Belief Merging in Dynamic Logic of Propositional Assignments

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Abstract. We study syntactical merging operations that are defined semantically by means of the Hamming distance between valuations; more precisely, we investigate the Σ-semantics, Gmax-semantics and max-semantics. We work with a logical language containing merging operators as connectives, as opposed to the metalanguage operations of the literature. We capture these merging operators as programs of Dynamic Logic of Propositional Assignments DL-PA. This provides a syntactical characterisation of the three semantically defined merging operators, and a proof system for DL-PA therefore also provides a proof system for these merging operators. We explain how PSPACE membership of the model checking and satisfiability problem of star-free DL-PA can be extended to the variant of DL-PA where symbolic disjunctions that are parametrised by sets (that are not defined as abbreviations, but are proper connectives) are built into the language. As our merging operators can be polynomially embedded into this variant of DL-PA, we obtain that both the model checking and the satisfiability problem of a formula containing possibly nested merging operators is in PSPACE.

Logics of knowledge and action: critical analysis and challenges

“…Beyond the embedding of CL-PC that we have recalled in Sect. 3.5, the central role of DL-PA is confirmed by DL-PA accounts of update and revision operations [54], belief merging operations [63], abstract argumentation theories and their modification [33], and answer-set programs and their modification [36]; moreover, its epistemic extension, public announcement logic with assignments, solves the epistemic frame problem [114,115]. As to logics with epistemic operators, we have recalled that S5 is inadequate as a logic of knowledge and should be replaced by S4.2; furthermore, we have shown that the definition of common knowledge by means of the Greatest Fixpoint Axiom GFP(CK J ) is at least questionable.…”

Qualitative uncertainty and dynamics of argumentation through dynamic logic

“…Regarding the latter, methods imported from the belief change literature can be used; for instance, if a new piece of information ψ that is inconsistent with ϕ is to be added, one could do so by means of an AGM belief revision operator [1]. In that respect, DL-PA has been shown useful to capture belief change operators [47], and these have been applied in turn to AFs [35,36].…”

Belief Integration and Source Reliability Assessment

“…Unknown does not mean the same for all, as commonly assumed in the theory of belief merging [12,17,7,4,9,5]. The user who created the hoax article is not to be trusted much on other additions.…”

“…The relative reliability of the sources may not be easy to obtain, as witnessed by the large amount of work done assuming equal reliability [12,17,7,4,9,5]. A recent line of research has tried to address this problem by deriving this kind of metainformation from the merging process itself: Booth and Meyer and Liberatore [3,15] used the history of previous revisions to perform the following; Liberatore [16] exploited merging examples.…”