Abstract
Publisher Summary This chapter discusses that the proper treatment of quantification in ordinary English, have been published, the literature on Montague's theory. Linguistic research, using Montague's theory, for instance by the use of a Montague grammar as a tool for descriptions of syntactical properties of a fragment of a natural language, is rapidly growing and is getting very complicated as can be seen from the recent literature. Since Montague's theory is formulated (in UG) in a strict mathematical manner, it suggests itself to reflect upon the premises, assumptions, and basic properties of the algebraic treatment. This helps to construct new fragments of natural languages within Montague's theory that must not necessarily be the extensions of fragments already known.
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