Awareness Logic: A Kripke-Based Rendition of the Heifetz-Meier-Schipper Model

Belardinelli, Gaia; Rendsvig, Rasmus K.

doi:10.1007/978-3-030-65840-3_3

Cited by 2 publications

(4 citation statements)

References 16 publications

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“…Beyond the introduction of Kripke lattice models, 3 the main contribution of the paper is a set of technical results situating these models with respect to the HMS and FH models. These comprise three results about the equivalences of model classes (see Figure 1), and as corollaries, two completeness results for Kripke lattice models.…”

Section: Introductionmentioning

confidence: 99%

“…As a reviewer of the short version of this paper[3] pointed out, then HMS take explicit knowledge as foundational, and derive awareness from it. This makes the one-dimensional representation justified, if not even desirable.…”

mentioning

confidence: 99%

“…[15] argues that this boils down to a difference in philosophical interpretation 3. First introduced in the short version of this paper,[3].…”

mentioning

confidence: 99%

“…At(O) contains the atoms that have a defined truth value in every s ∈ O 7. We thank a reviewer of the short version of this paper[3] for this wording.…”

mentioning

confidence: 99%

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Awareness Logic: Kripke Lattices as a Middle Ground between Syntactic and Semantic Models

Belardinelli¹,

Rendsvig²

2021

Preprint

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The literature on awareness modeling includes both syntaxfree and syntax-based frameworks. Heifetz, Meier & Schipper (HMS) propose a lattice model of awareness that is syntax-free. While their lattice approach is elegant and intuitive, it precludes the simple option of relying on formal language to induce lattices, and 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 our model 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 where originally proposed.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Awareness Logic: Kripke Lattices as a Middle Ground between Syntactic and Semantic Models

Belardinelli¹,

Rendsvig²

2021

Preprint

Self Cite

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

Belardinelli

Rendsvig

2022

Journal of Logic and Computation

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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.

show abstract

Awareness Logic: A Kripke-Based Rendition of the Heifetz-Meier-Schipper Model

Cited by 2 publications

References 16 publications

Awareness Logic: Kripke Lattices as a Middle Ground between Syntactic and Semantic Models

Awareness Logic: Kripke Lattices as a Middle Ground between Syntactic and Semantic Models

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

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