# Phased Labeled Logics of Conditional Goals

## Abstract

In this paper we introduce phased labeled logics of conditional goals. Labels are used to impose restrictions on the proof theory of the logic. The restriction discussed in this paper is that a proof rule can be blocked in a derivation due to the fact that another proof rule has been applied earlier in the derivation. We call a set of proof rules that can be applied in any order a phase in the proof theory. We propose a one-phase logic of goals containing four proof rules, and we show that it is equivalent to a four-phase logic of goals in which each phase contains exactly one proof rule. The proof theory of the four-phase logic of goals is much more effcient, because other orderings no longer have to be considered.

## Preview

Unable to display preview. Download preview PDF.

### References

- 1.C. Boutilier. Toward a logic for qualitative decision theory. In
*Proceedings of the KR’94*, pages 75–86, 1994.Google Scholar - 2.J. Doyle, Y. Shoham, and M.P. Wellman. The logic of relative desires. In
*Sixth International Symposium on Methodologies for Intelligent Systems*, Charlotte, North Carolina, 1991.Google Scholar - 3.J. Doyle and M.P. Wellman. Preferential semantics for goals. In
*Proceedings of the AAAI’91*, pages 698–703, 1991.Google Scholar - 4.D. Gabbay.
*Labelled Deductive Systems*, volume 1. Oxford University Press, 1996.Google Scholar - 5.H. Geffner and J. Pearl. Conditional entailment: bridging two approaches to default reasoning.
*Artificial Intelligence*, 53:209–244, 1992.CrossRefMathSciNetGoogle Scholar - 6.P. Haddawy and S. Hanks. Representations for decision-theoretic planning: Utility functions for dead-line goals. In
*Proceedings of the KR’92*, pages 71–82, 1992.Google Scholar - 7.Z. Huang and J. Bell. Dynamic goal hierarchies. In
*Intelligent Agent Systems: Theoretical and Practical Issues*, LNAI 1027, pages 88–103. Springer, 1997.Google Scholar - 8.J. Lang. Conditional desires and utilities-an alternative approach to qualitative decision theory. In
*Proceedings of the ECAI’96*, pages 318–322, 1996.Google Scholar - 9.D. Makinson. On a fundamental problem of deontic reasoning. In P. McNamara and H. Prakken, editors,
*Norms, Logics and Information Systems. New Studies on Deontic Logic and Computer Science*. IOS Press, 1998.Google Scholar - 10.J. Pearl. From conditional oughts to qualitative decision theory. In
*Proceedings of the UAI’93*, pages 12–20, 1993.Google Scholar - 11.S.-W. Tan and J. Pearl. Qualitative decision theory. In
*Proceedings of the AAAI’94*, 1994.Google Scholar - 12.S.-W. Tan and J. Pearl. Specification and evaluation of preferences under uncertainty. In
*Proceedings of the KR’94*, pages 530–539, 1994.Google Scholar - 13.Y.-H. Tan and L.W.N. van der Torre. How to combine ordering and minimizing in a deontic logic based on preferences. In
*Deontic Logic, Agency and Normative Systems. Proceedings of the ΔEON’96*, Workshops in Computing, pages 216–232. Springer, 1996.Google Scholar - 14.L.W.N. van der Torre.
*Reasoning about Obligations: Defeasibility in Preference-based Deontic Logic*. PhD thesis, Erasmus University Rotterdam, 1997.Google Scholar - 15.L.W.N. van der Torre. Labeled logics of conditional goals. In
*Proceedings of the ECAI’98*, pages 368–369. John Wiley & Sons, 1998.Google Scholar - 16.L.W.N. van der Torre and Y.-H. Tan. Cancelling and overshadowing: two types of defeasibility in defeasible deontic logic. In
*Proceedings of the IJCAI’95*, pages 1525–1532. Morgan Kaufman, 1995.Google Scholar - 17.L.W.N. van der Torre and Y.-H. Tan. The many faces of defeasibility in defeasible deontic logic. In D. Nute, editor,
*Defeasible Deontic Logic*, pages 79–121. Kluwer, 1997.Google Scholar - 18.L.W.N. van der Torre and Y.-H. Tan. Deliberate robbery, or the calculating Samaritan. In
*Proceedings of the ECAI’98 Workshop on Practical Reasoning and Rationality (PRR’98)*, 1998.Google Scholar - 19.L.W.N. van der Torre and Y.-H. Tan. Diagnosis and decision making in normative reasoning.
*Artificial Intelligence and Law*, 1998.Google Scholar - 20.L.W.N. van der Torre and Y.-H. Tan. Prohairetic Deontic Logic (PDL). In
*this volume*, 1998.Google Scholar - 21.L.W.N. van der Torre and Y.-H. Tan. Two-phase deontic logic. 1998. Submitted.Google Scholar
- 22.L.W.N. van der Torre and E. Weydert. Goals, desires, utilities and preferences. In
*Proceedings of the ECAI’98 Workshop on Decision Theory meets Artificial Intelligence*, 1998.Google Scholar