A Gabbay-Rule Free Axiomatization of T×W Validity
Source: Journal of Philosophical Logic, Volume 27, Number 5, October 1998 , pp. 435-487(53)
The semantical structures called T×W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, _O, which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator . However, these structures are also suitable for interpreting an extended language, _SO, containing a further possibility operator ^s which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history simultaneity operator. In the present paper we provide an infinite set of axioms in _SO, which is shown to be strongly complete forT×W-validity. Von Kutschera (1997) contains a finite axiomatization of T×W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions.
Document Type: Regular paper
Affiliations: 1: Centro Studi San Salvador, Telecom Italia, San Marco 4826, I-30124 Venezia, Italy. E-mail: email@example.com 2: Dipartimento di Matematica P. ed A., Via Belzoni 7, I-35131 Padova, Italy. E-mail: firstname.lastname@example.org
Publication date: 1998-10-01