The notion of a fragment was coined by Montague 1974 to illustrate the formal handling of certain puzzles, such as de dicto/de re, in a truth-conditional semantics for natural language. The idea of a fragment is methodological: given the vastness of a natural language, one begins with a system which is of limited data coverage, but formally explicit and functionally complete relative to a certain goal or standard.
Once a small fragment has been defined, there arises the task of upscaling, such as adding the treatment of another puzzle. Unfortunately, however, upscaling may turn out to be difficult or even impossible, depending on the assumptions of the initial fragment and the standard of functional completeness. For example, despite half a century of intensive research there is still no coherent formal account of a single natural language, verified computationally as nearly complete.
This paper proposes a new kind of fragment, called center fragment, designed to ensure the longterm success of upscaling. Its functional standard is the model of natural language communication of agent-oriented Database Semantics (DBS), based on the algorithm of time-linear LA-grammar and the data structure of proplets. Its language data are selected to represent the primary semantic relations of natural language, namely (a) functor-argument structure and (b) coordination, in their most basic form. The approach is illustrated with applications to four languages with distinctively different word orders, namely English, German, Korean, and Russian.
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