[en] Makinson and van der Torre [14] introduce a number of in- put/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe [20,21] has developed some more I/O logics to include systems without the rule of weakening of the output (or principle of inheritance). We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases−a common form of reasoning. Sec- ond, we show how to inject a new (as we call it, “aggregative”) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and complete- ness theorems for the proposed systems with respect to their intended semantics.
Disciplines :
Computer science
Author, co-author :
PARENT, Xavier ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
Torre, Leendert W. N. Van Der
External co-authors :
no
Language :
English
Title :
Sing and Dance!" - Input/Output Logics without Weakening
Publication date :
2014
Event name :
DEON 2014
Event date :
July 2014
Audience :
International
Main work title :
Deontic Logic and Normative Systems - 12th International Conference DEON 2014, Ghent, Belgium, July 12-15, 2014. Proceedings
Broome, J.: Rationality Through Reasoning. Wiley-Blackwell, West Sussex (2013)
Chisholm, R.: Contrary-to-duty imperatives and deontic logic. Analysis 24, 33-36 (1963)
Dosen, K.: Negation in the light of modal logic. In: Gabbay, D., Wansing, H. (eds.) What is Negation?, pp. 77-86. Springer, Heidelberg (1999)
Forrester, J.: Gentle murder, or the adverbial Samaritan. Journal of Philosophy 81, 193-197 (1984)
Goble, L.: A logic of good, should, and would: Part I. Journal of Philosophical Logic 19, 169-199 (1990)
Goble, L.: A proposal for dealing with deontic dilemmas. In: Lomuscio, A., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 74-113. Springer, Heidelberg (2004)
Goble, L.: Prima facie norms, normative conflicts and dilemmas. In: Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.) Handbook of Deontic Logic and Normative Systems, pp. 241-352. College Publications, London (2013)
Hansen, J.: Imperative logic and its problems. In: Gabbay, D., Horty, J., Parent, X., van der Meyden, R., van der Torre, L. (eds.) Handbook of Deontic Logic and Normative Systems, pp. 499-544. College Publications, London (2013)
Hansen, J.: Reasoning about permission and obligation. In: Hansson, S.O. (ed.) David Makinson on Classical Methods for Non-Classical Problems, pp. 287-333. Springer (2014)
Makinson, D.: On a fundamental problem in deontic logic. In: Namara, P.M., Prakken, H. (eds.) Norms, Logics and Information Systems. Frontiers in Artificial Intelligence and Applications, pp. 29-54. IOS Press, Amsterdam (1999)
Makinson, D., van der Torre, L.: Input/output logics. Journal of Philosophical Logic 29(4), 383-408 (2000)
Makinson, D., van der Torre, L.: Constraints for input/output logics. Journal of Philosophical Logic 30(2), 155-185 (2001)
McLaughlin, R.N.: Further problems of derived obligation. Mind 64(255), 400-402 (1955)
Parent, X., van der Torre, L.: Aggregative deontic detachment for normative reasoning (short paper). In: Eiter, T., Baral, C., Giacomo, G.D. (eds.) Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning, KR 2014. AAAI Press (2014)
Priest, G.: Paraconsistent logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 6, pp. 287-393. Springer (2002)
Stolpe, A.: Normative consequence: The problem of keeping it whilst giving it up. In: van der Meyden, R., van der Torre, L. (eds.) DEON 2008. LNCS (LNAI), vol. 5076, pp. 174-188. Springer, Heidelberg (2008)
Stolpe, A.: Norms and Norm-System Dynamics. Ph.D. thesis, Department of Philosophy, University of Bergen, Norway (2008)
von Wright, G.: Norm and Action: A Logical Enquiry. Routledge & Kegan Paul PLC (1963)