A Revised Projectivity Calculus for Inclusion and Exclusion Reasoning

This page provides the hyperlinks to and some basic information about the article "A Revised Projectivity Calculus for Inclusion and Exclusion Reasoning" published in the Journal of Logic, Language and Information.

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Author: Ka-fat CHOW

Homepage: My homepage

Email: kfzhouy@yahoo.com

Abstract: We present a Revised Projectivity Calculus (denoted RC) that extends the scope of inclusion and exclusion inferences derivable under the Projectivity Calculus (denoted C) developed by Icard (2012). After pointing out the inadequacies of C, we introduce four opposition properties (OPs) which have been studied by Chow (2012, 2017) and are more appropriate for the study of exclusion reasoning. Together with the monotonicity properties (MPs), the OPs will form the basis of RC instead of the additive/multiplicative properties used in C. We also prove some important results of the OPs and their relation with the MPs. We then introduce a set of projectivity signatures together with the associated operations and conditions for valid inferences, and develop RC by inheriting the key features of C. We then show that under RC, we can derive some inferences that are not derivable under C. We finally discuss some properties of RC and point to possible directions of further studies.

Keywords: inclusion; exclusion; opposition properties; projectivity signatures; Natural Logic