This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle of compositionality, (...) a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

Guerzoni and Sharvit (Linguistics and Philosophy 30:361–391, 2007) provide an argument that plural, but not singular, wh-phrases may contain a negative polarity item in their restriction, and connect this with the semantic property of exhaustivity. I will show that this claim is factually incorrect, and that the theory of negative polarity licensing does not need to be complicated by taking number distinctions into account. In addition, I will argue that number distinctions do not appear to be relevant for polarity items (...) in the restriction of definite noun phrases either. (shrink)

The grammatical constraints on anaphoric binding, known as binding principles, are observed to form a classical square of oppositions. These constraints are then analysed as the effect of phase quantifiers over reference markers in grammatical obliqueness hierarchies, and the resulting phase quantifiers are shown to be organised in a square of logical duality. The impact of this result on the distinction between quantificational and referential nominals as well as on the logical foundations of the semantics of nominals in general is (...) discussed. (shrink)