Phase Quantification and Frame Theory

In my contribution I will provide an outline of how two major strands in Löbner’s work can be combined in a dynamic game theoretical semantics: phase quantification (PQ) and frame theory (FT). In a first step a formal analysis of PQ in (dynamic) arrow logic is presented. Based on this analysis it is shown in the second step that frame theory must not be understood as being an alternative to standard Tarskian semantics. Rather it must be seen as an extension of such a semantics. The extension developed in this contribution combines the formal frame theory developed in Petersen 2007 with the analysis of PQ in arrow logic developed in this paper. In contrast to other dynamic formalisms like Dynamic Predicate Logic, the dynamic aspect is already located in the lexicon. For example, although adjectives like ‘late’ are basically interpreted as properties of states, they admit in addition of an interpretation where they denote relations between states (or, to be precise, basic frames representing partial descriptions of objects in the sense of Löbner 2012, 2013 and Petersen 2007). The paper is organized as follows: In sections (1) and (2) the empirical data used by Löbner for his account of PQ as well as counterexamples discussed in Mittwoch (1993) are presented. In section (3) the formal analysis of PQ in arrow logic is developed. In the final section it is outlined how this formal analysis can be used to arrive at a satisfying formal theory of frames.