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Erschienen in: Soft Computing 11/2012

01.11.2012 | Focus

Reasoning about ignorance and contradiction: many-valued logics versus epistemic logic

verfasst von: Didier Dubois

Erschienen in: Soft Computing | Ausgabe 11/2012

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Abstract

This paper tries to reinterpret three- and four-valued logics of partial ignorance and contradiction in the light of epistemic logic. First, we try to cast Kleene three-valued logic in the setting of a simplified form of epistemic logic. It is a two-tiered logic that embeds propositional logic into another propositional setting. The use of modalities enables Kleene truth values to be expressed at the syntactic level. Kleene logic is then a fragment of the simplified epistemic logic where modalities are in front of literals only. Kleene truth-tables can then be retrieved, while preserving tautologies of classical logic. Kleene logic connectives can be seen as set-valued extensions of Boolean logic ones, but the compositionality of Kleene logic leads to a lack of expressiveness and inferential power compared to the proposed epistemic logic. This methodology is then extended to Belnap four-valued logic, which is tailored to the handling of inconsistent information from various sources. A non-regular modal setting for reasoning about contradiction is obtained, where the adjunction law does not hold. It is a special case of a fragment of the monotonic modal logic EMN.

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Fußnoten
1
\({\mathbb{V}}_{3}\) is sometimes denoted by 3.
 
2
For clarity we do not use the same notation as in propositional logic for connectives.
 
3
A point of view Belnap did not adopt.
 
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Metadaten
Titel
Reasoning about ignorance and contradiction: many-valued logics versus epistemic logic
verfasst von
Didier Dubois
Publikationsdatum
01.11.2012
Verlag
Springer-Verlag
Erschienen in
Soft Computing / Ausgabe 11/2012
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-012-0833-5

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