I should clarify its meaning. To do so, I draw on cognitive psychology’s notions of separable and integral dimensions (see Garner, 1974; Maddox, 1992; and Melara, 1992, among others). A set of quality dimensions are said to be integral if one cannot assign an object a value in one dimension without giving it a value in one or more others. For example, an object cannot be given a hue without also giving it a brightness, and the pitch of a sound always goes along with its loudness. Dimensions that are not integral are said to be separable, as is the case with the size and hue dimensions. This distinction allows a domain to be defined as a set of integral dimensions separable from all other dimensions.

The notion of a domain has been used to some extent in cognitive linguistics (e.g., Croft, 2002; Croft & Cruse, 2004; Langacker, 1986). Langacker (1986) presented his notion of a basic domain as follows:

It is however necessary to posit a number of “basic domains,” that is, cognitively irreducible representational spaces or fields of conceptual potential. Among these basic domains are the experience of time and our capacity for dealing with two- and three-dimensional spatial configurations. There are basic domains associated with various senses: color space (an array of possible color sensations), coordinated with the extension of the visual field; the pitch scale; a range of possible temperature sensations (coordinated with positions on the body); and so on. Emotive domains must also be assumed. It is possible that certain linguistic predications are characterized solely in relation to one or more basic domains, for example, time for [BEFORE], color space for [RED], or time and the pitch scale for [BEEP]. However most expressions pertain to higher levels of conceptual organization and presuppose non-basic domains for their semantic characterization. (p. 5)

Langacker’s notion of domain fits well with the one I present. Besides basic domains, Langacker also talked about abstract domains, for which identifying the underlying dimensions is more difficult. In general, though, it seems that the notion of a domain within cognitive linguistics has a broader meaning than I intend (see Gardenfors & Lohndorf, 2013, for a narrower use). Croft and Cruse (2004, chap. 2), for example, even identified domains with frames.

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