The Logic of Justified Belief Change, Soft Evidence and Defeasible Knowledge Alexandru Baltag Bryan Renne ∗ Sonja Smets † University of Amsterdam Institute for Logic, Language and Computation Abstract We present a logic for reasoning about the evidence-based knowledge and beliefs and the evidential dynamics of non-logically-omniscient agents. We do this by adapting key tools and techniques from Dynamic Epistemic Logic, Justification Logic, and Belief Revision so as to provide a lightweight, yet fine- grained approach that characterizes well-known epistemic and doxastic attitudes in terms of the evidential reasoning that justifies these attitudes. We then add the dynamic operations of evidence introduction, evidence-based inference, strong acceptance of new evidence (evidential “upgrade”), and irrevocable acceptance of additional evidence (evidential “update”). We exemplify our theory by providing a formal dynamic account of Lehrer’s well-known Gettier-type scenario involving the famous Ferrari and the infamous Messrs. Nogot and Havit. 1 Introduction As shown by the famous Gettier counterexamples [8], “knowledge” cannot simply be equated with “justified true belief.” But what is the missing ingredient in this old Platonic equation? While epistemologists have proposed different answers to fill the gap, all would agree that not just any justification will do in order to turn an item of true belief into knowledge. It is essential that “knowledge” comes equipped with a correct, or “good,” justification. Taking this insight as our starting point, we offer in this paper a new formalization for a plethora of notions ranging from justified belief to defeasible knowledge, each of which comes with its own justification based on how well an agent’s evidence supports her epistemic attitude. The so-called Defeasibility Theory defines “knowledge” as true justified belief that is stable under be- lief revision with any new evidence : “if a person has knowledge, then that person’s justification must be sufficiently strong that it is not capable of being defeated by evidence that he does not possess” (Pappas and Swain [13]). One of the problems is interpreting what “evidence” means in this context. One possible interpretation, considered by at least one author [15], takes “evidence” to mean “any proposition,” meaning we include possible misinformation : “real knowledge” should be robust even in the face of false evidence. This interpretation corresponds to our “infallible knowledge” modality K, which could be called “absolutely unrevisable belief.” This is a fully introspective type of knowledge, satisfying all the laws of the modal system S5. However, the most common interpretation of Defeasibility Theory is to take it as requiring persistence of belief only in the face of “any true information.” The resulting notion of “knowledge” was formalized by c 2012 Springer-Verlag Berlin Heidelberg. The original publication is available at www.springerlink.com. Citation: Alexan- dru Baltag, Bryan Renne, and Sonja Smets. The Logic of Justified Belief Change, Soft Evidence and Defeasible Knowledge. In L. Ong and R. de Queiroz, editors, Proceedings of the 19th Workshop on Logic, Language, Information and Computation (WoLLIC 2012), volume 7456 of Lecture Notes in Computer Science, pages 168–190, Buenos Aires, Argentina. Springer-Verlag Berlin Heidelberg, 2012. ∗ Funded by an Innovational Research Incentives Scheme Veni grant from the Netherlands Organisation for Scientific Research (NWO). † Funded in part by an Innovational Research Incentives Scheme Vidi grant from the Netherlands Organisation for Scientific Research (NWO) and by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 283963. 1