Interpreting an action from what we perceive and what we expect

International audienceIn update logic as studied by Baltag, Moss, Solecki and van Benthem, little attention is paid to the interpretation of an action by an agent, which is just assumed to depend on the situation. This is actually a complex issue that nevertheless complies to some logical dynamics. In this paper, we tackle this topic. We also deal with actions that change propositional facts of the situation. In parallel, we propose a formalism to accurately represent an agent's epistemic state based on hyperreal numbers. In that respect, we use infinitesimals to express what would surprise the agents (and by how much) by contradicting their beliefs. We also use a subjective probability to model the notion of belief. It turns out that our probabilistic update mechanism satisfies the AGM postulates of belief revision

AGM-Like Paraconsistent Belief Change

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations

A Rational and Efficient Algorithm for View Revision in Databases

The dynamics of belief and knowledge is one of the major components of any autonomous system that should be able to incorporate new pieces of information. In this paper, we argue that to apply rationality result of belief dynamics theory to various practical problems, it should be generalized in two respects: first of all, it should allow a certain part of belief to be declared as immutable; and second, the belief state need not be deductively closed. Such a generalization of belief dynamics, referred to as base dynamics, is presented, along with the concept of a generalized revision algorithm for Horn knowledge bases. We show that Horn knowledge base dynamics has interesting connection with kernel change and abduction. Finally, we also show that both variants are rational in the sense that they satisfy certain rationality postulates stemming from philosophical works on belief dynamics

The Dynamics of Group Knowledge and Belief

5th International Workshop On Philosophy and Logic of Social Reality. 15-17 November 2019.Hokkaido University, Sapporo, Japa