Hostname: page-component-848d4c4894-r5zm4 Total loading time: 0 Render date: 2024-07-05T21:03:53.514Z Has data issue: false hasContentIssue false

A Qualitative Theory of Cognitive Attitudes and their Change

Published online by Cambridge University Press:  06 April 2021

EMILIANO LORINI*
Affiliation:
IRIT-CNRS, Toulouse University, Toulouse, France (e-mail: Emiliano.Lorini@irit.fr)

Abstarct

We present a general logical framework for reasoning about agents’ cognitive attitudes of both epistemic type and motivational type. We show that it allows us to express a variety of relevant concepts for qualitative decision theory including the concepts of knowledge, belief, strong belief, conditional belief, desire, conditional desire, strong desire, and preference. We also present two extensions of the logic, one by the notion of choice and the other by dynamic operators for belief change and desire change, and we apply the former to the analysis of single-stage games under incomplete information. We provide sound and complete axiomatizations for the basic logic and for its two extensions.

Type
Original Article
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alchourrón, C. E., Gardenfors, P. and Makinson, D. 1985. On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic 50, 510530.CrossRefGoogle Scholar
Amor, N. B., Fargier, H., Sabbadin, R. and Trabelsi, M. 2019. Possibilistic games with incomplete information. In Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence (IJCAI 2019), 15441550.Google Scholar
Anglberger, A. J., Gratzl, N. and Roy, O. 2015. Obligation, free choice, and the logic of weakest permissions. The Review of Symbolic Logic 8, 807827.CrossRefGoogle Scholar
Aucher, G. 2005. A combined system for update logic and belief revision. In Intelligent Agents and Multi-Agent Systems, 7th Pacific Rim International Workshop on Multi-Agents (PRIMA 2004). LNCS, vol. 3371. Springer, 117.Google Scholar
Aumann, R. 1999. Interactive epistemology I: Knowledge. International Journal of Game Theory 28, 3, 263300.CrossRefGoogle Scholar
Aumann, R. and Brandenburger, A. 1995. Epistemic conditions for Nash equilibrium. Econometrica 63, 11611180.CrossRefGoogle Scholar
Balbiani, P., Herzig, A. and Troquard, N. 2008. Alternative axiomatics and complexity of deliberative stit theories. Journal of Philosophical Logic 37, 4, 387406.CrossRefGoogle Scholar
Baltag, A., Moss, L. and Solecki, S. 1998. The logic of public announcements, common knowledge and private suspicions. In Proceedings of TARK’98. Morgan Kaufmann, 4356.Google Scholar
Baltag, A. and Moss, L. S. 2004. Logics for epistemic programs. Synthese 139, 2, 165224.CrossRefGoogle Scholar
Baltag, A. and Smets, S. 2008. A qualitative theory of dynamic interactive belief revision. In Proceedings of LOFT 7. Texts in Logic and Games, vol. 3. Amsterdam University Press, 1360.Google Scholar
Baltag, A. and Smets, S. 2009. Talking your way into agreement: Belief merge by persuasive communication. In Proceedings of the Second Multi-Agent Logics, Languages, and Organisations Federated Workshops (MALLOW), vol. 494. CEUR.Google Scholar
Belnap, N., Perloff, M. and Xu, M. 2001. Facing the Future: Agents and Choices in Our Indeterminist World. Oxford University Press.Google Scholar
Benferhat, S., Dubois, D., Prade, H. and Williams, M.-A. 2002. A practical approach to revising prioritized knowledge bases. Studia Logica 70, 105130.CrossRefGoogle Scholar
Boolos, G. 1993. The Logic of Provability. Cambridge University Press.Google Scholar
Boutilier, C. 1993. Revision sequences and nested conditionals. In Proceedings of the 13th International Joint Conference on Artificial Intelligence (IJCAI 1993). Morgan Kaufmann, 519525.Google Scholar
Boutilier, C. 1994. Towards a logic for qualitative decision theory. In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR’ 94). AAAI Press, 7586.Google Scholar
Brafman, R. I. and Tennenholtz, M. 1996. On the foundations of qualitative decision theory. In Proceedings of the Thirteenth National Conference on Artificial Intelligence (AAAI’96). AAAI Press, 12911296.Google Scholar
Brafman, R. I. and Tennenholtz, M. 2000. An axiomatic treatment of three qualitative decision criteria. Journal of the ACM 47, 3, 452482.CrossRefGoogle Scholar
Cohen, P. R. and Levesque, H. J. 1990. Intention is choice with commitment. Artificial Intelligence 42, 213261.CrossRefGoogle Scholar
Darwiche, A. and Pearl, J. 1997. On the logic of iterated belief revision. Artificial Intelligence 89, 1–2, 129.Google Scholar
De Giacomo, G. 1995. Decidability of Class-Based Knowledge Representation Formalisms. Ph.D. thesis, Università di Roma “La Sapienza”.Google Scholar
Doyle, J. and Thomason, R. 1999. Background to qualitative decision theory. The AI Magazine 20, 2, 5568.Google Scholar
