Nominal tense logic and other sorted intensional frameworks
Blackburn, Patrick Rowan
This thesis introduces of a system of tense logic called nominal tense logic (NTL), and several extensions. Its primary aim is to establish that these systems are logically interesting, and can provide useful models of natural language tense, temporal reference, and their interaction. Languages of nominal tense logic are a simple augmentation of Priorean tense logic. They add to the familiar Priorean languages a new sort of atomic symbol, nominals. Like propositional variables, nominals are atomic sentences and may be freely combined with other wffs using the usual connectives. When interpreting these languages we handle the Priorean components standardly, but insist that nominals must be true at one and only one time. We can think of nominals as naming this time. Logically, the change increases the expressive power of tensed languages. There are certain intuitions about the flow of time, such as irreflexivity, that cannot be expressed in Priorean languages; with nominals they can. The effects of this increase in expressive power on the usual model theoretic results for tensed languages discussed, and completeness and decidability results for several temporally interesting classes of frames are given. Various extensions of the basic system are also investigated and similar results are proved. In the final chapter a brief treatment of similarly referential interval based logics is presented. As far as natural language semantics is concerned, the change is an important one. A familiar criticism of Priorean tense logic is that as it lacks any mechanism for temporal reference, it cannot provide realistic models of natural language temporal usage. Natural language tense is at least partly about referring to times, and nowadays the deictic and anaphoric properties of tense are a focus of research. The thesis presents a uniform treatment of certain temporally referring expressions such as indexicals, and simple discourse phenomena.