Abstract
In this paper, three systems of constructive and inconsistency-tolerant description logic are motivated and defined semantically. Moreover, sound and complete tableau calculi for these systems are presented.
S.P. Odintsou acknowledges support by the Alexander von Humboldt-Stiftung.
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References
S. Akama, On Constructive Modality, in: S. Akama (ed.), Logic, Language and Computation, Kluwer Academic Publishrs, Dordrecht, 1997, 143–158.
A. Almukdad and D. Nelson, Constructible Falsity and Inexact Predicates Journal of Symbolic Logic 29 (1984), 231–233.
F. Baader and U. Sattler, An Overview of Tableau Algorithms for Description Logics Studia Logica 69 (2001), 5 40.
F. Baader et al. (eds.), The Description Logic Handbook, Cambridge University Press, Cambridge, 2003.
N. Belnap, A Useful Four-Valued Logic, in: J.M. Dunn and G. Epstein (eds.) Modern Uses of Multiple-Valued LogicReidel, Dordrecht, 8–37, 1977.
P. Blackburn, M. de Rijke and Y. Venema, Modal Logic, Cambridge Tracts in Teoretical Computer Science 53, Cambridge University Press, Cambridge, 2001.
R. Bull, MIPC as the Formalisation of an Intuitionistic Concept of Modality Journal of Symbolic Logic 31 (1966), 609–616.
D. van Dalen, Intuitionistic Logic, in: D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic. Vol.111: Alternatives to Classical Logic, Reidel, Dordrecht, 1986, 225–339.
F. Donini, M. Lenzerini, D. Nardi, and A. Schaerf, Reasoning in Description Logics, in: G. Brewka (ed.), Principles of Knowledge Representation, CSLI Publications, Stanford, 1996, 191–236.
M. Bozié’s and K. Dosen, Models for Normal Intuitionistic Modal Logics Studio Logica 43 (1984), 217–245.
J.M. Dunn, Partiality and its Dual Studio Logica66 (2000), 5–40.
G. Fischer Servi, On Modal Logic with an Intuitionistic Base, Studio Logica, 36 (1977), 141–149.
G. Fischer Servi, Axiomatizations for some Intuitionistic Modal Logics Rend. Sem. Mat. Univers. Polit.42 (1984), 179–184.
D. Gabbay, A. Kurucz, F. Wolter, and M. Zakharyaschev Many-Dimensional Modal Logics: Theory and Applicationsbook manuscript, 2002.
C. Grefe, Fischer Servi’s Intuitionistic Modal Logic has the Finite Model Property, in: M. Kracht et al. (eds.), Advances in Modal logic. Vol. 1., CSLI Lecture Notes 87, 1998, 85–98.
Yu. Gurevich, Intuitionistic Logic with Strong Negation, Studia Logica 27 (1977), 49–49.
C. Lutz and U. Sattler, The Complexity of Reasoning with Boolean Modal Logic, in: F. Wolter et al. (eds.), Advances in Modal Logic. Volume 3, World Scientific Publishers, Singapore, 2002, 329–348.
S.P. Odintsov, Algebraic Semantics for Paraconsitent Nelson’s Logic, 2002, to appear in: Journal of Logic and Computation.
S.P. Odintsov, On the Embedding of Nelson’s Logics, Bulletin of the Section of Logic, 31 /4 (2002), 241–248.
H. Ono, On some Intuitionistic Modal Logics, Publ. Res. Inst. Math. Sci. Kyoto Univ. 13 (1977), 687–722.
H. Ono and N.-Y. Suzuki, Relations between Intuitionistic Modal Logics and Intermediate Predicate Logics, Reports on Mathematical Logic 22 (1989), 65–87.
P.F. Patel-Schneider, A Four-valued Semantics for Terminological Logics, Artificial Intelligence 38, No. 3 (1989), 319–351.
A.K. Simpson, The Proof Theory and Semantics of Intuitionistic Modal Logic, PhD Thesis, University of Edinburg, 1994.
V. Sotirov, Modal Theories With Intuitionistic Logic, in: Mathematical Logic. Proceedings of the Conference on Mathematical Logic, Dedicated to the Memory of A.A. Markov (1903–1979), Sofia, September 22–23, 1980, Sofia, 1984, 139–171.
R. Thomason, A Semantical Study of Constructive Falsity, Zeitschrift für mathematische Logik and Grundlagen der Mathematik, 15 (1969), 247–257.
A. Waaler and L. Wallen, Tableaux for Intuitionistic Logic, in: M. D’Agostino et al. (eds.), Handbook of Tableaux Methods, Kluwer Academic Publishers, Dordrecht, 1999, 255–296.
H. Wansing, The Logic of Information Structures, Lecture Notes in Al 681, Springer-Verlag, Berlin, 1993.
H. Wansing, Tarskian Structured Consequence Relations and Functional Completeness, Math. Logic Quarterly 41 (1995), 73–92.
H. Wansing, Negation, in: L. Goble (ed.), The Blackwell Guide to Philosophical Logic, Basil Blackwell Publishers, Cambridge/Ma., 2001, 415–436.
F. Wolter and M. Zakharyaschev, Intuitionistic Modal Logic, in: A. Cantini et al. (eds.), Logic and Foundations of Mathematics, Kluwer Academic Publishers, Dordrecht, 1999, 227–238.
F. Wolter and M. Zakharyaschev, Intuitionistic Modal Logics as Fragments of Classical Bimodal Logics, in: E. Orlowska (ed.), Logic at Work, Springer Verlag, Berlin, 1999, 168–186.
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Odintsov, S.P., Wansing, H. (2003). Inconsistency-tolerant Description Logic: Motivation and Basic Systems. In: Hendricks, V.F., Malinowski, J. (eds) Trends in Logic. Trends in Logic, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3598-8_11
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DOI: https://doi.org/10.1007/978-94-017-3598-8_11
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