Merging frameworks for interaction

Toward a Dynamic Logic of Questions

“…This is analogous to the proof in [4]. The key points to observe are the right procedural changes in the recursion axiom for (a) atomic statements, and (b) the modalities affected by the action.…”

“…To make this procedural information explicit, van Benthem, Gerbrandy, Hoshi & Pacuit 2009 [4] have introduced protocols into dynamic-epistemic logic. This results in modified versions of the public announcement logic P AL, which now encode procedural as well as factual and epistemic information.…”

Johan van Benthem on Logic and Information Dynamics

“…closed under product update with any epistemic actions): not only epistemic PDL, but also epistemic mu-calculus [88] and other logics; the extension of DEL to fact-changing events [76]; the exploration of games, strategies, rationality and game-theoretic solutions using DEL [56,[77][78][79]; analogues of DEL for preference change [82,77]; the systematic comparison and merge of DEL with Epistemic Temporal Logic [92] and with other frameworks for interaction such as STIT logics [112]; the dynamic logic of questions and issues, leading to the development of ''interrogative DEL'' [105]; extensions of DEL dealing with the inferential dynamics and awareness [101], as well as the evidential dynamics and evidence-managing actions [106]; etc.…”

“…But now the focus is on temporal aspects of information flow. In a series of joint papers [85,92,96], van Benthem and his collaborators gave an explicit formalization of the implicit temporal processes generated by DEL-style event models; compared this setting with epistemic-temporal logic (ETL) as investigated by Parikh and Ramanujam [176] (or in a different version by Fagin et al [129], under the name of ''interpreted systems''), by showing how DEL-generated models can be embedded in ETL forests; characterized the forests corresponding to DEL-generated models (for both the classical version of DEL with ''hard'' information, and the beliefrevision-friendly version with ''soft'' information), in terms of general and natural semantic constraints (e.g. Perfect Recall, ''No Miracles'' etc.…”

Can Doxastic Agents Learn? On the Temporal Structure of Learning

“…We say that a forest satisfies propositional stability iff for all h, he ∈ H we have p ∈ V (he) iff p ∈ V (h). Theorem 2.13 (van Benthem et al [5]). An ET L-model H is isomorphic to the forest generated by the sequential product update of an epistemic model according to some state-dependent DEL-protocol iff it satisfies P R(N ), U N M (N ), SY N (G) and Propositional Stability.…”