Dynamic logic of preference upgrade

Abstract

Statements not only update our current knowledge, but also have other dynamic effects. In particular, suggestions or commands 'upgrade' our preferences by changing the current order among worlds. We present a complete logic of knowledge update plus preference upgrade that works with dynamic-epistemic-style reduction axioms. This system can model changing obligations, conflicting commands, or 'regret'. We then show how to derive reduction axioms from arbitrary definable relation changes. This style of analysis also has a product update version with preferences between actions, as well as worlds. Some illustrations are presented involving defaults and obligations. We conclude that our dynamic framework is viable, while admitting a further extension to more numerical 'utility update'.

Johan van Benthem on Logic and Information Dynamics

“…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].…”

“…For many such choices, the resulting preference operator P/w on sentences (''w is preferred to /'') can be defined in terms of the basic preference modality ½ and a universal modality U. In joint work with Liu [82], van Benthem introduces relation transformers in DEL-style to model specific preference-changing actions (such as ''suggestions'' and various kinds of ''commands''), then generalize them to a very wide class of PDL-format transformers (in which the new relation can be defined from the old one using the regular PDL operations). This format allows one to ''read off'' reduction axioms (for the corresponding actions) from the PDL definitions in an automatic manner.…”

“…Starting with his older work with van Eijck and Frolova [46], continuing with his work with Otterloo and Roy [77], Liu [82], Girard and Roy [94], as well as the Ph.D. theses by Liu [169], Roy [184], Girard [137] and Zvesper [203], written under his supervision, and then with his more recent papers [91,117] and books [102,113], Johan van Benthem has worked towards a dynamic approach to preference logics. The basic semantic setting is given by modal betterness models, 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.…”

Intentions and Assignments

“…In this paper we show that assignments are well-suited to model intention dynamics. Indeed, assignments capture the locality of intention dynamics better than other operations like announcements [8] and upgrades [2,11], where locality means that the process of reconsidering (or generating) an agent's intention does not affect the other intentions of the agent.…”