Epistemic logics for sceptical agents

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985955%3A_____%2F16%3A00471689" target="_blank" >RIV/67985955:_____/16:00471689 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1093/logcom/exv009" target="_blank" >http://dx.doi.org/10.1093/logcom/exv009</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1093/logcom/exv009" target="_blank" >10.1093/logcom/exv009</a>

Result language

angličtina

Original language name

Epistemic logics for sceptical agents

Original language description

In this article, we introduce an epistemic modal operator modelling knowledge over distributive non-associative full Lambek calculus with a negation. Our approach is based on the relational semantics for substructural logics: we interpret the elements of a relational frame as information states consisting of collections of data. The principal epistemic relation between the states is the one of being a reliable source of information, on the basis of which we explicate the notion of knowledge as information confirmed by a reliable source. From this point of view it is natural to define the epistemic operator formally as the backward-looking diamond modality. The framework is a generalization and extension of the system of relevant epistemic logic proposed by Majer and Pelis (2009, college Publications, 123-135) and developed by Bilkova et al. (2010, college Publications, 22-38). The system is modular in the sense that the axiomatization of the epistemic operator is sound and complete with respect to a wide class of background logics, which makes the system potentially applicable to a wide class of epistemic contexts. Our system admits a weak form of logical omniscience (the monotonicity rule), but avoids stronger ones (a necessitation rule and a K-axiom) as well as some closure properties discussed in normal epistemic logics (like positive and negative introspection). For these properties we provide characteristic frame conditions, so that they can be present in the system if they are considered to be appropriate for some specific epistemic context. We also prove decidability of the weakest epistemic logic we consider, using a filtration method. Finally, we outline further extensions of our framework to a multiagent system.

Czech name

—

Czech description

—

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

AA - Philosophy and religion

OECD FORD branch

—

Project

<a href="/en/project/GA13-21076S" target="_blank" >GA13-21076S: Foundations of logic in the light of new results of philosophy and science</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2016

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Logic and Computation

ISSN

0955-792X

e-ISSN

—

Volume of the periodical

26

Issue of the periodical within the volume

6

Country of publishing house

GB - UNITED KINGDOM

Number of pages

27

Pages from-to

1815-1841

UT code for WoS article

000392844500003

EID of the result in the Scopus database

2-s2.0-85014581350