Definiteness-indefiniteness category and logical quantification

Abstract

This work has been written within the "Logic and Language" project, realized under a cooperation agreement between the Institute of Slavic Studies of the Polish Academy of Sciences and the Institute of Bulgarian Language of the Bulgarian Academy of Sciences. The publication of a many-volume Bulgarian Polish Grammar (12 monographs), and of a Polish-Bulgarian Contrastive Grammar, from now on: Synthesis, is completed. Theories of mathematical logic are satisfied in perfect way in a natural language, which is shown by our understanding of the semantic definiteness / indefiniteness category as a system of scope-based quantification notions. A natural language complements and modifies logical theories. For example, understanding of the definiteness / indefiniteness category as a sentence category follows from the language material, especially in article languages. In such languages, quantification of the predicate is a necessary prerequisite for interpretation. Also introduction of the notions of strong and weak quantification meanings is motivated, for example, by the need to distinguish between the meanings of expressions like Pol. pewien x, jakiś x / bułg. njakoj x, njakakyv x on the nominal phrase level, and by understanding of the ambiguity of quantification expressions like Bulg. vinagi, ponjakoga / Pol. zawsze, czasami. The fact of treating the definiteness / indefiniteness category as a sentence category expands understanding of the incomplete quantification notion also with respect to the verbal phrase, rather than, as in Ajdukiewicz's approach, with respect to the nominal phrase only. Similarly, a proper name in a natural language is not a unique name, like in mathematical logic, but requires additional unique quantification. A networkbased description of time is the first attempt at this type of description in the subject literature. In the present article, I stress that fact that quantification of states and events understood as in Petri net theory reveals the dependence between the aspectual and temporal meanings of verb, and proves that the information on time and aspect need not be dealt with separately. Keywords: scope-based quantification, definiteness/indefiniteness, strong and weak quantification meanings, incomplete quantification, state quantification and imperfect aspect, event quantification and perfect aspect, network-based description of time, Petri nets.