Belief revision by examples

A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but the problem of obtaining the reliability of the sources given the result of a previous merging. As an example, the relative reliability of two sensors can be assessed given some certain observation, and allows for subsequent mergings of data coming from them

The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions

AbstractWe consider the computational complexity of evaluating nested counterfactuals over a propositional knowledge base. A counterfactualp>qis a conditional query with the meaning “Ifpwould be true in the knowledge base, would it then hold that alsoqis true,” which is different from material implicationp⇒q. A nested counterfactual is a counterfactual statement where the premisepor the conclusionqis a counterfactual. Statements of the formp1>(p2…(pn>q)…) intuitively correspond to conditional queries involving a sequence of revisions. We show that evaluating such statements isΠP2-complete and that this task becomes PSPACE-complete if negation is allowed in a nesting of this form. We also consider nesting a counterfactual in the premise, i.e., (p>q)>r, and show that evaluating such statements isΠP4-complete, thus most likely much harder than evaluatingp>(q>r). Finally, we also address iterated nestings in the premise and the mix of nestings in the premise and the conclusion

The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions

We consider the computational complexity of evaluating nested counterfactuals over a propositional knowledge base. Counterfactual implication p ? q models a statement "if p, then q," where p is known or expected to be false, and is different from material implication p ) q. A nested counterfactual is a counterfactual statement where the conclusion q is a (possibly negated) counterfactual. Statements of the form p 1 ? (p 2 ? \Delta \Delta \Delta (p n ? q) \Delta \Delta \Delta) intuitively correspond to hypothetical queries involving a sequence of revisions. We show that evaluating such statements is \Pi P 2 -complete, and that this task becomes PSPACE-complete if negation is allowed in the nesting. We also consider nesting a counterfactual in the premise, i.e. (p ? q) ? r and show that evaluating such statements is most likely much harder than evaluating p ? (q ? r). 1 Introduction A counterfactual is a conditional statement "if p, then q," where the premise p is eit..