Abstract
We introduce a new kind of logic for agents in different localities, which works in tiers or layers. At the base are local worlds with their own logic. Above them is a global logic that takes statements from the local worlds and combines them. This allows communications between the different localities.
We give a basic example using first order logic as the local logic and propositional calculus at the global level. As a more sophisticated example we use the algebraic specification language CASL and take the locations as specifications. Moreover we then permit the combination of such specifications according to the architectural specifications of CASL.
Although we only consider two layers in the present paper, we see no reason why the approach should not be extended to any finite number of tiers. We prove soundness and completeness proofs for our logics.
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References
Akman, V., Surav, M.: Steps toward formalizing context. AI Magazine 17(3), 55–72 (1996)
Bidoit, M., Mosses, P.D.: CASL User Manual: Introduction to Using the Common Algebraic Specification Language. Springer, Heidelberg (2004)
Borgida, A., Serafini, L.: Distributed description logics: Assimilating information from peer sources. In: Spaccapietra, S., March, S., Aberer, K. (eds.) Journal on Data Semantics I. LNCS, vol. 2800, pp. 153–184. Springer, Heidelberg (2003)
Bouquet, P., Serafini, L.: On the Difference between Bridge Rules and Lifting Axioms. In: Blackburn, P., Ghidini, C., Turner, R.M., Giunchiglia, F. (eds.) CONTEXT 2003. LNCS, vol. 2680, pp. 80–93. Springer, Heidelberg (2003)
Buvač, S., Buvač, V., Mason, I.A.: Metamathematics of contexts. Fundamenta Informaticae 23(2/3/4), 263–301 (1995)
COFI: CASL, The Common Algebraic Specification Language, Summary. CoFI Language Design Task Group on Language Design (March 25, 2001), http://www.brics.dk/Projects/CoFI/-Documents/-CASL/-Summary/ (2001)
Cengarle, M.V.: Formal Specifications with Higher-Order Parametrization. PhD thesis, Ludwig-Maximilians-Universität, München (1994)
Cruz, R.P.: Tiered Logic with Applications to Contextualizing Logics. PhD thesis, Monash University, Melbourne, Australia (in preparation)
Cruz, R.P., Crossley, J.N.: Tiered logic method for assisting agents. Technical Report Technical Report 2008/232. Monash University, Clayton School of Information Technology, Clayton, Victoria, Australia, http://www.csse.monash.edu.au/publications/2008/tr-2008-232-abs.html
Gabbay, D., Nossum, R.T.: Structured contexts with fibred semantics. In: Working Papers of the AAAI Fall Symposium on Context in Knowledge Representation and Natural Language, pp. 48–57. American Association for Artificial Intelligence, Menlo Park (1997)
Ghidini, C., Serafini, L.: Distributed first order logics. In: Baader, F., Schultz, K.U. (eds.) Frontiers of Combining Systems 2, pp. 121–139. Research Studies Press/Wiley, Berlin (1998)
Giunchiglia, F., Ghidini, C.: Local models semantics, or contextual reasoning = locality + compatibility. Artificial Intelligence 127(2), 221–259 (2000)
Henkin, L.: The completeness of the first-order functional calculus. Journal of Symbolic Logic 14, 159–166 (1949)
Yǎn, L., Shírán, D.: Chinese Mathematics: A Concise History. Oxford University Press, Oxford (1987); Translated from the Chinese by J.N. Crossley and A.W.-C. Lun
Lüttich, K., Mossakowski, T.: Specification of ontologies in CASL. In: Varzi, A.C., Vieu, L. (eds.) Proceedings of the International Conference on Formal Ontology in Information Systems (FOIS 2004), pp. 140–150. IOS Press, Amsterdam (2004)
McCarthy, J., Buvač, S.: Formalizing Context (Expanded Notes). In: Buvač, S., Iwańska, Ł. (eds.) Working Papers of the AAAI Fall Symposium on Context in Knowledge Representation and Natural Language, pp. 99–135. American Association for Artificial Intelligence, Menlo Park (1997)
Nossum, R.T.: A decidable multi-modal logic of context. J. Applied Logic 1, 119–133 (2003)
Poernomo, I.H., Crossley, J.N., Wirsing, M.: Adapting proofs-as-programs. Springer, New York (2005)
Serafini, L., Bouquet, P.: Comparing formal theories of context in AI. Artificial Intelligence 155, 41–67 (2004/2005))
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Cruz, R.P., Crossley, J.N. (2010). Tiered Logic for Agents in Contexts. In: Filipe, J., Fred, A., Sharp, B. (eds) Agents and Artificial Intelligence. ICAART 2009. Communications in Computer and Information Science, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11819-7_15
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DOI: https://doi.org/10.1007/978-3-642-11819-7_15
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