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DEFINING KNOWLEDGE IN TERMS OF BELIEF: THE MODAL LOGIC PERSPECTIVE

Published online by Cambridge University Press:  05 October 2009

JOSEPH Y. HALPERN ,
DOV SAMET  and
ELLA SEGEV
JOSEPH Y. HALPERN*
Affiliation:
Computer Science Department, Cornell University
DOV SAMET*
Affiliation:
The Faculty of Management, Tel Aviv University
ELLA SEGEV*
Affiliation:
Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology
*
*COMPUTER SCIENCE DEPARTMENT, CORNELL UNIVERSITY, ITHACA, NY 14853 E-mail:halpern@cs.cornell.edu
†THE FACULTY OF MANAGEMENT, TEL AVIV UNIVERSITY, TEL AVIV 69978, ISRAEL E-mail:samet@post.tau.ac.il
‡FACULTY OF INDUSTRIAL ENGINEERING AND MANAGEMENT, TECHNION - ISRAEL INSTITUTE OF TECHNOLOGY, TECHNION CITY, HAIFA 32000, ISRAEL, E-mail:esegev@ie.technion.ac.il
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Abstract

The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last 50 years, is studied here in the framework of epistemic and doxastic logics. Three notions of definability are considered: explicit definability, implicit definability, and reducibility, where explicit definability is equivalent to the combination of implicit definability and reducibility. It is shown that if knowledge satisfies any set of axioms contained in S5, then it cannot be explicitly defined in terms of belief. S5 knowledge can be implicitly defined by belief, but not reduced to it. On the other hand, S4.4 knowledge and weaker notions of knowledge cannot be implicitly defined by belief, but can be reduced to it by defining knowledge as true belief. It is also shown that S5 knowledge cannot be reduced to belief and justification, provided that there are no axioms that involve both belief and justification.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 3 , September 2009 , pp. 469 - 487
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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