Epistemic Multilateral Logic

Abstract

We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati & Schlöder, 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic $\mathbf {S5}$ modulo an appropriate translation. The logical framework developed provides the basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve.

Eavesdropping: What is it good for?

“…One can find roots of this general picture inLyons 1977, Recanati 1987, von Fintel & Gillies 2007, 2008, Dowell 2011, Krifka 2014, Murray 2014, Greenberg & Wolf 2018, Krifka 2019, Incurvati & Schlöder 2020 …”

Logical Multilateralism

“…This, however, as Steinberger says, is not done with Restall's reading but here all we get is a view on the meaning of logical constants in light of their role in the interplay between sets of assertions and denials 9. Another approach that should be mentioned is by Incurvati and Schlöder[24,25] who give an account of a multilateral epistemic logic, which is based on a Rumfittian natural deduction system with signed formulas extended to modal logic with an operator which is explained in terms of the speech act of weak assertion.…”