Propositional Forms of Judgemental Interpretations

EasyChair Preprint 221, version 2

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. 

Keyphrases: Judgemental Interpretation, formal semantics, type theory

@booklet{EasyChair:221,
  author    = {Tao Xue and Zhaohui Luo and Stergios Chatzikyriakidis},
  title     = {Propositional Forms of Judgemental Interpretations},
  doi       = {10.29007/kv25},
  howpublished = {EasyChair Preprint 221},
  year      = {EasyChair, 2018}}