When 'knowing whether' is better than 'knowing that'

Martin Cooper (1, 2) , Andreas Herzig (3, 4) , Faustine Maffre (3) , Frédéric Maris (1) , Elise Perrotin (3) , Pierre Régnier (1)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 UT3 - Université Toulouse III - Paul Sabatier
3 IRIT-LILaC - Logique, Interaction, Langue et Calcul
4 CNRS - Centre National de la Recherche Scientifique

We study a simple epistemic logic with a restricted language where formulas are boolean combinations of (epistemic) atoms: sequences of 'know-ing whether' operators followed by propositional variables. Our language is strictly more expressive than existing restricted languages, where atoms are sequences of epistemic operators and negations followed by propositional variables (in other words: atoms are epistemic formulas without conjunctions and disjunctions). Going further beyond existing approaches , we also introduce a 'common knowledge of a group whether' operator. We give an axiomatiza-tion for this logic and show that the model checking and satisfiability problems can be reduced to their classical counterparts.

Domaines: Intelligence artificielle [cs.AI]

Martin Cooper, Andreas Herzig, Faustine Maffre, Frédéric Maris, Elise Perrotin, et al.. When 'knowing whether' is better than 'knowing that'. 13èmes Journées d’Intelligence Artificielle Fondamentale (JIAF 2019), Jul 2019, Toulouse, France. ⟨hal-02302984⟩