Indiana University School of Informatics
Research
Faculty Research Profiles

Michael Dunn

Faculty Title

Professor of Informatics Emeritus

Research Statement

Dunn’s major activity recently has been as founding dean of the School of Informatics, the first new school at Indiana University in twenty-eight years. The School focuses on the application of information technology to domain specific problems.

Dunn’s research continues to focus on information based logics and relations between logic and computer science. He is particularly interested in the so-called “sub-structural logics” including intuitionistic logic, relevance logic, linear logic, BCK-logic, and the Lambek Calculus. He has developed an algebraic approach to these and many other logics under the heading of “gaggle theory” (for generalized galois logics), which is contained in Dunn’s book with Gary Hardegree Algebraic Methods in Philosophical Logic (Oxford, 2001).

The representation theorem for gaggles generalizes the Jonsson-Tarski representation of Boolean algebras with operators, and shows how an n-ary logical operation in substructural and many other logics can be understood using a n + 1-placed accessibility relation on states (much as with the Kripke semantics for modal logic where a unary modality such as possibility can be understood using an binary accessibility relation on “possible worlds”).

This can be used to model combinatory logic by combining two simple ideas. First, understand application as a binary operation, and represent it using a ternary relation. Second, replace the ternary relation with an indexed set of binary relations. Now one proposition (set of states) can be understood as a set of actions, and can be applied to another (thought of as just a set of states). This model combines information (static) with computation (dynamic) in a single model. A similar idea allows one to represent relation algebras as relational databases (this time turn in both sets of states for the corresponding actions). He is working on ideas for extending this general approach to Pratt’s dynamic logic, Hoare’s logic of programs, as well as to action algebras and related structures.

Dunn has recently presented this work at conferences at the Institute of Logic at the Russian Academy of Sciences, the Argonne National Laboratory, ISE ’03, and Trends in Logic (Warsaw).

Grants

CLIOH Project (Cultural Library Indexing Our Heritage), POI (with D. Bailey and M. Palakal), IMLS, $250,000 (2001–02).

Select Publications

  • Algebraic Methods in Philosophical Logic (with G. Hardegree), Oxford University Press, 485 pp., 2001
  • “The Concept of Information and the Development of Modern Logic,” in Non-classical Approaches in the Transition from Traditional to Modern Logic (2000), ed. W. Stelzner, de Gruyter, pp. 423–448.
  • “The Trilattice of Constructive Truth Values,” (with Y. Shramko and T. Takenaka), Journal of Language and Computation, vol. 11, No. 6, pp. 761–788, December 2001.
  • “Ternary Relational Semantics and Beyond: Programs as Data and Programs as Instructions,” Logical Studies, no. 8, Institute of Logic, Russian Academy of Sciences, Special Issue: Proceedings of the International Conference Third Smirnov Readings, May 2001.
  • “A Representation of Relation Algebras Using Routley-Meyer Frames,” in Logic, Meaning and Computation (2001), eds. C.A. Anderson and M. Zeleny, Kluwer, pp. 71–108.

More Information

Michael Dunn

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