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In recent years, semantical partiality has emerged as an important concept in philosophical logic as well as in the study of natural language semantics. This is a study in spatial model theory, the theory of partially defined models.

This monograph grew out of research at Xerox PARC and the Center for the Study of Language and Information (CSLI) during the first year of CSLI's existence. The Center was created as a meeting place for people from many different research traditions and there was much interest in seeing how the various approaches could be joined in a common effort to understand the complexity of language and information. CSLI was thus an ideal environment for our group and our enterprise. Our original goal was to see how a well-developed linguistic the- ory, such as lexical-functional grammar, could be joined...