Skip to main content
SpringerLink
Log in

Verifying time, memory and communication bounds in systems of reasoning agents

  • Published:
Synthese Aims and scope Submit manuscript

Abstract

We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion of its available computational resources or bandwidth to the problem. We present a novel temporal epistemic logic, BMCL-CTL, which allows us to describe a set of reasoning agents with bounds on time, memory and the number of messages they can exchange. The bounds on memory and communication are expressed as axioms in the logic. As an example, we show how to axiomatise a system of agents which reason using resolution and prove that the resulting logic is sound and complete. We then show how to encode a simple system of reasoning agents specified in BMCL-CTL in the description language of the Mocha model checker (Alur et al., Proceedings of the tenth international conference on computer-aided verification (CAV), 1998), and verify that the agents can achieve a goal only if they are prepared to commit certain time, memory and communication resources.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Adjiman P., Chatalic P., Goasdoué F., Rousset M.-C., Simon L. (2004) Distributed reasoning in a peer-to-peer setting. In: Mántaras R.L., Saitta L. (eds) Proceedings of the 16th European conference on artificial intelligence, ECAI’2004, including prestigious applicants of intelligent systems, PAIS 2004, Valencia. IOS Press, Spain, pp 945–946

    Google Scholar 

  • Ågotnes T., Alechina N. (2006) Knowing minimum/maximum n formulae. In: Brewka G., Coradeschi S., Perini A., Traverso P. (eds) Proceedings of the 17th European conference on artificial intelligence (ECAI 2006). IOS Press, Riva del Garda, Italy, pp 317–321

    Google Scholar 

  • Ågotnes, T., & Walicki, M. (2005). Strongly complete axiomatizations of knowing atmost in standard syntactic assignments. In F. Toni & P. Torroni (Eds.), Pre-proceedings of the 6th international workshop on computational logic in multi-agent systems (CLIMA VI), City University, London, UK.

  • Albore, A., Alechina, N., Bertoli, P., Ghidini, C., Logan, B., & Serafini, L. (2006). Model-checking memory requirements of resource-bounded reasoners. In Proceedings of the twenty-first national conference on artificial intelligence (AAAI 2006) (pp. 213–218). Melano Park, CA: AAAI Press.

  • Alechina N., Bertoli P., Ghidini C., Jago M., Logan B., Serafini L. (2006a) Verifying space and time requirements for resource-bounded agents. In: Stone P., Weiss G. (eds) Proceedings of the fifth international joint conference on autonomous agents and multi-agent systems (AAMAS 2006). IEEE Press, Hakodate, Japan, pp 217–219

    Chapter  Google Scholar 

  • Alechina N., Bertoli P., Ghidini C., Jago M., Logan B., Serafini L. (2006b) Verifying space and time requirements for resource-bounded agents. In: Edelkamp S., Lomuscio A., Serafini L. (eds) Proceedings of the fourth workshop on model checking and artificial intelligence (MoChArt-2006). Riva del Garda , Italy, pp 16–30

    Google Scholar 

  • Alechina N., Jago M., Logan B. (2006c) Modal logics for communicating rule-based agents. In: Brewka G., Coradeschi S., Perini A., Traverso P. (eds) Proceedings of the 17th European conference on artificial intelligence (ECAI 2006). IOS Press, Riva del Garda, Italy, pp 322–326

    Google Scholar 

  • Alechina, N., Logan, B., Nga, N. H., & Rakib, A. (2008a). Reasoning about other agents’ beliefs under bounded resources. In J.-J. C. Meyer & J. Broersen (Eds.), Pre-proceedings of the KR2008 workshop on knowledge representation for agents and multi-agent systems (KRAMAS 2008) (pp. 4–18), Sydney, Australia.

  • Alechina, N., Logan, B., Nga, N. H., & Rakib, A. (2008b). Verifying time, memory and communication bounds in systems of reasoning agents. In L. Padgham, D. Parkes, J. Müller, & S. Parsons (Eds.), Proceedings of the seventh international conference on autonomous agents and multi-agent systems (AAMAS 2008) (Vol. 2, pp. 736–743). Estoril, Portugal: IFAAMAS.

  • Alechina, N., Logan, B., & Whitsey, M. (2004). A complete and decidable logic for resource-bounded agents. In Proceedings of the third international joint conference on autonomous agents and multi-agent systems (AAMAS 2004) (pp. 606–613). New York: ACM Press.

  • Alekhnovich M., Ben-Sasson E., Razborov A.A., Wigderson A. (2002) Space complexity in propositional calculus. SIAM Journal of Computing 31(4): 1184–1211

    Article  Google Scholar 

  • Alur, R., Henzinger, T. A., & Kupferman, O. (1997). Alternating-time temporal logic. In Proceedings of the 38th IEEE FOCS 1997 (pp. 100–109).

  • Alur, R., Henzinger, T. A., Mang, F. Y. C., Qadeer, S., Rajamani, S. K., & Tasiran, S. (1998). Mocha: Modularity in model checking. In Proceedings of the tenth international conference on computer-aided verification (CAV). Lecture Notes in Computer Science (Vol. 1427, pp. 521–525). Springer.

