Paraconsistent belief revision: constructive models and new operations

• Grant number: 17/10836-0
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: September 01, 2017
• End date: August 31, 2018
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Marcelo Esteban Coniglio
• Grantee: Rafael Rodrigues Testa
• Supervisor: Eduardo Leopoldo Ferme
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Universidade da Madeira (UMa), Portugal
• Associated to the scholarship: 14/22119-2 - Advances and new perspectives on paraconsistent belief revision, BP.PD

Abstract

This research will continue the initial postdoctoral project by advancing the development of Paraconsistent Belief Revision systems, namely AGMp and AGMo, in order to present solutions to some open problems present in the literature. As formally demonstrated, the formal results can be directly applied to any systems based on paraconsistent logics that extend classical logic.Specifically, the semi-revision operations (already defined in the first phase of this research) will be presented via postulates, which will surface the intuitive notion underlying this operation: notably, by delegating the task of accepting (or not) the new sentence to be incorporated into the epistemic state by the selection mechanism, the postulate of success is challenged. In addition, the respective representation theorem will be demonstrated.The local semi-revision operation will be defined by postulates and formal construction. The main feature of this operation is that the new sentence to be incorporated can be accepted, or even rejected, in such a way that only a part of the epistemic state is kept (or made) consistent. Like external and semi-revision, this operation was originally defined by Sven Hansson for belief bases.Defining it in the paraconsistent context is something natural given its proximity to belief bases - despite their motivation differences and logical justifications, both theories allow us to deal with contradictory epistemic states in a rational way.In addition to the semi-revision constructions, other operations will be developed. Notably, the recent advances in belief bases will be studied in order to adapt them to the paraconsistent systems given their already mentioned relations. Two constructive models will be presented in the paraconsistent systems, namely: (i) epistemic entrenchment, model in which all beliefs are ordered according to their relevance to the epistemic state, and therefore the less epistemically entrenched beliefs are more easily abandoned when necessary, and (ii) Grove spheres, a model based on possible worlds (consistent maximal subsets of language). The interest in developing these models is the possibility of applying, in a direct way, the results obtained in AGMp and AGMo to the systems already present in the literature - systems that are based on such models. (AU)