Chapter

Logic, Rationality, and Interaction

Volume 6953 of the series Lecture Notes in Computer Science pp 61-73

A Semantic Model for Vague Quantifiers Combining Fuzzy Theory and Supervaluation Theory

  • Ka Fat ChowAffiliated withThe Hong Kong Polytechnic University

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Abstract

This paper introduces a semantic model for vague quantifiers (VQs) combining Fuzzy Theory (FT) and Supervaluation Theory (ST), which are the two main theories on vagueness, a common source of uncertainty in natural language. After comparing FT and ST, I will develop the desired model and a numerical method for evaluating truth values of vague quantified statements, called the Modified Glöckner’s Method, that combines the merits and overcomes the demerits of the two theories. I will also show how the model can be applied to evaluate truth values of complex quantified statements with iterated VQs.

Keywords

vague quantifiers Generalized Quantifier Theory Fuzzy Theory Supervaluation Theory Modified Glöckner’s Method