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Logics for Belief as Maximally Plausible Possibility

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Abstract

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 (corresponding—semantically—to a binary Kripke relation), while the latter is merely a classical operator (corresponding—semantically—to a neighborhood function). We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \(\phi \) if (1) she cannot rule out \(\phi \) (that is, it is not the case that she is certain that \(\lnot \phi \)), (2) she judges \(\phi \) to be plausible and (3) she does not judge \(\lnot \phi \) to be plausible. We consider four interaction properties between certainty and plausibility and study how these properties translate into properties of belief (e.g. positive and negative introspection and their converses). 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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Acknowledgements

I am grateful to two anonymous reviewers for helpful and constructive comments. This research was supported by a grant from UC Davis.

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  1. University of California Davis, Davis, CA, USA

    Giacomo Bonanno

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Correspondence to Giacomo Bonanno.

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Bonanno, G. Logics for Belief as Maximally Plausible Possibility. Stud Logica 108, 1019–1061 (2020). https://doi.org/10.1007/s11225-019-09887-w

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