There are several three-valued logical systems. They give the impression of a scattered landscape. The majority of the works on this subject gives the truth tables, sometimes an Hilbert style axiomatization in a basic propositional language and a completeness theorem with respect to those truth tables. We show that all the reasonable connectives in three-valued logics can be built starting from few of them. Nevertheless, the issue of the usefulness of each system in relation with the third truth value is often neglected. Here, we review the interpretations of the third truth value. Then, we focus on the unknown case, suggested by Kleene. We show that any formula in three-valued logics can be encoded as a fragment of an epistemic logic (formulae of modal depth 1, with modalities in front of literals), preserving all tautologies and inference rules. We study in particular, the translation of Kleene, Godel, Lukasiewicz and Nelson logics. This work enables us to lay bare the limited expressive power of three-valued logics in uncertainty management.
Ciucci, D.E., & Dubois, D. (2012). Three-Valued Logics for Incomplete Information and Epistemic Logic. In Logics in Artificial Intelligence (pp. 147-159). springer [10.1007/978-3-642-33353-8_12].
|Citazione:||Ciucci, D.E., & Dubois, D. (2012). Three-Valued Logics for Incomplete Information and Epistemic Logic. In Logics in Artificial Intelligence (pp. 147-159). springer [10.1007/978-3-642-33353-8_12].|
|Titolo:||Three-Valued Logics for Incomplete Information and Epistemic Logic|
|Autori:||Ciucci, DE; Dubois, D|
|Presenza di un coautore afferente ad Istituzioni straniere:||No|
|Tipo:||Capitolo o saggio|
|Carattere della pubblicazione:||Scientifica|
|Data di pubblicazione:||2012|
|Titolo del libro:||Logics in Artificial Intelligence|
|Appare nelle tipologie:||03 - Contributo in libro|