4 research outputs found
Nominal tense logic and other sorted intensional frameworks
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