Relevant Minimal Change in Belief Update

Relevance in Belief Update

“…Recall, however, that the authors of that work define belief update in terms of prime implicants (PI). Although we are not aiming at focusing on PI-based update operators -as they significantly deviate in nature from KM update operators-, we note that Forbus' KM update operator, which, as stated in Corollary 3 respects the notion of relevance formalized in this article, is not equivalent to its PI-based counterpart, defined by Perrussel et al (2012), which respects the notion of relevance formalized by its originators. This remark -which is exemplified through the following example-suggests, in turn, that PI-based relevance acts differently in relation to relevance presented herein.…”

“…Therefore, we derive, from condition (F ), that [K ϕ] = {a, b}, {a, ¬b} ; i.e., K ϕ = Cn(a). As stated in the Introduction, the only work on relevance-sensitive belief update that bears on the approach described herein is that by Perrussel et al (2012). Recall, however, that the authors of that work define belief update in terms of prime implicants (PI).…”

“…This remark -which is exemplified through the following example-suggests, in turn, that PI-based relevance acts differently in relation to relevance presented herein. b, ¬c, d, e}, {¬a, ¬b, ¬c, d, e}, {a, b, ¬c, ¬d, e}, {¬a, ¬b, ¬c, ¬d, e} , whereas, b, ¬c, d, e}, {¬a, ¬b, ¬c, d, e}, {a, b, ¬c, ¬d, e} -refer to Example 3 in (Perrussel et al, 2012) for details on how the set of worlds [K P I F ϕ] is produced. Therefore, [K F ϕ] = [K P I F ϕ], thus, K F ϕ = K P I F ϕ.…”

“…attention. Indeed, to the best of our knowledge, the only work that directly bears on the approach adopted herein is that by Perrussel, Marchi, Thévenin, and Zhang (2012). Nevertheless, that work departs from the classical framework of Katsuno and Mendelzon, as it considers belief update by handling prime implicants; thus, a significant deviation from the KM postulates, as well as their semantic characterization, was required.…”