Dictionary Structure and Probability Measures

Dict ionary definitions are logical combina t ions of basic markers. Defini t ions can be reduced to dis junct ions of meanings, which are conjunct ions of markers . T h e set of words which can take on a m e a n i n g is its lexical representation set, and u n d e r natura l condi t ions such sets are partially ordered by inc lus ion in the same way as the mean i ngs are ordered by implicat ion. T o each set of lexical representa t ion sets, however, there m a y exist several, nontrivial ly different, m in ima l dictionaries. W h e n a probabil i ty measu re is imposed on a dictionary, certain condit ional probabil i t ies can be ex tended to measu res on algebras genera ted by lexical representa t ion sets bu t not those generated by cor responding sets of markers .