  • Amir E., McIlraith S.A. (2005) Partition-based logical reasoning for first-order and propositional theories. Artificial Intelligence 162(1–2): 49–88

    Article  Google Scholar 

  • Benerecetti M., Giunchiglia F., Serafini L. (1998) Model checking multiagent systems. Journal of Logic and Computation 8(3): 401–423

    Article  Google Scholar 

  • Bordini R., Fisher M., Visser W., Wooldridge M. (2004) State-space reduction techniques in agent verification. In: Jennings N.R., Sierra C., Sonenberg L., Tambe M. (eds) Proceedings of the third international joint conference on autonomous agents and multi-agent systems (AAMAS-2004). ACM Press, New York, pp 896–903

    Google Scholar 

  • Clarke E.M., Emerson E.A., Sistla A.P. (1986) Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Transactions on Programming Languages and Systems 8(2): 244–263

    Article  Google Scholar 

  • Duc H. (1997) Reasoning about rational, but not logically omniscient, agents. Journal of Logic and Computation 5: 633–648

    Article  Google Scholar 

  • Elgot-Drapkin J.J., Perlis D. (1990) Reasoning situated in time I: Basic concepts. Journal of Experimental and Theoretical Artificial Intelligence 2: 75–98

    Article  Google Scholar 

  • Emerson E.A., Halpern J.Y. (1985) Decision procedures and expressiveness in the temporal logic of branching time. Journal of Computer and System Science 30(1): 1–24

    Article  Google Scholar 

  • Esteban, J. L., & Torán, J. (1999). Space bounds for resolution. In C. Meinel & S. Tison (Eds.), Proceedings of the STACS 99, 16th annual symposium on theoretical aspects of computer science, Trier, Germany. Lecture Notes in Computer Science (Vol. 1563, pp. 551–560), Springer.

  • Fagin R., Halpern J.Y., Moses Y., Vardi M.Y. (1995) Reasoning about knowledge. MIT Press, Cambridge, Mass.

    Google Scholar 

  • Faltings B., Yokoo M. (2005) Introduction: Special issue on distributed constraint satisfaction. Artificial Intelligence 161(1–2): 1–5

    Article  Google Scholar 

  • Fisher, M., & Ghidini, C. (1999). Programming resource-bounded deliberative agents. In Proceedings of the sixteenth international joint conference on artificial intelligence (IJCAI’99) (pp. 200–206). Stockholm, Sweden: Morgan Kaufmann.

  • Grant J., Kraus S., Perlis D. (2000) A logic for characterizing multiple bounded agents. Autonomous Agents and Multi-Agent Systems 3(4): 351–387

    Article  Google Scholar 

  • Haken A. (1985) The intractability of resolution. Journal of Theoretical Computer Science 39(2–3): 297–308

    Article  Google Scholar 

  • Halpern J.Y., Moses Y., Vardi M.Y. (1994) Algorithmic knowledge. In: Fagin R. (eds) Proceedings of the 5th conference on theoretical aspects of reasoning about knowledge, 1994. Morgan Kaufmann, Pacific Grove, CA, pp 255–266

    Google Scholar 

  • Jago, M. (2006). Logics for resource-bounded agents. Ph.D. thesis, University of Nottingham.

  • Jung, H., & Tambe, M. (2005, September 15–17). On communication in solving distributed constraint satisfaction problems. In M. Pechoucek, P. Petta, & L. Z. Varga (Eds.), Proceedings of the multi-agent systems and applications IV, 4th international central and eastern european conference on multi-agent systems, CEEMAS 2005, Budapest, Hungary. Lecture Notes in Computer Science (Vol. 3690, pp. 418–429), Springer.

  • Konolige K. (1986) A deduction model of belief. Morgan Kaufmann, San Francisco

    Google Scholar 

  • Provan, G. M. (2002, April 22–25). A model-based diagnosis framework for distributed embedded systems. In D. Fensel, F. Giunchiglia, D. L. McGuinness, & M.-A. Williams (Eds.), Proceedings of the eights international conference on principles and knowledge representation and reasoning (KR-02) (pp. 341–352). Toulouse, France: Morgan Kaufmann.

  • Pucella, R. (2004, January 4–6). Deductive algorithmic knowledge. In AI&M 1-2004, eighth international symposium on artificial intelligence and mathematics, Fort Lauderdale, FL, USA.

  • Wooldridge M., Dunne P.E. (2006) On the computational complexity of coalitional resource games. Artificial Intelligence 170(10): 835–871

    Article  Google Scholar 

  • Yao, A. C.-C. (1979, April 30–May 2), Some complexity questions related to distributive computing (preliminary report). In Conference record of the eleventh annual ACM symposium on theory of computing (pp. 209–213). Atlanta, GA: ACM.

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, University of Nottingham, Nottingham, NG8 1BB, UK

    Natasha Alechina, Brian Logan, Hoang Nga Nguyen & Abdur Rakib

Authors
  1. Natasha Alechina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brian Logan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hoang Nga Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abdur Rakib
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Natasha Alechina.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alechina, N., Logan, B., Nguyen, H.N. et al. Verifying time, memory and communication bounds in systems of reasoning agents. Synthese 169, 385–403 (2009). https://doi.org/10.1007/s11229-009-9557-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-009-9557-1

Keywords

Search

Navigation