Semantics with clusters of properties

In model-theoretic semantics, we represent the core of predicate meaning by intension. Another notion, clusters of characteristic properties ("dimensions"), serving as conceptual guidelines that help us identify the denotation in each context of use, has intrigued scholars from a variety of disciplines for years. Typical examples are the prototype and exemplar theories, which are prevalent in the study of concepts in cognitive psychology. Model-theoretic theories often appeal to clusters of properties/features/criteria/propositions etc. However, there is no systematic account of the role of clusters. Stipulations are made in each case separately regarding the presence of clusters and/or their various effects. I propose a detailed formal model, which incorporates two kinds of clusters into our denotational representation of predicate meaning. For example, the interpretation of the predicate chair includes in each context in this model a set of individuals (chairs), necessary properties (like piece of furniture) and typical characteristics of chairs (like: has a back, four legs, etc.). I illustrate the use of this model in semantics with one case study: contextual restrictions in universal generalizations with every, any, and generic a. I propose that these quantifying expressions access the cluster of their first argument and use it in different systematic ways (determined by their semantics) to construct their domain. In virtue of this feature, the present proposal captures the similarities, as well as the precise differences between the interpretations of statements with every, any, and generic a (with a given predicate as their first argument).