A Four-Valued Dynamic Epistemic Logic

Abstract

Epistemic logic is usually employed to model two aspects of a situation: the factual and the epistemic aspects. Truth, however, is not always attainable, and in many cases we are forced to reason only with whatever information is available to us. In this paper, we will explore a four-valued epistemic logic designed to deal with these situations, where agents have only knowledge about the available information (or evidence), which can be incomplete or conflicting, but not explicitly about facts. This layer of available information or evidence, which is the object of the agents' knowledge, can be seen as a database. By adopting this sceptical posture in our semantics, we prepare the ground for logics where the notion of knowledge-or more appropriately, belief-is entirely based on evidence. The technical results include a set of reduction axioms for public announcements, correspondence proofs, and a complete tableau system. In summary, our contributions are twofold: on the one hand we present an intuition and possible application for many-valued modal logics, and on the other hand we develop a logic that models the dynamics of evidence in a simple and intuitively clear fashion. Keywords Many-valued logics • Epistemic logic • Paraconsistent logics • Public announcements • Multi-agent systems • Evidence ments that greatly improved this work. I am very grateful to the anonymous reviewers as well, who gave me very detailed and useful feedback. I would also like to thank my colleagues from the RUG who participated in a discussion of a preliminary version of this paper, and all those present at the LIRa seminar in the ILLC/UvA who gave me very relevant suggestions. Research supported by Ammodo KNAW project "Rational Dynamics and Reasoning".

Iterative social consolidations: Forming beliefs from many-valued evidence and peers’ opinions

“…The motivation of their paper differs from ours in many ways and is more closely related to our previous work (see, e.g. [32,34]).…”

“…Recently, a series of logics have emerged with the purpose of modelling agents who possess evidence [13,21,29,34,37,38,[41][42][43][44]. Given this setting, then, we pose the following problem: how to consolidate this evidence into beliefs?…”

“…As in our previous papers [33,35], we use the four-valued epistemic logic (FVEL) that we developed in [32,34] as a base. The resulting system is reminiscent of [6,7]: agents are represented as nodes and peer relations are represented as as edges, while belief is decided iteratively via modal operators B 0 , B 1 , etc.…”

“…In this section we explore a variant of FVEL [34] proposed in [35]. The only difference here is our new definitions for belief.…”

“…From a logical point of view, perhaps the closest work to ours is being done by Sedlár and Majer [36]. They use a four-valued paraconsistent logic that is very close to the one we used previously in [32,34] and on which the current formalism is based. Their work features a sourcerelated interpretation of the modal accessibility relation.…”