In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourrón/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step.
Unable to display preview. Download preview PDF.
- Alchourrón, C., Gärdenfors, P. and Makinson, D., 1985: On the logic of theory change: partial meet contraction and revision functions, J. Symbolic Logic 50, 510–530.Google Scholar
- Alchourrón, C. and Makinson, D., 1982: On the logic of theory change: contraction functions and their associated revision functions, Theoria 48, 14–37.Google Scholar
- Hansson, B., 1969: An analysis of some deontic logics, Nous 3, 373–398. Reprinted in R. Hilpinen (ed.), Deontic Logic: Introductory and Systematic Readings, Reidel, Dordrecht, 1971 and 1981, pp. 121–147.Google Scholar
- Hansson, S. O. and Makinson, D., 1997: Applying normative rules with restraint, in M. L. Dalla Chiara et al. (eds), Logic and Scientific Methods, Kluwer Acad. Publ., Dordrecht, pp. 313–332.Google Scholar
- Makinson, D., 1994: General patterns in nonmonotonic reasoning, in D. Gabbay et al. (eds), Handbook of Logic in Artificial Intelligence and Logic Programming, Vol. 3, Oxford University Press, pp. 35–110.Google Scholar
- Makinson, D., 1997: Screened revision, Theoria 63, 14–23.Google Scholar
- Makinson, D., 1999: On a fundamental problem of deontic logic, in P. McNamara and H. Prakken (eds), Norms, Logics and Information Systems. New Studies in Deontic Logic and Computer Science, Frontiers in Artificial Intelligence and Applications 49, IOS Press, Amsterdam, pp. 29–53.Google Scholar
- Makinson, D. and van der Torre, L., 2000: Input/output logics, J. Philos. Logic 29, 383–408.Google Scholar
- Poole, D., 1988: A logical framework for default reasoning, Artificial Intelligence 36, 27–47.Google Scholar
- Reiter, R., 1980: A logic for default reasoning, Artificial Intelligence 13, 81–132.Google Scholar
- van der Torre, L. W. N., 1997: Reasoning about Obligations: Defeasibility in Preference-Based Deontic Logic, Ph.D. Thesis, Erasmus University of Rotterdam, Tinbergen Institute Research Series 140, Amsterdam.Google Scholar
- van der Torre, L. W. N., 1998: Phased labeled logics of conditional goals, in Logics in Artificial Intelligence, Proceedings of the Sixth European Workshop on Logics in AI (JELIA'98), Lecture Notes in Comput. Sci. 1489, Springer, Berlin, pp. 92–106.Google Scholar
- van der Torre, L.W. N. and Tan, Y.-H., 1999: Contrary-to-duty reasoning with preferencebased dyadic obligations, Ann. Math. Artificial Intelligence 27, 49–78.Google Scholar