Formal semantic analysis of the progressive
Abstract
Formal semantics constitutes the framework of this thesis, and the aim is to characterise the
semantics of the progressive, as it appears in sentence (1).
(1) Max was running towards the station
Among the problems is one known as the "imperfective paradox". According to intuitions, sentence
(1) entails (2), but no entailment holds between (3) and (4).
(1) Max was running towards the station
(2) Max ran towards the station
(3) Max was running to the station
(4) Max ran to the station
Since (1) and (3) would seem to have the same logical form, they ought to have similar entailments.
Why is this not so?
This thesis is divided into two parts. The first part, containing chapters 2 to 5, evaluates the
current formal theories that tackle the imperfective paradox. Solving the imperfective paradox consists
of two tasks: the first is to characterise a semantic distinction between (2) and (4), and the
second is to supply a semantic analysis of the progressive that is sensitive to this distinction and so
results in a solution to the imperfective paradox. According to how the current theories tackle these
two tasks, they can be classified into three camps which I will name as follows: the Heterogeneous
Strategy (adopted by Dowty, Taylor and Cooper) provides one approach for fulfilling the first task,
the Eventual Outcome Strategy (adopted by Dowty, Cooper and Hinrichs) provides an approach for
defining the semantics of the progressive, and the Event-based Strategy (adopted by Parsons and
Bach) provides a further alternative for achieving the two tasks at hand. All these strategies are
intuitively motivated, but we will argue that they are ultimately untenable. The Heterogeneous
Strategy and the Event-based Strategy fail to mesh with the treatment of point adverbials such as
"At 3pm", and the Eventual Outcome Strategy produces a definition of the progressive that is
viciously circular. Thus although the current theories that tackle the imperfective paradox are
highly intuitively motivated, we will ultimately show that the formulations of these intuitions give
rise to conflicts and tensions when it comes to explaining the natural language data.
The second part of the thesis, containing chapters 6 and 7, offers a new approach for tackling
the imperfective paradox. This new approach invokes two tools; the interval-based temporal logic
IQ (Richards 1986), and Moens' (1987) event-based AI model of temporal reference. IQ is an
interval-based temporal logic with several innovations. First, unlike the previous interval-based
theories, IQ maintains a high level of homogeneity: an atomic sentence is true at an interval I only
if it is true at all subintervals of I. Second, IQ offers a technique whereby temporal expressions can
have representations that receive their semantic interpretation with respect to context.
We use the roles of homogeneity and context in IQ to characterise the semantics of aspect,
where the characterisation is based on Moens' model. This provides an arena in which to tackle the
imperfective paradox anew. We explain the entailment between (1) and (2), and at the same time
explain why no entailment holds between (3) and (4). Furthermore, we overcome the problems
concerning the treatment of adverbials such as "At 3pm" that are encountered in the Heterogeneous
Strategy and the Event-based Strategy, and, since we do not adopt the Eventual Outcome Strategy
in defining the progressive, we overcome that strategy's problem of circularity. Hence our solution
to the imperfective paradox will provide answers to the puzzles posed in the earlier chapters of the
thesis.