Logics of communication and change

Abstract

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Johan van Benthem on Logic and Information Dynamics

“…Johan van Benthem is also the most influential champion of the DEL approach, as well as one of the most active contributors to this field (through a long sequence of papers [56,62,64,80,86,90], including some with many of his Ph.D. students [66, 82, 98, 92-94, 101, 105, 119, 134, 157, 158, 198, 203] and other collaborators [76,89,106,114], as well as through his recent book [102]). …”

“…Among the many other contributions of van Benthem to the development of DEL we mention here: the novel and conceptually fertile notion of conditional common knowledge [76], introduced initially by van Benthem as a tool for the complete axiomatization of the logic of public announcements and common knowledge; the study of the limit behavior of iterated public announcements and their application to game-theoretic notions [79]; the study of the dynamicepistemic logic of distributed knowledge and of the ''actualization'' of distributed knowledge via public communication [73]; the investigation of the properties of the dynamic inference system induced by public announcements [63]; the introduction (in joint work with van Eijck and Kooi) of a hierarchy of ''levels of conditional knowledge'' known as epistemic PDL 8 , and its use as a static logical basis for a new axiomatization of DEL [76]; the subsequent investigation of stronger logics that are ''product-closed'' (i.e. 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.…”

“…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.…”

“…Baltag and Smets went on to propose a qualitative product update construction for general belief-revision with arbitrary event models [14,15,17], construction that was later called ''Priority Update'' by van Benthem, who generalized this idea further to a conception of ''belief revision as a special case of preference merge'', using concepts from Social Choice Theory [81]. In a separate line of work with Liu [82], van Benthem proposed a different kind of generalization of belief upgrades, in the form of relational transformers expressible in PDL format; this idea was later combined with epistemic PDL and with factchanging actions (substitutions) by van Eijck [76], and further generalized in the so-called GDDL by Girard et al [138].…”

Intentions and Assignments

“…The aim of this work is propose a logical approach to intention dynamics based on the notion of assignment [7,3]. The function of an assignment is to associate the truth value of a certain formula ϕ to a propositional atom p. We combine a static modal logic of belief and choice with three kinds of dynamic modalities and corresponding three kinds of assignments: assignments operating on an agent's beliefs, assignments operating on the agent's choices and assignments operating on the objective world.…”