The Representation of Inconsistent Information in a Dynamic Model-Theoretic Semantics

THE REPRESENTATION OF INCONSISTENT INFORMATION IN A DYNAMIC MODEL-THEORETIC SEMANTICS Douglas B. Moran Department of Computer Science Oregon State University Corvallis, Oregon 97331 ABSTRACT Model-theoretic semantics provides a computationally attractive means of representing the semantics of natural language. However, the models used in this formalism are static and are usually infinite. Dynamic models are incomplete models that include only the information needed for an application and to which information can be added. Dynamic models are basically approximations of larger conventional models, but differ is several interesting ways. The difference discussed here is the possibility of inconsistent information being included in the model. If a computation causes the model to expand, the result of that computation may be different than the result of performing that same computation with respect to the newly expanded model (i.e. the result is inconsistent with the information currently in the dynamic model). Mechanisms are introduced to eliminate these local (temporary) inconsistencies, but the most natural mechanism can introduce permanent inconsistencies in the information contained in the dynamic model. These inconsistencies are similar to those that people have in their knowledge and beliefs. The mechanism presented is shown to be related to both the intensional isomorphism and impossible worlds approaches to thi~ problem. I. INTRODUCTION In model-theoretic semantics, the semantics of a sentence is represented with a logical formula, and its meaning is the result of evaluating that formula with respect to a logical model. The model-theoretic semantics used here is that given in The proper treatment of quantification in ordinar~ English (PTQ) [Montague 1973], but the problems and results discussed here apply to similar systems and theories. From the viewpoint of natural language understanding, the conventional ~oO~l-theoretic semantics used in descriptive theories has two basic problems: (I) the information contained in a mod~ is complete and unchanging whereas the information possessed by a person listening to an utterance is incomplete and may be changed by the understanding of that utterance, and (2) the models are usually presumed to be infinite, whereas a person possesses only finite information. Dynamic model-theoretic semantics [Friedman, Warren, and Moran 1978, 1979; Moran 1980] addresses these problems by allowing the models to contain incomplete information and to have information added to the model. A dynamic model is a "good enough" approximation to an infinite model when it contains the finite subset of information that is needed to determine the meanings of the sentences actually presented to the system. Dynamic model-theoretic semantics allows the evaluation of a formula to cause the addition of information to the model. This interaction of the evaluation of a formula and the expansion of the model produces several linguistically interesting side-effects, and these have been labelled model-theoretic pra~matics [Moran 19~0]. One of these effects occurs when the information given by an element of the model is expanded between the time when that element is identified as the denotation of a sub-expression in the formula and the time when it is used in combination with other elements. If the …

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