In recent years, it has become common in the linguistics and philosophy literature to assume that events and processes are ontologically distinct entities, on a par with objects and substances. At the same time, the idea that time-based episodic knowledge should be represented as a collection of interrelated eventualities has gained increasing acceptance in the computational linguistics and articial intelligence literature. Contrary to what one might expect, a search through the prior literature in linguistics and philosophy reveals no account in which these sortal distinctions play a direct role in adequately explaining the problem of aspectual composition and the closely related imperfective paradox. In the computational linguistics and artificial intelligence literature, moreover, relatively little attention has been paid to either problem. In the first part of the dissertation, I investigate the hypothesis that the parallel ontological distinctions introduced above may be directly employed in an explanatory formal account of the problem of aspectual composition and the imperfective paradox. In so doing, I develop a synthesis of proposals by Hinrichs (1985), Krifka (1989; 1992) and Jackendo (1991) which makes correct predictions in many cases not considered by these authors. In particular, the account is the first to adequately explain the syntactic and semantic behavior of non-individuating accomplishment expressions, such as Jack pour some amount of wort into the carboy, which are too vague to individuate a single event but nevertheless behave like other Vendlerian accomplishments. In the second part of the dissertation, I explore the potential computational applications of the linguistic account, by way of two case studies. In the first one, I follow Moens (1987) in showing how a calculus of eventualities can facilitate the implementation of a simple statement verifier which allows for a much greater range of natural language queries than is usually the case with temporal databases. In the second, more preliminary study, I examine the relevance of the model-theoretic analysis to discourse interpretation, within the context of devising a program which produces simple microworld animations using short narrative descriptions as input specifications.