Awareness logic: Kripke lattices as a middle ground between syntactic and semantic models

Research output: Contribution to journalJournal articlepeer-review

  • Gaia Belardinelli
  • Rasmus Kræmmer Rendsvig
The literature on awareness modelling includes both syntax-free and syntax-based frameworks. Heifetz, Meier and Schipper (HMS) propose a lattice model of awareness that is syntax-free. While their lattice approach is elegant and intuitive, it does not explicitly distinguish uncertainty from unawareness. Contra this, the most prominent syntax-based solution, the Fagin–Halpern (FH) model, accounts for this distinction and offers a simple representation of awareness but lacks the intuitiveness of the lattice structure. Here, we combine these two approaches by providing a lattice of Kripke models, induced by atom subset inclusion, in which uncertainty and unawareness are separate. We show that our model is equivalent to both HMS and FH models by defining transformations between them which preserve satisfaction of formulas of a language for explicit knowledge and obtain completeness through our and HMS’ results. Lastly, we prove that the Kripke lattice model can be shown equivalent to the FH model (when awareness is propositionally determined) also with respect to the language of the Logic of General Awareness, for which the FH model was originally proposed.
Original languageEnglish
Article number3
JournalJournal of Logic and Computation
Volume33
Issue number6
Pages (from-to)1186-1215
Number of pages30
ISSN0955-792X
DOIs
Publication statusPublished - 2023

ID: 329142763