
arXiv: 2106.12868
AbstractThe 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.
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Computer Science - Artificial Intelligence, Mathematics - Logic, Mathematical logic and foundations, Computer science, Logic in Computer Science (cs.LO), FOS: Economics and business, Artificial Intelligence (cs.AI), Economics - Theoretical Economics, FOS: Mathematics, Theoretical Economics (econ.TH), Computer Science - Multiagent Systems, Logic (math.LO), Multiagent Systems (cs.MA)
FOS: Computer and information sciences, Computer Science - Logic in Computer Science, Computer Science - Artificial Intelligence, Mathematics - Logic, Mathematical logic and foundations, Computer science, Logic in Computer Science (cs.LO), FOS: Economics and business, Artificial Intelligence (cs.AI), Economics - Theoretical Economics, FOS: Mathematics, Theoretical Economics (econ.TH), Computer Science - Multiagent Systems, Logic (math.LO), Multiagent Systems (cs.MA)
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