A Logical Approach to Qualitative and Quantitative Reasoning

Abstract

Reasoning with qualitative and quantitative uncertainty is required in some real-world applications [6]. However, current extensions to logic programming with uncertainty support representing and reasoning with either qualitative or quantitative uncertainty. In this paper we extend the language of Hybrid Probabilistic Logic programs [29,27], originally introduced for reasoning with quantitative uncertainty, to support both qualitative and quantitative uncertainty. We propose to combine disjunctive logic programs [10,19] with Extended and Normal Hybrid Probabilistic Logic Programs (EHPP [27] and NHPP [29]) in a unified logic programming framework, to allow directly and intuitively to represent and reason in the presence of both qualitative and quantitative uncertainty. The semantics of the proposed languages are based on the answer sets semantics and stable model semantics of extended and normal disjunctive logic programs [10,19]. In addition, they also rely on the probabilistic answer sets semantics and the stable probabilistic model semantics of EHPP [27] and NHPP .