Abstract
The operation of deletion plays an important role in many areas of applied logic. However, there are a number of logical difficulties relating to the removal of elements from a database. These difficulties are usually handled by executing the operation of deletion on the meta-level.
In Gabbay et al. 2002, we argued that bringing the operation of deletion to the object level was a useful exercise and we analysed how this can be achieved in resource bounded logics such as linear logic.
In this paper, we continue the investigation by analysing ways of effecting object level deletion for logics which do not have a resource bound on the number of times a formula can be used.
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Alchourrón, C. A. and D. Makinson: 1982, ‘On the Logic of Theory Change: Contraction Functions and their Associated Revision Functions’, Theoria 48, 14–37.
Alchourrón, C. A. and D. Makinson: 1985, ‘The Logic of Theory Change: Safe Contraction’, Studia Logica 44, 405–422.
Alchourrón, C. A., P. Gärdenfors and D. Makinson: 1985, ‘On the Logic of Theory Change: Partial Meet Contraction and Revision Functions’, The Journal of Symbolic Logic 50, 510–530.
Anderson, A. R. and N. D. Belnap: 1975, Entailment, Vol. 1, Princeton University Press.
Connolly, T., C. Begg and A. Strachan: 1999, Database Systems: A Practical Approach to Design, Implementation and Management, 2nd edn, Addison-Wesley.
Darwiche, A. and J. Pearl: 1994, ‘On the Logic of Iterated Belief Revision’, in Ronald Fagin (ed.), Proceedings of the 5th International Conference on Principles of Knowledge Representation and Reasoning, Pacific Grove, CA, Morgan Kaufmann, pp. 5–23.
Darwiche, A. and J. Pearl: 1997, ‘On the Logic of Iterated Belief Revision’, Artificial Intelligence 89, 1–29.
Date, C. J. and H. Darwen: 1997, A Guide to the SQL Standard: A User's Guide to the Standard Database Language, 4th edn, Addison-Wesley Longman, Inc.
Freund, M. and D. Lehmann: 1994, ‘Belief Revision and Rational Inference’, Technical Report TR 94–16, The Leibniz Center for Research in Computer Science, Institute of Computer Science, Hebrew University.
Gabbay, D. M.: 1996, Labelled Deductive Systems, Oxford University Press.
Gabbay, D. M. and O. Rodrigues: 1997, ‘Structured Belief Bases: A Practical Approach to Prioritised Base Revision’, in Dov M. Gabbay, Rudolf Kruse, Andreas Nonnengart, and Hans Jürgen Ohlbach (eds.), Proceedings of First International Joint Conference on Qualitative and Quantitative Practical Reasoning, Springer-Verlag, pp. 267–281.
Gabbay, D. M.: 1998, Elementary Logic: A Procedural Perspective, Prentice Hall.
Gabbay, D. M.: 1999, ‘Compromise Update and Revision: A Position Paper’, in B. Fronhoffer and R. Pareschi (eds.), Dynamic Worlds, Kluwer, pp. 111–148.
Gabbay, D. M. and N. Olivetti: 2000, Goal Directed Proof Theory, Kluwer.
Gabbay, D. M., O. Rodrigues and A. Russo: 2000, ‘Revision by Translation’, in B. Bouchon-Meunier, R. Yager and L. A. Zadeh (eds.), Information, Uncertainty and Fusion: Proceedings of IPMU 98, Kluwer, pp. 3–32.
Gabbay, D. M. and J. Woods: 2004, The Reach of Abduction: Insight and Trial, A Practical Logic of Cognitive Systems, Vol. 2, Elsevier.
Gabbay, D. M., O. Rodrigues and J. Woods: 2002, ‘Belief Contraction, Anti-formulae and Resource Overdraft: Part I Deletion in Resource Bounded Logics’, Logic Journal of the IGPL 10, 601–652.
Gabbay, D. M., O. Rodrigues and J. Woods: in preparation, ‘Belief Contraction, Anti-formulae and Resource Overdraft: Part III Fine Tuning of the Deletion Process’.
Gabbay, D. M., O. Rodrigues and J. Woods: in preparation, ‘Existence and Anti-existence in Non-classical Logics’.
Gärdenfors, P.: 1978, ‘Conditionals and Changes of Belief’, Acta Philosophica Fennica 30, 381–404.
Gärdenfors, P.: 1982, ‘Rules for Rational Changes of Belief’, in T. Pauli (ed.), Philosophical Essays Dedicated to Lannart Åqvist on His Fiftieth Birthday, Vol. 34 of Philosophical Studies, Philosophical Society and the Department of Philosophy, Uppsala University, pp. 88–101.
Gärdenfors, P.: 1988, Knowledge in Flux: Modeling the Dynamics of Epistemic States, Cambridge, MA, London, England, A Bradford Book – The MIT Press.
Girard, J. Y.: 1998, ‘Light Linear Logic, Information and Computation’, 143(2), 175–204.
Groff, J. R. and P. N. Weinberg: 1999, SQL: The Complete Reference, Osborne/McGraw-Hill.
Grosof, B. N.: 1992, Updating and Structure in Non-montonic Theories, Ph.D. Thesis.
Hansson, S. O.: 1999, A Textbook of Belief Dynamics: Theory Change and Database Updating, Dodrdrecht, Kluwer Academic Publishers.
Kurosh, A. G.: 1963, General Algebra, Chelsea Publishing Commpany.
Lehmann, D.: 1995, ‘Belief Revision, Revised’„ in Proceedings of the 14th International Joint Conference of Artificial Intelligence (IJCAI-95), pp. 1534–1540.
Olivetti, N. and L. Terracini: 1992, ‘N-prolog and Equivalence of Logic Programs’, Journal of Logic, Language and Information 1, 253–340.
Restall, G.: 2000, An Introduction to Substructural Logics, New York, Routledge, ISBN 0-415-21534-X.
Rodrigues, O.: 1998, A Methodology for Iterated Information Change, Ph.D. thesis, Department of Computing, Imperial College.
Woods, J.: 1974, The Logic of Fiction: Philosophical Soundings of Deviant Logic, The Hague and Paris, Mouton.
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Gabbay, D.M., Rodrigues, O., Woods, J. (2009). Belief Contraction, Anti-Formulae and Resource Overdraft:Part II Deletion In Resource Unbounded Logics. In: Rahman, S., Symons, J., Gabbay, D.M., Bendegem, J.P.v. (eds) Logic, Epistemology, and the Unity of Science. Logic, Epistemology, And The Unity Of Science, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-2808-3_16
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DOI: https://doi.org/10.1007/978-1-4020-2808-3_16
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