Modal Logics for Reasoning about Multiagent Systems

Modal Logics for Reasoning about Multiagent Systems

Nikolay V. Shilov, Natalia Garanina
Copyright: © 2009 |Pages: 6
ISBN13: 9781599048499|ISBN10: 1599048493|EISBN13: 9781599048505
DOI: 10.4018/978-1-59904-849-9.ch160
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MLA

Shilov, Nikolay V., and Natalia Garanina. "Modal Logics for Reasoning about Multiagent Systems." Encyclopedia of Artificial Intelligence, edited by Juan Ramón Rabuñal Dopico, et al., IGI Global, 2009, pp. 1089-1094. https://doi.org/10.4018/978-1-59904-849-9.ch160

APA

Shilov, N. V. & Garanina, N. (2009). Modal Logics for Reasoning about Multiagent Systems. In J. Rabuñal Dopico, J. Dorado, & A. Pazos (Eds.), Encyclopedia of Artificial Intelligence (pp. 1089-1094). IGI Global. https://doi.org/10.4018/978-1-59904-849-9.ch160

Chicago

Shilov, Nikolay V., and Natalia Garanina. "Modal Logics for Reasoning about Multiagent Systems." In Encyclopedia of Artificial Intelligence, edited by Juan Ramón Rabuñal Dopico, Julian Dorado, and Alejandro Pazos, 1089-1094. Hershey, PA: IGI Global, 2009. https://doi.org/10.4018/978-1-59904-849-9.ch160

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Abstract

It becomes evident in recent years a surge of interest to applications of modal logics for specification and validation of complex systems. It holds in particular for combined logics of knowledge, time and actions for reasoning about multiagent systems (Dixon, Nalon & Fisher, 2004; Fagin, Halpern, Moses & Vardi, 1995; Halpern & Vardi, 1986; Halpern, van der Meyden & Vardi, 2004; van der Hoek & Wooldridge, 2002; Lomuscio, & Penczek, W., 2003; van der Meyden & Shilov, 1999; Shilov, Garanina & Choe, 2006; Wooldridge, 2002). In the next paragraph we explain what are logics of knowledge, time and actions from a viewpoint of mathematicians and philosophers. It provides us a historic perspective and a scientific context for these logics. For mathematicians and philosophers logics of actions, time, and knowledge can be introduced in few sentences. A logic of actions (ex., Elementary Propositional Dynamic Logic (Harel, Kozen & Tiuryn, 2000)) is a polymodal variant of a basic modal logic K (Bull & Segerberg, 2001) to be interpreted over arbitrary Kripke models. A logic of time (ex., Linear Temporal Logic (Emerson, 1990)) is a modal logic with a number of modalities that correspond to “next time”, “always”, “sometimes”, and “until” to be interpreted in Kripke models over partial orders (discrete linear orders for LTL in particular). Finally, a logic of knowledge or epistemic logic (ex., Propositional Logic of Knowledge (Fagin, Halpern, Moses & Vardi, 1995; Rescher, 2005)) is a polymodal variant of another basic modal logic S5 (Bull & Segerberg, 2001) to be interpreted over Kripke models where all binary relations are equivalences.

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