Propositional Forms of Judgemental Interpretations

Authors: Tao Xue, Zhaohui Luo and Stergios Chatzikyriakidis

Paper Information

Title:Propositional Forms of Judgemental Interpretations
Authors:Tao Xue, Zhaohui Luo and Stergios Chatzikyriakidis
Proceedings:NLCS pre-workshop papers
Editors: Larry Moss, Valeria de Paiva and Ash Asudeh
Keywords:Formal Semantics, Type Theory, Judgemental Interpretation

ABSTRACT. In type-theoretical semantics, sentences may often be interpreted as judgements, rather than propositions. When interpreting composite sentences such as those involving negations and conditionals, one may want to turn a judgemental interpretation into a proposition in order to obtain an intended semantics. In this paper, we propose a new negation operator $\NOT$ for constructing propositional forms of judgemental interpretations. NOT is introduced axiomatically, with five axiomatised laws to govern its behaviour, and several examples are given to illustrate its use in semantic interpretation. In order to justify NOT, we employ a heterogeneous equality to prove its laws and, since the addition of heterogeneous equality to type theories is consistent, so is our introduction of the NOT operator. Also discussed is how to use the negation operator in event semantics.

Talk:Jul 07 11:30 (Session 26K: Contributed papers)