The Orthologic of Epistemic Modals

03/06/2022
by   Wesley H. Holliday, et al.
0

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∧ p ('p, but it might be that not p') appears to be a contradiction, p does not entail 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 predict that p∧ p, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace p∧ p with a contradiction; 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 this 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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
09/16/2019

A Substructural Epistemic Resource Logic: Theory and Modelling Applications

We present a substructural epistemic logic, based on Boolean BI, in whic...
research
03/09/2018

Inquisitive bisimulation

Inquisitive modal logic InqML is a generalisation of standard Kripke-sty...
research
07/22/2019

Exploiting Belief Bases for Building Rich Epistemic Structures

We introduce a semantics for epistemic logic exploiting a belief base ab...
research
03/03/2015

An Introduction to Logics of Knowledge and Belief

This chapter provides an introduction to some basic concepts of epistemi...
research
07/11/2023

An Acceptance Semantics for Stable Modal Knowledge

We observe some puzzling linguistic data concerning ordinary knowledge a...
research
12/22/2015

Restricted Predicates for Hypothetical Datalog

Hypothetical Datalog is based on an intuitionistic semantics rather than...
research
07/28/2023

DELPHIC: Practical DEL Planning via Possibilities (Extended Version)

Dynamic Epistemic Logic (DEL) provides a framework for epistemic plannin...

Please sign up or login with your details

Forgot password? Click here to reset