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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2019-07-01
|
| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1907.09098v1 |
| _version_ | 1818017992967979008 |
|---|---|
| author | Adam Bjorndahl Aybüke Özgün |
| author_facet | Adam Bjorndahl Aybüke Özgün |
| author_sort | Adam Bjorndahl |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T07:34:01Z |
| format | Article |
| id | doaj.art-8395a8dd1c5746b883c51dd68de76ae6 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-04-14T07:34:01Z |
| publishDate | 2019-07-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-8395a8dd1c5746b883c51dd68de76ae62022-12-22T02:05:45ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802019-07-01297Proc. TARK 2019688110.4204/EPTCS.297.5:41Uncertainty About EvidenceAdam Bjorndahl0Aybüke Özgün1 Carnegie Mellon University ILLC, University of Amsterdam & Arché, University of St. Andrews 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.http://arxiv.org/pdf/1907.09098v1 |
| spellingShingle | Adam Bjorndahl Aybüke Özgün Uncertainty About Evidence Electronic Proceedings in Theoretical Computer Science |
| title | Uncertainty About Evidence |
| title_full | Uncertainty About Evidence |
| title_fullStr | Uncertainty About Evidence |
| title_full_unstemmed | Uncertainty About Evidence |
| title_short | Uncertainty About Evidence |
| title_sort | uncertainty about evidence |
| url | http://arxiv.org/pdf/1907.09098v1 |
| work_keys_str_mv | AT adambjorndahl uncertaintyaboutevidence AT aybukeozgun uncertaintyaboutevidence |