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Journal of Logic and Computation
Article . 2022 . Peer-reviewed
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Article . 2023
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Article . 2021
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Awareness logic: Kripke lattices as a middle ground between syntactic and semantic models

Authors: Gaia Belardinelli; Rasmus K. Rendsvig;

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

Abstract

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.

Country
Denmark
Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
Average
Green
hybrid
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