Dubois, D., Lorini, E. and Prade, H. 2017. The strength of desires: A logical approach. Minds and Machines 27, 1, 199231.CrossRefGoogle Scholar
Fagin, R., Halpern, J., Moses, Y. and Vardi, M. 1995. Reasoning about Knowledge. MIT Press, Cambridge, Massachusetts.Google Scholar
Gargov, G. and Goranko, V. 1993. Modal logic with names. Journal of Philosophical Logic 22, 607636.CrossRefGoogle Scholar
Harel, D., Kozen, D. and Tiuryn, J. 2000. Dynamic Logic. MIT Press, Cambridge, Massachusetts.CrossRefGoogle Scholar
Hemaspaandra, E. 1996. The price of universality. Notre Dame Journal of Formal Logic 37, 2, 174203.Google Scholar
Hintikka, J. 1962. Knowledge and Belief: an Introduction to the Logic of the Two Notions. Cornell University Press.Google Scholar
Humberstone, I. L. 1992. Direction of fit. Mind 101, 401, 5983.CrossRefGoogle Scholar
Icard, T. F., Pacuit, E. and Shoham, Y. 2010. Joint revision of beliefs and intention. In Proceedings of the Twelfth International Conference on Principles of Knowledge Representation and Reasoning (KR 2010). AAAI Press, 572574.Google Scholar
Lewis, D. 1979. A problem about permission. In Essays in Honour of Jaakko Hintikka. 163175.CrossRefGoogle Scholar
Liu, F. 2011. Reasoning about Preference Dynamics. Springer.CrossRefGoogle Scholar
Lorini, E. 2013. Temporal STIT logic and its application to normative reasoning. Journal of Applied Non-Classical Logics 23, 4, 372399.CrossRefGoogle Scholar
Lorini, E. 2017. Logics for games, emotions and institutions. If-CoLog Journal of Logics and their Applications 4, 9, 30753113.Google Scholar
Lutz, C. and Sattler, U. 2000. The complexity of reasoning with boolean modal logics. In Proceedings of the Third Conference on Advances in Modal logic (AiML 3). World Scientific, 329348.Google Scholar
Marsh, K. and Wallace, H. 2005. The influence of attitudes on beliefs: Formation and change. In The Handbook of Attitudes, Albarracin, D., Johnson, B. T. and Zanna, M. P., Eds. Lawrence Erlbaum Ass., 369395.Google Scholar
Meyer, J. J. C., van der Hoek, W. and van Linder, B. 1999. A logical approach to the dynamics of commitments. Artificial Intelligence 113, 1–2, 140.Google Scholar
Passy, S. and Tinchev, T. 1991. An essay in combinatorial dynamic logic. Information and Computation 93, 263332.CrossRefGoogle Scholar
Paternotte, C. 2011. Rational choice theory. In SAGE Handbook for the Philosophy of Social Sciences, Jarvie, I. and Zamora-Bonilla, J., Eds. SAGE Publications Inc., 307321.CrossRefGoogle Scholar
Platts, M. 1979. Ways of Meaning. Routledge, and Kegan Paul.Google Scholar
Rott, H. 2009. Shifting priorities: Simple representations for 27 iterated theory change operators. In Towards Mathematical Philosophy: Papers from the Studia Logica conference Trends in Logic IV, Makinson, D., Malinowski, J., and Wansing, H., Eds. Springer, 269296.Google Scholar
Searle, J. 1979. Expression and Meaning. Cambridge University Press.CrossRefGoogle Scholar
Shoham, Y. 2009. Logical theories of intention and the database perspective. Journal of Philosophical Logic 38, 6, 633647.CrossRefGoogle Scholar
Spohn, W. 1982. How to make sense of game theory. In Philosophy of Economics, vol. 2, 239270.CrossRefGoogle Scholar
Spohn, W. 1988. Ordinal conditional functions: A dynamic theory of epistemic states. In Causation in Decision, Belief Change and Statistics. Kluwer, 105134.Google Scholar
van Benthem, J. 2007. Dynamic logic for belief revision. Journal of Applied Non-Classical Logics 17, 2, 129155.CrossRefGoogle Scholar
van Benthem, J., Girard, P. and Roy, O. 2009. Everything else being equal: A modal logic for ceteris paribus preferences. Journal of Philosophical Logic 38, 83125.CrossRefGoogle Scholar
van Benthem, J. and Liu, F. 2007. Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17, 2, 157182.CrossRefGoogle Scholar
van Ditmarsch, H., van der Hoek, W. and Kooi, B. 2007. Dynamic Epistemic Logic, vol. 337. Synthese Library, Springer.Google Scholar
van Ditmarsch, H. P. 2005. Prolegomena to dynamic logic for belief revision. Synthese 147, 2, 229275.CrossRefGoogle Scholar
van Eijck, J. 2008. Yet more modal logics of preference change and belief revision. In New Perspectives on Games and Interaction. Texts in Logic and Games, vol. 4. Amsterdam University Press, 81104.Google Scholar
Wellman, M. P. and Doyle, J. 1991. Preferential semantics for goals. In Proceedings of the Ninth National conference on Artificial intelligence (AAAI’91), 698703.Google Scholar
Wooldridge, M. 2000. Reasoning about Rational Agents. MIT Press, Cambridge.Google Scholar
Wright, G. H. V. 1963. The Logic of Preference. Edinburgh University Press.Google Scholar
Wright, G. H. V. 1972. The logic of preference reconsidered. Theory and Decision 3, 140169.CrossRefGoogle Scholar