A conjectured axiomatization of two-dimensional Reichenbachian tense logic

The present paper has grown out of a need for improved understanding of the technical aspects of the systems of tense logic that have been proposed and applied by Stuttgart people like Franz Giunthner, Christian Rohrer and I myself in connection with the Deutsche Forschungsgemeinschaft (DFG) research project "Die Beschreibung mit hilfe der Zeitlogik von Zeitformen und Verbalperiphrasen im Franzosischen, Portugiesischen und Spanischen". The systems in question were presented and put to work in the following series of contributions (see the Bibliography at the end of this paper): Aqvist (1976), Aqvist and Giinthner (1977), Aqvist, Giunthner and Rohrer (1977), Aqvist, Giinthner and Rohrer (1977a), Aqvist (1977) and Aqvist (1977a). These papers are all somehow based on the Appendix to my essay Aqvist (1973), where a version of the so-called multiple indexing technique in modal logic is presented. In Aqvist (1976) this technique was used so as to yield a reconstruction of the Reichenbachian doctrine of verb tenses (see Reichenbach, 1947, Section 51) in the framework of a two-dimensional tense logic; in the five remaining papers a more powerful logic was