TY - JOUR

T1 - Awareness logic

T2 - Kripke lattices as a middle ground between syntactic and semantic models

AU - Belardinelli, Gaia

AU - Rendsvig, Rasmus Kræmmer

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

U2 - 10.1093/logcom/exac009

DO - 10.1093/logcom/exac009

M3 - Journal article

VL - 33

SP - 1186

EP - 1215

JO - Journal of Logic and Computation

JF - Journal of Logic and Computation

SN - 0955-792X

IS - 6

M1 - 3

ER -