TIERED LOGIC FOR AGENTS

Rosalito Perez Cruz, John Newsome Crossley

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 specificationsm. 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.

References

  1. Akman, V. and Surav, M. (1996). Steps toward formalizing context. AI Magazine, 17(3):55-72.
  2. Bidoit, M. and Mosses, P. D. (2004). CASL User Manual: Introduction to Using the Common Algebraic Specification Language. Springer, Berlin, Heidelberg, New York.
  3. Borgida, A. and Serafini, L. (2003). Distributed description logics: Assimilating information from peer sources. In Journal of Data Semantics, volume 1, pages 153- 184,.
  4. Buvac?, S., Buvac?, V., and Mason, I. A. (1995). Metamathematics of contexts. Fundamenta Informaticae, 23(2/3/4):263-301.
  5. CASL (2001). CASL, The Common Algebraic Specification Language, Summary, 25 March 2001. CoFI Language Design Task Group on Language Design. http://www.brics.dk/Projects/CoFI/ Documents/CASL/Summary/.
  6. Cengarle, M. V. (1994). Formal Specifications with Higher-Order Parametrization. PhD thesis, LudwigMaximilians-Universität, München.
  7. Cruz, R. P. (2008). Tiered Logic with Applications to Contextualizing Logics. PhD thesis, Monash University, Melbourne, Australia. In preparation.
  8. Cruz, R. P. and Crossley, J. N. (2008). 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.
  9. Gabbay, D. and Nossum, R. T. (1997). Structured contexts with fibred semantics. In Buvac?, S. and IwaÁska, L., editors, Working Papers of the AAAI Fall Symposium on Context in Knowledge Representation and Natural Language, pages 48-57, Menlo Park, California. American Association for Artificial Intelligence.
  10. Ghidini, C. and Serafini, L. (1998). Distributed first order logics. In Baader, F. and Schultz, K. U., editors, Frontiers of Combining Systems 2, pages 121-139, Berlin. Research Studies Press/Wiley.
  11. Giunchiglia, F. and Ghidini, C. (2000). Local models semantics, or contextual reasoing = locality + compatibility. Artificial Intelligence, 127(2):221-259.
  12. Henkin, L. (1949). The completeness of the first-order functional calculus. Journal of Symbolic Logic, 14:159- 166.
  13. Li Yan and Du Shiran (1987). Chinese Mathematics: A Concise History. Oxford University Press, Oxford. Translated from the Chinese by J.N. Crossley and A.W.-C. Lun.
  14. L üttich, K. and Mossakowski, T. (2004). Specification of ontologies in CASL. In Varzi, A. C. and Vieu, L., editors, Proceedings of the International Conference on Formal Ontology in Information Systems (FOIS2004), pages 140-150, Amsterdam. IOS PRess.
  15. Poernomo, I. H., Crossley, J. N., and Wirsing, M. (2005). Adapting proofs-as-programs. Springer, New York.
Download


Paper Citation


in Harvard Style

Perez Cruz R. and Newsome Crossley J. (2009). TIERED LOGIC FOR AGENTS . In Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART, ISBN 978-989-8111-66-1, pages 369-376. DOI: 10.5220/0001120803690376


in Bibtex Style

@conference{icaart09,
author={Rosalito Perez Cruz and John Newsome Crossley},
title={TIERED LOGIC FOR AGENTS},
booktitle={Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,},
year={2009},
pages={369-376},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001120803690376},
isbn={978-989-8111-66-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Agents and Artificial Intelligence - Volume 1: ICAART,
TI - TIERED LOGIC FOR AGENTS
SN - 978-989-8111-66-1
AU - Perez Cruz R.
AU - Newsome Crossley J.
PY - 2009
SP - 369
EP - 376
DO - 10.5220/0001120803690376