Abstract
This paper introduces \(\text {4QL}^{\!\text {Bel}}\), a four-valued rule language designed for reasoning with paraconsistent and paracomplete belief bases as well as belief structures. Belief bases consist of finite sets of ground literals providing (partial and possibly inconsistent) complementary or alternative views of the world. As introduced earlier, belief structures consist of constituents, epistemic profiles and consequents. Constituents and consequents are belief bases playing different roles. Agents perceive the world forming their constituents, which are further transformed into consequents via the agents’ or groups’ epistemic profile.
In order to construct \(\text {4QL}^{\!\text {Bel}}\), we extend 4QL, a four-valued rule language permitting for many forms of reasoning, including doxastic reasoning. Despite the expressiveness of \(\text {4QL}^{\!\text {Bel}}\), we show that its tractability is retained.
Supported by the Polish National Science Centre grant 2015/19/B/ST6/02589.
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Notes
- 1.
For an open-source implementations of 4QL see http://4ql.org. The inter4ql 3.0 interpreter includes some features for querying belief bases, implemented by A. Bułanowski.
- 2.
Here we adjust the syntax used in implementations of 4QL (see http://4ql.org).
- 3.
Note that due to the acyclicity of the reference graph, new modules not referring to other modules are obtained in this step.
References
de Amo, S., Pais, M.S.: A paraconsistent logic approach for querying inconsistent databases. Int. J. Approx. Reason. 46, 366–386 (2007)
Balbiani, P., Pearce, D., Uridia, L.: On logics of group belief in structured coalitions. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS, vol. 10021, pp. 97–111. Springer, Cham (2016). doi:10.1007/978-3-319-48758-8_7
Béziau, J.Y., Carnielli, W., Gabbay, D. (eds.): Handbook of Paraconsistency. College Publications, Norcross (2007)
Cholvy, L., Hunter, A.: Information fusion in logic: a brief overview. In: Gabbay, D.M., Kruse, R., Nonnengart, A., Ohlbach, H.J. (eds.) ECSQARU/FAPR -1997. LNCS, vol. 1244, pp. 86–95. Springer, Heidelberg (1997). doi:10.1007/BFb0035614
Cholvy, L., Hunter, A.: Merging requirements from a set of ranked agents. Knowl.-Based Syst. 16(2), 113–126 (2003)
da Costa, N., Bueno, O.: Belief change and inconsistency. Log. Anal. 41(161–163), 31–56 (1998)
Dunin-Kęplicz, B., Strachocka, A.: Tractable inquiry in information-rich environments. In: Proceedings of the 24th IJCAI, pp. 53–60 (2015)
Dunin-Kęplicz, B., Strachocka, A.: Paraconsistent argumentation schemes. Web Intell. 14, 43–65 (2016)
Dunin-Kęplicz, B., Szałas, A.: Epistemic profiles and belief structures. In: Jezic, G., Kusek, M., Nguyen, N.-T., Howlett, R.J., Jain, L.C. (eds.) KES-AMSTA 2012. LNCS, vol. 7327, pp. 360–369. Springer, Heidelberg (2012). doi:10.1007/978-3-642-30947-2_40
Dunin-Kęplicz, B., Szałas, A.: Taming complex beliefs. In: Nguyen, N.T. (ed.) Transactions on Computational Collective Intelligence XI. LNCS, vol. 8065, pp. 1–21. Springer, Heidelberg (2013). doi:10.1007/978-3-642-41776-4_1
Dunin-Kęplicz, B., Szałas, A.: Indeterministic belief structures. In: Jezic, G., Kusek, M., Lovrek, I., J. Howlett, R., Jain, L.C. (eds.) Agent and Multi-agent Systems: Technologies and Applications. AISC, vol. 296, pp. 57–66. Springer, Cham (2014). doi:10.1007/978-3-319-07650-8_7
Dunin-Kęplicz, B., Szałas, A., Verbrugge, R.: Tractable reasoning about group beliefs. In: Dalpiaz, F., Dix, J., Riemsdijk, M.B. (eds.) EMAS 2014. LNCS, vol. 8758, pp. 328–350. Springer, Cham (2014). doi:10.1007/978-3-319-14484-9_17
Dunin-Kęplicz, B., Verbrugge, R.: Teamwork in Multi-Agent Systems. A Formal Approach. Wiley, Hoboken (2010)
Fagin, R., Halpern, J.: Belief, awareness, and limited reasoning. Artif. Intell. 34(1), 39–76 (1988)
Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. MIT Press, Cambridge (2003)
van Harmelen, F., Lifschitz, V., Porter, B.: Handbook of Knowledge Representation. Elsevier, Amsterdam (2007)
Małuszyński, J., Szałas, A.: Living with inconsistency and taming nonmonotonicity. In: Moor, O., Gottlob, G., Furche, T., Sellers, A. (eds.) Datalog 2.0 2010. LNCS, vol. 6702, pp. 384–398. Springer, Heidelberg (2011). doi:10.1007/978-3-642-24206-9_22
Małuszyński, J., Szałas, A.: Logical foundations and complexity of 4QL, a query language with unrestricted negation. J. Appl. Non-Class. Logics 21(2), 211–232 (2011)
Małuszyński, J., Szałas, A.: Partiality and inconsistency in agents’ belief bases. In: Barbucha, D., Le, M., Howlett, R., Jain, L. (eds.) Frontiers in Artificial Intelligence and Applications, vol. 252, pp. 3–17. IOS Press, Amsterdam (2013)
Meyer, J.J.C., van der Hoek, W.: Epistemic Logic for Computer Science and Artificial Intelligence. Cambridge University Press, Cambridge (1995)
Priest, G.: Special issue on impossible worlds. Notre Dame J. Formal Logic 38(4), 481–660 (1997)
Priest, G.: Paraconsistent belief revision. Theoria 67(3), 214–228 (2001)
Szałas, A.: How an agent might think. Logic J. IGPL 21(3), 515–535 (2013)
Tanaka, K.: The AGM theory and inconsistent belief change. Logique & Analyse 48(189–192), 113–150 (2005)
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Białek, Ł., Dunin-Kęplicz, B., Szałas, A. (2017). Rule-Based Reasoning with Belief Structures. In: Kryszkiewicz, M., Appice, A., Ślęzak, D., Rybinski, H., Skowron, A., Raś, Z. (eds) Foundations of Intelligent Systems. ISMIS 2017. Lecture Notes in Computer Science(), vol 10352. Springer, Cham. https://doi.org/10.1007/978-3-319-60438-1_23
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