Year: 2026
Type: article
Abstract: In studies of bundled modalities, we encode a complex conceptual notion into the semantics of a single modal operator and study its logic.Although there is already a substantial body of work on various concrete bundled operators, we still lack a general understanding of them.In this paper, we provide a general theory of the expressivity and axiomatization of bundled modalities.We offer a uniform way to define bisimulations for arbitrary bundled modalities and justify our definition by the corresponding Hennessy-Milner property.We also define a special class of bundled modalities called positive-negative-independent bundles.This class of bundles, together with their duals, cover most bundled modalities studied in the literature, and their axiomatizations can be done with the help of a more abstract notion of convex neighborhood semantics and corresponding representation results.As case studies, we axiomatize the "someone knows" bundle a∈A a φ over S5-models, the "disagreement within group" bundle a,b∈A a φ ∧ b ¬φ over KD45-models, and the "belief without knowledge" bundle Bφ ∧ ¬Kφ over S4.2-models.* The authors thank three anonymous referees for their helpful comments, and also the audience at the workshop "Bundles in Logic" at Lorentz Center.
DOI: 10.4204/eptcs.447.17
Authors: Yifeng Ding, Yuanzhe Yang
Institution: Peking University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7166464676
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