April 30, 2022

# Paraconsistent Belief Revision: An Algebraic Investigation

### Abstract

This paper offers a logico-algebraic investigation of AGM belief revision based on the logic of paradox (
$$\mathrm {LP}$$
). First, we define a concrete belief revision operator for
$$\mathrm {LP}$$
, proving that it satisfies a generalised version of the traditional AGM postulates. Moreover, we investigate to what extent the Levi and Harper identities, in their classical formulation, can be applied to a paraconsistent account of revision. We show that a generalised Levi-type identity still yields paraconsistent-based revisions that are fully compatible with the AGM postulates. The main outcome is that, once the classical AGM framework is lifted up to an appropriate level of generality, it still appears as a regulative ideal for treating of paraconsistent-based epistemic operators.

April 30, 2022 at 04:12PM