The logical structure underlying temporal references in natural language
Bruce, Bertram C.
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Temporal references in natural language include tenses and other time relations, references to specific times, and a variety of phrases such as "present", "later", "when", "how often", and "never". Their high frequency of occurrence reflects the importance of time to the users of natural language. Although the structure underlying temporal references may appear complicated, it is a working assumption of this thesis that a sound logical explanation of its characteristics can be made. The frequent use of temporal references makes a correct exhibition of their underlying structure vital to a full understanding of natural language. Such an understanding is important in teaching and translating, indeed in all uses of natural language. In addition, understanding language better should aid in the design of computer programs which process natural languages. Chapter 2 of this thesis surveys some relevant work on temporal references, both to show what has been done and to show the scope of the problem. Despite the divergence in terminology and viewpoint, a unified theory can be derived which relates and extends the previous work. The new theory is presented in Chapter 3. It is a formal system which models the intuitive meaning of tenses, time relations, and other references to the time of events. The system precisely defines and shows the interrelationships of concepts which are often only vaguely defined. By its generality and its logical foundation, the system is able to serve as a skeleton for further studies of time in language. To illustrate some of the features of the system a question answering computer program, called Chronos, was written which accepts information in the form of tensed sentences and answers questions about the time of events. This program is discussed in Chapter 4. Chapter 5 discusses a problem which arises when we consider assigning truth values to statements about events occurring at times other than the present. The problem is to define a logic for unknown outcomes which retains the two valued tautologies. A logic is presented which has two kinds of implication: a material implication for which all the classical tautologies hold, and a strict implication defined in terms of logical necessity. The strict implication fragment of this logic is shown to be slightly stronger than the Lewis (1959) system S5, although it avoids many of the so-called paradoxes of material implication. The logic of Chapter 5 is a useful extension of the system for tenses (Chapter 3) to situations in which future (and perhaps past) events may have the truth value "unknown". Chapter 6 is a discussion section which evaluates the tense system, the logic for unknown outcomes, and the program Chronos. Several possibilities for extending the thesis are discussed.