Open AccessNegation as Cancellation, Connexive Logic, and qLPm
Author(s) -
Heinrich Wansing,
Daniel Skurt
Publication year - 2018
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v15i2.4869
Subject(s) - negation , logical consequence , presentation (obstetrics) , computer science , linguistics , epistemology , artificial intelligence , natural language processing , cognitive science , arithmetic , mathematics , philosophy , programming language , psychology , medicine , radiology
In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s minimally inconsistent Logic of Paradox with q-entailment (quasi-entailment) as introduced by Grzegorz Malinowski.