Cross-sortal Predication and Polysemy

Cross-sortal Predication and Polysemy Petr Šimon, Chu-Ren Huang Department of Chinese and Bilingual Studies Hong Kong Polytechnic University Kowloon, Hong Kong {petr.simon,churenhuang}@gmail.com Abstract This paper develops new treatment of the problem of cross-sortal predication and co- predication in particular. We argue that the solution to these predicate-argument sort mismatches can be solved by a more flexible treatment of polysemy based on the notion of dependent type and dynamic construction of meaning. Keywords: lexical semantics, formal semantics, type theory, ontology, generative lexicon 1 Introduction Cross-sortal predication is natural language phenomenon, which has not been paid much attention to, per- haps more in lexicographic circles where it serves as a sense disambiguating tool (Cruse, 2000b). This phenomenon nevertheless plays an important role in the development of formal account of lexical seman- tics and could be seen as one of fundamental problems whose solution could lead to better understanding of semantic well-formedness of natural language expressions. As argued in (Borschev and Partee, 2001), the biggest challenge for formal lexical semantics is the establishment of a relation between types and sorts as well as a formulation of a theory that would account for the contribution of sorts to the semantic well-formedness of expressions. We suggest that cross-sortal predication plays such an important role in the development of formal lexical semantics for three reasons. Firstly because it involves the problem of compositionality and in particular the conditions under which certain predicate can be applied to certain argument even in cases when the sort of the argument mismatches the domain of the predicate. Secondly, it introduces a problem of identity of an argument in composition of predicates. And thirdly, cross-sortal predication seems to be quite common even cross-linguistically and thus calls for a general and flexible solution. 1.1 Types and sorts What we call here sort is usually referred to as type, lexical type or ontological type, usually without any detailed specification as to what these might be and especially how are they related to the classical logical types. Typically, inheritance among sorts and few other relations such as meronymy are assumed. We will, however, draw a line between sorts and types, at least within classical formal semantics. We use the term sort for everything that would be typically recognised as being an entity (in classical logic: Montagovian type e or Churchian ι). Informally, sorts would be viewed as elements of the set of entities, organised in a directed graph, which can be viewed as a hierarchical structure along the inheritance path. For the discussion within classical formal semantics, we reserve the term type to refer to truth values, o, and to entities in general, ι. Other ground types might be also added, such as times τ or possible worlds ω and naturally new types can be constructed from the basic ones. We might, for example, find useful the event type ϵ, which we could construct as functional type from the type of entities ι and times τ, reflecting the intuition that events are mapping between …

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