Lower Bound Founded Logic of Here-and-There

Pedro Calabar (1) , Jorge Fandinno (2) , Torsten Schaub (3) , Sebastian Schellhorn (3)

1 Universidade da Coruña
2 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
3 University of Potsdam = Universität Potsdam

A distinguishing feature of Answer Set Programming is that all atoms belonging to a stable model must be founded. That is, an atom must not only be true but provably true. This can be made precise by means of the constructive logic of Here-and-There, whose equilibrium models correspond to stable models. One way of looking at foundedness is to regard Boolean truth values as ordered by letting true be greater than false. Then, each Boolean variable takes the smallest truth value that can be proven for it. This idea was generalized by Aziz to ordered domains and applied to constraint satisfaction problems. As before, the idea is that a, say integer, variable gets only assigned to the smallest integer that can be justified. In this paper, we present a logical reconstruction of Aziz’ idea in the setting of the logic of Here-and-There. More precisely, we start by defining the logic of Here-and-There with lower bound founded variables along with its equilibrium models and elaborate upon its formal properties. Finally, we compare our approach with related ones and sketch future work.

Mots clés: Logic of Here-and-There

Domaines: Intelligence artificielle [cs.AI]; Logique en informatique [cs.LO]

Pedro Calabar, Jorge Fandinno, Torsten Schaub, Sebastian Schellhorn. Lower Bound Founded Logic of Here-and-There. 16th European Conference on Logics in Artificial Intelligence (JELIA 2019), May 2019, Rende, Italy. pp.509-525. ⟨hal-02486108⟩