The Thirty-Third AAAI Conference on Artificial Intelligence (AAAI-19) Disjunctive Normal Form for Multi-Agent Modal Logics Based on Logical Separability Liangda Fang,1 Kewen Wang,2 Zhe Wang,2 Ximing Wen3 1Department of Computer Science, Jinan University, China 2School of Information and Communication Technology, Griffith University, Australia 3Guangdong Institute of Public Administration, Guangzhou, China
[email protected], fk.wang,zhe.wangg@griffith.edu.au,
[email protected] Abstract and the action preconditions. If a normal form is defined such that its entailment check, bounded conjunction and for- Modal logics are primary formalisms for multi-agent systems getting are tractable, then both progression and entailment but major reasoning tasks in such logics are intractable, which check in the normal form are tractable (Bienvenu, Fargier, impedes applications of multi-agent modal logics such as au- tomatic planning. One technique of tackling the intractabil- and Marquis 2010). As a result, in the normal form, an ef- ity is to identify a fragment called a normal form of multi- fective search algorithm is obtained. In the case of proposi- agent logics such that it is expressive but tractable for reason- tional logic, a normal form can be disjunctive normal form ing tasks such as entailment checking, bounded conjunction (DNF), conjunctive normal form (CNF) or prime implicate. transformation and forgetting. For instance, DNF of proposi- Usually, a planner based on DNF is faster than those based tional logic is tractable for these reasoning tasks. In this pa- on CNF and prime implicate (To, Pontelli, and Son 2011; per, we first introduce a notion of logical separability and then To, Son, and Pontelli 2011).