INTRODUCTION

This paper is a tutorial on property-theoretic semantics: our aim is to provide an accessible account of property theory and its application to the formal semantics of natural language. We develop a simple version of property theory and provide the semantics for a fragment of English in the theory. We shall say more about the particular form of the theory in the next section but to begin with we outline the main reasons why we believe property-theoretic semantics to be worthy of attention.

INTENSIONALITY

The main motivation for the development of a theory of propositions and properties stems from the desire to develop an adequate account of intensionality in natural language. In this section we briefly review some possible approaches to intensionality in order to motivate the approach we shall eventually adopt.

INTENSIONALITY VIA POSSIBLE WORLDS

Traditional approaches to intensionality employ the notion of possible world. Propositions are taken to be sets of possible worlds and properties to be functions from individuals to propositions. The modal and doxastic operators are then unpacked as functions from propositions to propositions. For example, the modal operator of necessity is analysed as that function which maps a proposition P to that proposition which consists of all those worlds whose accessible worlds are elements of P. Different choices of the relation of accessibility between worlds yield different modal and doxastic notions. Kripke [127] introduced the possible world analysis of necessity and possibility while Hintikka [88] extended the analysis to deal with belief and knowledge.