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A logic of explicit knowledge (2005)
| Venue: | In L. Behounek and M. Bilkova (Eds.), Logica Yearbook 2004 |
| Citations: | 7 - 0 self |
BibTeX
@INPROCEEDINGS{Fitting05alogic,
author = {Melvin Fitting},
title = {A logic of explicit knowledge},
booktitle = {In L. Behounek and M. Bilkova (Eds.), Logica Yearbook 2004},
year = {2005},
pages = {11--22},
publisher = {Filosophia}
}
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Abstract
A well-known problem with Hintikka-style logics of knowledge is that of logical omniscience. One knows too much. This breaks down into two subproblems: one knows all tautologies, and one’s knowledge is closed under consequence. A way of addressing the second of these is to move from knowledge simpliciter, to knowledge for a reason. Then, as consequences become ‘further away ’ from one’s basic knowledge, reasons for them become more complex, thus providing a kind of resource measurement. One kind of reason is a formal proof. Sergei Artemov has introduced a logic of explicit proofs, LP. I present a semantics for this, based on the idea that it is a logic of knowledge with explicit reasons. A number of fundamental facts about LP can be established using this semantics. But it is equally important to realize that it provides a natural logic of more general applicability than its original provenance, arithmetic provability. 1
Keyphrases
explicit knowledge knowledge simpliciter explicit reason explicit proof formal proof resource measurement original provenance basic knowledge natural logic fundamental fact general applicability sergei artemov well-known problem logical omniscience arithmetic provability hintikka-style logic
