Abstract: 

Polarity tagging is the task of taking a sentence and indicating which words are in upward-entailing or downward-entailing positions.  So the topic is relevant to natural language semantics and to computational semantics. The talk will mainly be about the theory, and one would not need to know about the applications to understand it.

 

Prior work mainly worked with sentences drawn from relatively simple forms of categorial grammar, or it incorporated proof-theoretic tools based on the Lambek Calculus. While much of that work had interesting and useful results, the overall topic has not been extended to handle stronger grammatical formalisms which make useof flexible type systems.  It also had not been extended in a semantic way, in ways that we shall make precise.    This paper proposes such extensions. We work with type hierarchies built from preorders and monotone/antitone functions, rather than sets and functions.  We adapt higher-order combinators such as type raising and composition to the ordered setting, and crucially we do the same for argument raising as in Herman Hendriks' work.    Our exposition aims at the mathematics and tries to clarify some of the subtle points in this subject, points that easily lead to errors.