Paraconsistent Justification Logic: a Starting Point.
Che-Ping Su · Advances in Modal Logic · 2014
In his 2003 paper, Ten philosophical problems in belief revision, Sven Ove Hansson argues that sometimes belief revision might essentially involve inconsistent epistemic states, and that to better model belief revision requires well modeling inconsistent epistemic states. In this paper, we are going to develop a type of justification logic, which is intended to model the agent’s justification structure, when she is in an inconsistent epistemic state. We call the logic to be developed paraconsistent justification logic. The hope is that this logic could help us better model belief revision. More specifically, we will construct a three-valued justification logic system, which serves as the starting point of the research. Roughly speaking, the system reflects the idea that committing to a contradiction does not imply committing to everything. This idea is taken to be our basic assumption about inconsistent epistemic states. In addition, the main technical result of the paper is that quasi-realization theorem – which holds for standard two-valued justification logic systems – also holds for this three-valued system.