Affiliations: School of Computer Science and Engineering, Southeast University, 2#, Si Pai Lou, Nanjing, China. {seu_zzz, wangbiu, stzhang}@seu.edu.cn
Correspondence:
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Address for correspondence: School of Computer Science and Engineering, Southeast University, Sipailou 2#,Nanjing, Jiangsu Province, 210096 P. R. China
Note: [†] The work was supported by the National Science Foundation of China(Grant No.60803061), the National Science Foundation of China(Grant No.61272378), Natural Science Foundation of Jiangsu(Grant No.BK2008293), and the National High Technology Research and Development Program of China(Grant No.2015AA015406).
Abstract: This paper develops a logic programming language, GI-log, that extends answer set programming language with a new graded modality Kω where ω is an interval satisfying ω ⊆ [0, 1]. The modality is used to precede a literal in rules bodies, and thus allows for the representation of graded introspections in the presence of multiple belief sets: KωF intuitively means: it is known that the proportion of the belief sets where F is true is in the interval ω. We define the semantics of GI-log, study the relation to the languages of strong introspections, give an algorithm for computing solutions of GI-log programs, and investigate the use of GI-log for formalizing contextual reasoning, conformant planning with threshold, and modeling a graph problem.
