Abstract
In this article we describe a first-order extension of the deontic logic introduced in [1]. The main useful and interesting characteristic of this extended logic is that it not only provides the standard quantifiers of first-order logic, but it also has similar algebraic operators for actions as for the propositional version of [1]. Since the pioneering works of Hintikka and Kanger, little advance has been made in developing first-order deontic logics. Furthermore, to the best of our knowledge, the introduction of quantifiers in deontic action logics (i.e., deontic action logics where predicates are applied only to actions) has not been investigated in detail in the literature. This paper represents a significant step in addressing these problems. We also demonstrate the application of this novel logic to fault-tolerance by means of a simple example.
Keywords
- Modal Logic
- Axiomatic System
- Canonical Model
- Action Term
- Deontic Logic
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This work has been supported by NSERC and MRI through an ORF-RE grant.
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References
Castro, P.F., Maibaum, T.: Deontic action logic, atomic boolean algebra and fault-tolerance. Journal of Applied Logic 7(4), 441–466 (2009)
Wieringa, R.J., Meyer, J.J.: Applications of deontic logic in computer science: A concise overview. Deontic Logic in Computer Science, Normative System Specification (1993)
Castro, P.F.: Deontic Action Logics for the Specification and Analysis of Fault-Tolerance. PhD thesis, McMaster University, Department of Computing and Software (2009)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press (2000)
Meyer, J.: A different approach to deontic logic: Deontic logic viewed as variant of dynamic logic. Notre Dame Journal of Formal Logic 29 (1988)
Hintikka, J.: Quantifiers in deontic logic. In: Societas Scientiarum Fennica, Commentationes Humanarum Litterarum (1957)
Kanger, S.: New foundations for ethical theory. In: Deontic Logic: Introductory and Systematic Readings, Dordrecht (1971)
Emerson, E.: A Mathematical Introduction to Logic. Academic Press (1972)
Hughes, G.E., Cresswell, M.J.: A New Introduction to Modal Logic. Routledge (1996)
Fiadeiro, J.L., Maibaum, T.: Temporal theories as modularization units for concurrent system specification. Formal Aspects of Computing 4, 239–272 (1992)
Segerberg, K.: A deontic logic of action. Studia Logica 41, 269–282 (1982)
Gargov, G., Passy, S.: A note on boolean logic. In: Petkov, P.P. (ed.) Proceedings of the Heyting Summerschool. Plenum Press (1990)
Broersen, J.: Modal Action Logics for Reasoning about Reactive Systems. PhD thesis, Vrije University (2003)
Khosla, S., Maibaum, T.: The prescription and description of state-based systems. In: Banieqnal, B., Pnueli, H.A. (eds.) Temporal Logic in Computation. Springer, Heidelberg (1985)
Kent, S., Quirk, B., Maibaum, T.: Specifying deontic behaviour in modal action logic. Technical report, Forest Research Project (1991)
Castro, P.F., Aguirre, N.M., López Pombo, C.G., Maibaum, T.S.E.: Towards managing dynamic reconfiguration of software systems in a categorical setting. In: Cavalcanti, A., Deharbe, D., Gaudel, M.-C., Woodcock, J. (eds.) ICTAC 2010. LNCS, vol. 6255, pp. 306–321. Springer, Heidelberg (2010)
Makinson, D.: Quantificational reefs in deontic waters. In: Hilpinen, R. (ed.) New Studies in Deontic Logic, Dordrecht (1981)
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Castro, P.F., Maibaum, T.S.E. (2012). Towards a First-Order Deontic Action Logic. In: Mossakowski, T., Kreowski, HJ. (eds) Recent Trends in Algebraic Development Techniques. WADT 2010. Lecture Notes in Computer Science, vol 7137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28412-0_6
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DOI: https://doi.org/10.1007/978-3-642-28412-0_6
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