Vagueness and Learning: A Type-Theoretic Approach

Proceedings of the Third Joint Conference on Lexical and Computational Semantics (*SEM 2014), pages 151–159, Dublin, Ireland, August 23-24 2014. Vagueness and Learning: A Type-Theoretic Approach Raquel Fern´andez Institute for Logic, Language and Computation University of Amsterdam raquel.fernandez@uva.nl Staffan Larsson Department of Philosophy, Linguistics and Theory of Science University of Gothenburg sl@ling.gu.se Abstract We present a formal account of the mean- ing of vague scalar adjectives such as ‘tall’ formulated in Type Theory with Records. Our approach makes precise how percep- tual information can be integrated into the meaning representation of these pred- icates; how an agent evaluates whether an entity counts as tall; and how the proposed semantics can be learned and dynamically updated through experience. 1 Introduction Traditional semantic theories such as those de- scribed in Partee (1989) and Blackburn and Bos (2005) offer precise accounts of the truth- conditional content of linguistic expressions, but do not deal with the connection between meaning, perception and learning. One can argue, however, that part of getting to know the meaning of lin- guistic expressions consists in learning to identify the individuals or the situations that the expres- sions can describe. For many concrete words and phrases, this identification relies on perceptual in- formation. In this paper, we focus on characteris- ing the meaning of vague scalar adjectives such as ‘tall’, ‘dark’, or ‘heavy’. We propose a for- mal account that brings together notions from tra- ditional formal semanticswith perceptual informa- tion, which allows us to specify how a logic-based interpretation function is determined and modified dynamically by experience. The need to integrate language and percep- tion has been emphasised by researchers work- ing on the generation and resolution of referring This work is licensed under a Creative Commons Attribution 4.0 International Licence. Page numbers and proceedings footer are added by the organisers. Licence details: http: //creativecommons.org/licenses/by/4.0/ expressions (Kelleher et al., 2005; Reiter et al., 2005; Portet et al., 2009) and, perhaps even more strongly, on the field of robotics, where ground- ing language on perceptual information is critical to allow artificial agents to autonomously acquire and verify beliefs about the world (Siskind, 2001; Steels, 2003; Roy, 2005; Skocaj et al., 2010). Most of these approaches, however, do not build on theories of formal semantics for natural lan- guage. Here we choose to formalise our account in a theoretical framework known as Type Theory with Records (TTR), which has been shown to be suitable for formalising classic semantic aspects such as intensionality, quantification, and nega- tion (Cooper, 2005a; Cooper, 2010; Cooper and Ginzburg, 2011) as well as less standard phenom- ena such as linguistic interaction (Ginzburg, 2012; Purver et al., 2014), perception and action (Dob- nik et al., 2013), and semantic coordination and learning (Larsson, 2009). In this paper we use TTR to put forward an account of the semantics of vague scalar predicates like ‘tall’ that makes pre- cise how perceptual information can be integrated into their meaning representation; how an agent evaluates whether an entity counts as tall; and …

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