Qualitative decision theory via channel theory

Gerard Allwein, Yingrui Yang, William L. Harrison

DOI: http://dx.doi.org/10.12775/LLP.2011.005


We recast parts of decision theory in terms of channel theory concentrating on qualitative issues. Channel theory allows one to move between model theoretic and language theoretic notions as is necessary for an adequate covering. Doing so clarifies decision theory and presents the opportunity to investigate alternative formulations. As an example, we take some of Savage’s notions of decision theory and recast them within channel theory. In place of probabilities, we use a particular logic of preference. We introduce a logic for describing actions separate from the logic of preference over actions. The structures introduced by channel theory that represent the decision problems can be seen to be an abstract framework. This frame-work is very accommodating to changing the nature of the decision problems to handle different aspects or theories about decision making.


decision theory; channel theory; logics of preference; world decision problems

Full Text:



Barr, M., “∗-autonomous categories and linear logic”, Mathematical Structures in Computer Science 1 (1991): 159–178.

Barwise, J., and J. Seligman, Information Flow: The Logic of Distributed Systems, Cambridge University Press, 1997, Cambridge Tracts in Theoretical Computer Science 44.

Britz, K., J. Heidema, and W. Labuschagne, “Semantics for dual preferential entailment”, Journal of Philosophical Logic 38 (2009): 433–446.

Delgrande, J., T. Schaub, H. Tompits, and K. Wang, “A classiŢcation and survey of preference handling approaches in non-monotonic reasoning”, Computational Intelligence 20 (2004): 308–334.

Dubois, D., H. Fargier, H. Prade, and P. Penny, “Qualitative decision theory: From savage’s axioms to nonmonotonic reasoning”, Journal of Association of Computing Machinery 49 (2002): 455–495.

Gentzen, G., “Untersuchungen über das logische Schliessen”, Mathematische Zeitschrift 39 (1934): 176–210, 405–431.

Goguen, J., “Information integration in institutions” pages 1–48 in: L. Moss, editor, Thinking Logically: a Memorial Volume for Jon Barwise, Indiana University Press, 201x.

Jeffrey, R.C., The Logic of Decision, University Of Chicago Press, first edition, 1990.

Joyce, J., The Foundations of Causal Decision Theory, Cambridge University Press, 1999.

Kraus, S., D. Lehmann, and M. Magidor, “Nonmonotonic reasoning, preferential models and cumulative logics”, Artificial Intelligence 44 (1990): 167–207.

Lehmann, D., and M. Magidor, “What does a conditional knowledge base entail?”, Artificial Intelligence 55, 1992.

Mac Lane, S., Categories for the Working Mathematician, volume 5, Springer-Verlag, second edition, 1998.

Makinson, D., “How to go nonmonotonic”, pages 175–278 in: Handbook of Philosophical Logic, vol. 12, Springer, second edition, 2005.

Mendelson, E., Introduction to Mathematical Logic, Shapman and Hall, fourth edition, 1997.

Savage, L., The Foundations of Statistics, Dover, second edition, 1972.

Scott, D.S., “Background to formalization”, pages 411–435 in: Truth, Syntax, and Modality, North-Holland, 1973.

Scott, D.S., “Domains for denotational semantics”, pages 1–47 in: An extended version of the paper prepared for ICALP’82, Springer-Verlag, 1982.

Shoesmith, D.J., and T.J. Smiley, Multiple-Conclusion Logic, Cambridge University Press, 1978.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism