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Article Dans Une Revue Soft Computing Année : 2012

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

Résumé

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.

Dates et versions

hal-03413942 , version 1 (04-11-2021)

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Didier Dubois. Reasoning about ignorance and contradiction: many-valued logics versus epistemic logic. Soft Computing, 2012, 16 (11), pp.1817-1831. ⟨10.1007/s00500-012-0833-5⟩. ⟨hal-03413942⟩
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