An investigation of parametrized difference revision operators
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An investigation of parametrized difference revision operators Theofanis Aravanis1
· Pavlos Peppas1,2 · Mary-Anne Williams2
© Springer Nature Switzerland AG 2019
Abstract In this article, we provide the epistemic-entrenchment and partial-meet characterizations of a new, important class of concrete revision operators (all of which satisfy the AGM postulates for revision), called Parametrized Difference revision operators (PD operators, for short). PD operators are natural generalizations of Dalal’s revision operator, with a much greater range of applicability, hence, the epistemic-entrenchment and partial-meet characterizations of the latter are also provided, as a by-product. Lastly, we prove that PD operators satisfy the strong version of Parikh’s relevance-sensitive axiom for belief revision, showing that they are fully compatible with the notion of relevance. Keywords Belief revision · Parametrized difference revision operators · Dalal’s operator · Parikh’s relevance · Knowledge representation and reasoning · Artificial intelligence Mathematics Subject Classification (2010) 03B42 · 68T27
This article is an extension and elaboration of previous work, published in [3]. Theofanis Aravanis
[email protected] Pavlos Peppas [email protected] Mary-Anne Williams [email protected] 1
Department of Business Administration, University of Patras, Patras 265 00, Greece
2
Centre for Artificial Intelligence, FEIT, University of Technology Sydney, Sydney, NSW 2007, Australia
T. Aravanis et al.
1 Introduction Belief Revision is the study of knowledge in flux. The article that is widely considered to have marked the birth of the field is the seminal work of Alchourr´on et al. [1]. This work has given rise to a formal framework, now known as the AGM paradigm.1 In the context of AGM paradigm, a set of rationality postulates is given, the so-called AGM postulates for revision, which arguably any revision function should satisfy. Parikh was the first to identify that the AGM postulates for revision suffer from the inability to capture the notion of relevance [15]. To fully capture this intuition of local change, Parikh proposed an additional axiom, named (P), that is based on a syntax-splitting approach. Axiom (P) was further analysed in [23], where two different interpretations of it were identified, namely, the weak and the strong version of (P).2 In a recent work, [21, 22], Peppas and Williams introduced constructively and axiomatically an entire new class of concrete revision operators, all of which satisfy the AGM postulates for revision; they are called Parametrized Difference revision operators (for short, PD operators). PD operators are natural generalizations of Dalal’s revision operator [6], have low representational and computational cost, and high expressitivity. Peppas and Williams defined PD operators in terms of total preorders over possible worlds, called faithful preorders, and proved that they satisfy the weak version of axiom (P) [21]. Nevertheless, the epistemic-entrenchment, as well as the p
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