Sorts and Operators for Temporal Semantics [pdf]

Blackburn, P. and A. Lascarides, [1992] Sorts and Operators for Temporal Semantics, Proceedings of the Fourth Symposium on Logic and Language, Budapest, Hungary, 1992.

An essential part of natural language understanding, and hence of formal semantics, is the interpretation of temporal expressions. But the very variety of temporal phenomena---such as tense, aspect, aktionsart, temporal adverbials, and the temporal structure of extended text---has tended to result in formal semantic analyses using a wide variety of formal tools, often of a complex nature. It seems important to try and find unifying perspectives on this work, and above all, to try and gain some insight into the logical resources needed to deal with natural language temporal phenomena.

In this paper, we show how a wide variety of temporal expressions can be analysed using a simple modal language. The underlying language is well known in the AI literature: it's Halpern and Shoham's (1986) monotonic interval-based logic. However, as it stands, this language is insufficient for natural language analysis on at least two counts. The first problem is the Reference Problem: it lacks any mechanisms for temporal reference, which are essential for an adequate treatment of tense, adverbials and indexicals. The second problem is the Ontology Problem: the language doesn't reflect the wide variety of temporal ontologies, stemming from events, states and processes, which are essential for an adequate treatment of {\sc nl} aktionsart. We will show how these two defects can be removed in a simple and uniform way: sorting. Systematic use of sorting will result in simple frameworks suitable for modelling the semantics of a wide variety of natural language temporal expressions; moreover, as we shall see, the framework is strong enough to model them in a variety of ways.

This article falls into three main parts. In the first we will show that many different kinds of referential information can easily be marked in a propositional modal language by means of sorting. There are many kinds of temporal referential information; we will examine Reichenbachian reference times, indexicals and durations. In the second part of the article, we turn our attention to temporal ontology. It's a commonly held view in temporal semantics that in order to treat many temporal phenomena, one must do justice to the rich structures underlying temporal ontology. The classical work in this area is Vendler's (1967), though the ideas stretch back much earlier (Aristotle), and have been developed in many directions since (e.g., Moens and Steedman 1988, Nakhimovsky 1988, Lascarides 1991). We will see how sorting enables some of these ideas to modeled. In the third part we combine our sorted modal languages with ideas from the default logic literature.

author = {Patrick Blackburn and Alex Lascarides},
year = {2002},
title = {Sorts and Operators for Temporal Semantics},
booktitle = {Proceedings of the Fourth Symposium on Logic and  Language}, 
address = {Budapest}