34,892 research outputs found
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
Forgetting complex propositions
This paper uses possible-world semantics to model the changes that may occur
in an agent's knowledge as she loses information. This builds on previous work
in which the agent may forget the truth-value of an atomic proposition, to a
more general case where she may forget the truth-value of a propositional
formula. The generalization poses some challenges, since in order to forget
whether a complex proposition is the case, the agent must also lose
information about the propositional atoms that appear in it, and there is no
unambiguous way to go about this.
We resolve this situation by considering expressions of the form
, which quantify over all possible (but
minimal) ways of forgetting whether . Propositional atoms are modified
non-deterministically, although uniformly, in all possible worlds. We then
represent this within action model logic in order to give a sound and complete
axiomatization for a logic with knowledge and forgetting. Finally, some
variants are discussed, such as when an agent forgets (rather than
forgets whether ) and when the modification of atomic facts is done
non-uniformly throughout the model
Belief Revision in Science: Informational Economy and Paraconsistency
In the present paper, our objective is to examine the application of belief revision models to scientific rationality. We begin by considering the standard model AGM, and along the way a number of problems surface that make it seem inadequate for this specific application. After considering three different heuristics of informational economy that seem fit for science, we consider some possible adaptations for it and argue informally that, overall, some paraconsistent models seem to better satisfy these principles, following Testa (2015). These models have been worked out in formal detail by Testa, Cogniglio, & Ribeiro (2015, 2017)
Decrement Operators in Belief Change
While research on iterated revision is predominant in the field of iterated
belief change, the class of iterated contraction operators received more
attention in recent years. In this article, we examine a non-prioritized
generalisation of iterated contraction. In particular, the class of weak
decrement operators is introduced, which are operators that by multiple steps
achieve the same as a contraction. Inspired by Darwiche and Pearl's work on
iterated revision the subclass of decrement operators is defined. For both,
decrement and weak decrement operators, postulates are presented and for each
of them a representation theorem in the framework of total preorders is given.
Furthermore, we present two sub-types of decrement operators
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