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In this paper we first present a formal definition of dictionaries and introduce a semantic space of dictionaries which is used for giving formal meanings of entry words. Then we show that the semanti...c space is uniquely determined up to isomorphism. We also construct the semantic space which consists of infinite trees with no leaf and some other trees where only leaves are labeled. Hence we can simply take this semantic space when we discuss semantics of dictionaries. Finally we point out that our framework of dictionaries gives a mathematical foundation to Quillian's word concept problem.show more
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