Dear all,

We will have our next LIRa session tomorrow, on Thursday, 3 February 18:15.

Please use our recurring zoom link: https://uva-live.zoom.us/j/88142993494?pwd=d1BsQWR4T2UyK0Job29YNThjaGRkUT09 (Meeting ID: 881 4299 3494, Passcode: 352984)

You can find the details of the talk below.

Speaker: Wesley Holliday (University of California, Berkeley)

NOTE THE UNUSUAL TIME!

Date and Time: Thursday, February 3rd 2022, 18:15-19:45, Amsterdam time.

Venue: online.

Title: The Orthologic of Epistemic Modals

Abstract. My talk will be based on a joint paper with Matthew Mandelkern (NYU), “The Orthologic of Epistemic Modals” (https://escholarship.org/uc/item/0ss5z8g3). Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form ‘p, but it might be that not p’ appears to be a contradiction, 'might not p' does not entail 'not p', which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. Some theories predict that 'p and might not p', a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not allow substitution of logical equivalents; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In our paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a more concrete possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. Then we show how to extend our semantics to explain parallel phenomena involving probabilities and conditionals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary.

Hope to see you there!

The LIRa team