LIRa/GroLog Logic Afternoon

Speakers: Zoé Christoff (University of Groningen) and Aybüke Özgün (University of Amsterdam)

Date and Time: Thursday, December 3rd 2020, 15:30-17:30, Amsterdam time.

Schedule:

  • 15:30 Arrival

  • 15:45 First talk

  • 16:30 Break

  • 16:45 Second talk

  • 17:30 Drinks

 

Venue: online.

Zoé Christoff: Group Knowledge in Epistemic Logic with Names

(joint work with Marta Bílková and Olivier Roy)

In many situations, we refer to a group of agents using a label, say “Trump supporters” or “trolls”, without knowing exactly who the members of the group are. Sometimes, we even fail to know whether we, ourselves, are members of a given group. Yet, epistemic logic typically comes with the simplifying assumption that group membership is common knowledge among the entire population. In 1993 already, Grove and Halpern introduced a generalized epistemic logic relaxing this assumption and replacing the usual indexes to denote agents with abstract names that can have different referents, both individuals or groups, in different possible worlds. In that generalized framework, they replace the standard K_i modalities with modalities of the form S_n and E_n, for “someone with name n knows” and “everyone with name n knows”, respectively. In our current work, we discuss extensions of this generalized logic with group modalities for common knowledge and distributed knowledge.

Reference: A. J. Grove and J. Y. Halpern. Naming and Identity in Epistemic Logics Part I: The Propositional Case. Journal of Logic and Computation, 3(4):345–378, 08, 1993.

Aybüke Özgün: Uncertainty about Evidence

We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our models allow the set of possible worlds that a piece of evidence corresponds to to vary from one possible world to another, and therefore itself be the subject of uncertainty. Such structures can be viewed as (epistemically motivated) generalizations of topological spaces. In this context, there arises a natural distinction between what is actually entailed by the evidence and what the agent knows is entailed by the evidence—with the latter, in general, being much weaker. We provide a sound and complete axiomatization of the corresponding bi-modal logic of knowledge and evidence entailment, and investigate some natural extensions of this core system, including the addition of a belief modality and its interaction with evidence interpretation and entailment, and the addition of a “knowability” modality interpreted via a (generalized) interior operator.

This is joint work with Adam Bjorndahl.