Reasoning about knowledge, belief and certainty in hierarchical multi-agent systems

Abstract

Multi-agent systems (MAS) have received extensive studies in the last decade. However, little attention is paid to investigation on reasoning about logics in MAS with hierarchical structures. This paper proposes a complete quantified temporal KBC (knowledge, belief and certainty) logic and corresponding reasoning in hierarchical multi-agent systems (HMAS). The key point is that internal beliefs and certainty, and external belief and certainty are considered in our logic. The internal beliefs and certainty show every agent is autonomous, while the external belief and certainty indicate the mutual influence of mental attitudes between two different agents on different layers in HMAS. To interpret this logic, we propose four classes of corresponding quantified interpreted systems, and define first-order KBC axiomatisations over HMAS, which are sound and complete with respect to the corresponding semantical classes. Finally, we give a case study to show the advantages in terms of expressiveness of our logic.

Keywords

hierarchical multi-agent systems / quantified temporal KBC logic / quantified interpreted systems

References

[1] LenzenW. Recent work in epistemic logic. Acta Philosophica Fennica, 1978, 30(9): 200–219

[2] FaginR, Halpern J, MossY , VardiM. Reasoning About Knowledge. Cambridge: MIT Press, 1995

[3] MeyerJ J C, Van der Hoek W. Epistemic logic for AI and Computer Science. Cambridge: Cambridge University Press, 1995

[4] AumannR J, Brandenburger A. Epistemic conditions for nash equilibrium. Econometrica, 1995, 63(9): 116–180

[5] FaginR, Halpern J Y, VardiM Y . What can machines know? On the properties of knowledge in distributed systems.Journal of the ACM, 1992, 39(2): 328–378

[6] HoekW V D, MeyerJ J, TreurJ. Formal semantics of temporal epistemic reflection Logic. In: Proceedings of the 4th International Workshops on Meta-Programming in Logic. 1994, 332–352

[7] Van Der MeydenR. Axioms for knowledge and time in distributed systems with perfect recall. In: Proceedings of the 9th IEEE Symposium on Logic in Computer Science. 1993, 15–22

[8] LakemeyerG. Limited reasoning in first-order knowledge bases with full introspection. Artificial Intelligence, 1996, 84(1): 209–255

[9] LomuscioA, Colombetti M. QLB: a quantified logic for belief. In: Proceedings of the 3rd International Workshop on Agent Theories, Architectures, and Languages. 1996

[10] RenneB, SackJ, YapA. Logics of temporal-epistemic actions. Synthese, 2016, 193(3): 813–849

[11] ChenQ L, SuK L, HuY, HuGW. A complete coalition logic of temporal knowledge for multi-agent systems. Frontiers of Computer Science, 2015, 9(1): 75–86

[12] WuL J, SuK L, SattarA, Chen Q L, SuJ S , WuW. A complete firstorder temporal BDI logic for forest multi-agent systems. Knowledge- Based Systems, 2012, 27(3): 343–351

[13] LamarreP, ShohamY. Knowledge, certainty, belief, and conditionalisation, belief and certainty. In: Proceedings of the International Conference on Knowledge Representation and Reasoning. 1994, 415–424

[14] SuK L, SattarA, GovernatoriG , ChenQ L. A computational grounded logic of knowledge, belief and certainty. In: Proceedings of the 4th International Joint Conference on Autonomous Agents and Multi-agent Systems. 2005, 149–156

[15] VoorbraakF. The theory of objective knowledge and rational belief. In: Proceedings of Logics in AI, European Workshop. 1990, 499–515

[16] FollesdalD. Knowledge, identity, and existence. Theoria, 1967, 23(1): 1–27

[17] HintikkaY. Knowledge, identity, and existence. Nous, 1962, 1(1): 33–62

[18] LevesqueH. Knowledge representation and reasoning. Annual Reviews Computer Science, 1986, 30(1): 81–108

