ABSTRACT Reiter's default logic is one of the most prominent and well-studied approaches to nonmonotonic reasoning. Its evolution has resulted in diverse variants enjoying many interesting properties. This process however seems to be diverging because it has led to default logics that are difficult to compare due to different formal characterizations—sometimes even dealing with different objects of discourse. This problem is addressed in this paper in two ways. One the one hand, we elaborate on the relationships between different types of (...) default logics and discuss their differences wrt some basic properties. In particular, we show how two recently proposed variants, namely rational and CA-default logic, are related to each other and existing default logics. As an interesting byproduct, we obtain a cumulative counterpart to Lukasiewicz' variant of default logic. The resulting system is insofar surprising since it necessitates to refine the canonical way of assuring cumulativity in default logics. On the other hand, we pursue an integrating approach. We give a translation embedding rational and CA-default logic into a recently developed framework for default logics. This allows us not only to classify these variants, but it moreover provides us with semantical underpinnings that have been lacking so far. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

A consistency default is a propositional inference rule that asserts the consistency of a formula in its consequence. Consistency defaults allow for a straightforward encoding of domains in which it is explicitely known when something is possible. The logic of consistency defaults can be seen as a variant of cumulative default logic or as a generalization of justified default logic; it is also able to simulate Reiter default logic in the seminormal case. A semantical characterization of consistency defaults in terms (...) of processes and in terms of a fixpoint equation is given, as well as a normal form. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)