Vague size predicates

Vague predicates such as heap, tall, bald, near to, nicer than, etc., are characterized by their Sorites susceptibility and the existence of borderline cases. In attempting to develop a general theory, diverse vague predicates are often analyzed in rather broad natural language settings. Because this has proven to be rather difficult, the phenomenon of vagueness is studied here in a narrower and strictly formalized setting: Vague size predicates such as "roughly the same size" and "negligible in size with respect to" are studied within the framework of a formalized theory of parthood extended by size predicates. Such a restricted axiomatic framework has a number of advantages: (i) it is easier to analyze logical and semantical aspects of vagueness; (ii) it is possible to study the interrelations between precise quantitative facts and the interpretation of vague and qualitative predicates in a restricted class of models; (iii) it is possible to precisely analyze the logical properties of vague and qualitative size predicates which are fundamental to formalized deductive reasoning. All three aspects are critical for the representation and reasoning about many vague predicates as they are used in many sciences and in medicine.