Epistemic-entrenchment Characterization of Parikh’s Axiom

Epistemic-entrenchment Characterization of Parikh’s Axiom

Theofanis Aravanis, Pavlos Peppas, Mary-Anne Williams

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
Main track. Pages 772-778. https://doi.org/10.24963/ijcai.2017/107

In this article, we provide the epistemic-entrenchment characterization of the weak version of Parikh’s relevance-sensitive axiom for belief revision — known as axiom (P) — for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the second compartment should not be affected by the revision of K by φ. The above-mentioned characterization, essentially, constitutes additional constraints on epistemic-entrenchment preorders, that induce AGM revision functions, satisfying the weak version of Parikh’s axiom (P).
Keywords:
Knowledge Representation, Reasoning, and Logic: Belief Change
Knowledge Representation, Reasoning, and Logic: Reasoning about Knowlege and Belief