On Qualitative Reasoning with 'Most' and 'Typical': a logical approach

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Paulo A. S. Veloso,
Sheila R. M. Veloso.
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We examine a logical system, with generalized quantifiers, for expressing 'most' and 'typical' and reasoning about them. The intuition of 'most' as "all but for a 'negligible' set of exceptions" is made precise by means of filters. This gives a monotonic and conservative extension of classical firstorder logic, sharing with it several properties. For typical reasoning, special individuals are introduced by means of 'most' and internalized as constants, thus producing conservative extensions where one can reason about them as intended. Our logic, though related to default logics, is quite different, belonging to a family of closely connected systems with generalized quantifiers for qualitative reasoning about vague notions.
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