[19] LiuY M, Levesque H J. Tractable reasoning in first-order knowledge bases with disjunctive information. In: Proceedings of National Conference on Artificial Intelligence. 2005, 639–644

[20] KanekoM, Nagashima T. Game logic and its applications 1. Studia Logica, 1996, 57(1): 325–354

[21] KanekoM, Nagashima T. Game logic and its applications 2. Studia Logica, 1997, 58(1): 273–303

[22] BieberP. A Logic of communication in hostile environments. In: Proceedings of the 3rd IEEE Computer Security Foundations Workshop. 1990, 14–22

[23] CohenM, DamsM. A complete axiomatization of knowledge and cryptography. In: Proceedings of IEEE Symposium on Logic in Computer Science. 2007, 77–88

[24] WooldridgeM. Verifying that agents implement a communication language. In: Proceedings of the 16th National Conference on Artificial Intelligence and the 11th Innovative Applications of Artificial Intelligence Conference Innovative Applications of Artificial Intelligence. 1999, 52–57

[25] WooldridgeM, FisherM, HugetM, Parsons S. Model checking multiagent systems with MABLE. In: Proceedings of the 1st International Conference on Autonomous Agents and Multiagent Systems. 2002, 952–959

[26] SuK L, SattarA, LuoX Y. Model checking temporal logics of knowledge via OBDDs. Computer Journal, 2007, 50(4): 403–420

[27] BelardinelliF, Lomuscio A. A complete first-order logic of knowledge and time. In: Proceedings of the 11th International Conference on Principles of Knowledge Representation and Reasoning. 2008, 705–714

[28] BelardinelliF, Lomuscio A. Quantified epistemic logics for reasoning about knowledge in multi-agent systems. Artificial Intelligence, 2009, 173(9): 982–1013

[29] BelardinelliF, Lomuscio A. Interactions between time and knowledge in a first-order logic for multi-agent systems. In: Proceedings of the 12th International Conference on Principles of Knowledge Representation and Reasoning. 2010, 38–48

[30] BelardinelliF, Lomuscio A. First-order linear-time epistemic logic with group knowledge: an axiomatisation of the monodic fragment. Fundamenta Informaticae, 2010, 17(9): 175–190

[31] WooldridgeM, Jennings N. Intelligent agents: theory and practice. Knowledge Engineering Review, 1995, 10(2): 49–62

[32] WuL J, SuJ S, SuK L, Luo X Y, YangZ H . A concurrent dynamic logic of knowledge, belief, and certainty for multi-agent systems. Knowledge-Based Systems, 2010, 23(2): 162–168

[33] AdamE, Mandiau R. Roles and hierarchy in multi-agent organizations. In: Proceedings of the 4th International Central and Eastern European Conference on Multi-Agent Systems. 2005, 539–542

[34] Emadi AndaniM, Bahrami F, Jabehdar-MaralaniP, IjspeertA J . MODEM: a multiagent hierarchical structure to model the human motor control system. Biological Cybernetics, 2009, 101(5): 361–377

[35] ChoińskiD, Nocoń W, MetzgerM . Multi-agent system for hierarchical control with self-organising database. In: Proceedings of the 1st KES Symposium on Agent and Multi-Agent Systems: Technologies and Applications. 2007, 655–664

[36] BlackburnP, van Benthem J F A K, WolterF . Handbook of modal logic. Cambridge Tracts in Theoretical Computer Science, 2007, 53(2): 170–180

[37] ChagrovA, Zakharyaschev M. Modal Logic. Oxford: Clarendon Press, 1997

[38] HughesM J, Cresswell G E. A new introduction to modal logic. New York: Routledge, 1996

[39] HalpernJ Y, MeydenR V, VardiM Y. Complete axiomatisations for reasoning about knowledge and time. SIAM Journal on Computing, 2003, 33(3): 674–703

RIGHTS & PERMISSIONS

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg