Studia Logica:1-43 (forthcoming)

Giacomo Bonanno
University of California, Davis
We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction properties between certainty and plausibility and study how these properties translate into properties of belief. We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility, identify the corresponding logics and show that some notions considered in the literature are special cases of our framework.
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DOI 10.1007/s11225-019-09887-w
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References found in this work BETA

Is Justified True Belief Knowledge?Edmund Gettier - 1963 - Analysis 23 (6):121-123.
Dynamic Logic for Belief Revision.Johan van Benthem - 2007 - Journal of Applied Non-Classical Logics 17 (2):129-155.
Reducing Belief Simpliciter to Degrees of Belief.Hannes Leitgeb - 2013 - Annals of Pure and Applied Logic 164 (12):1338-1389.
Belief and Certainty.Dylan Dodd - 2017 - Synthese 194 (11):4597-4621.
The Lottery Paradox, Knowledge, and Rationality.Dana K. Nelkin - 2000 - Philosophical Review 109 (3):373-409.

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