Hostname: page-component-7c8c6479df-hgkh8 Total loading time: 0 Render date: 2024-03-28T22:33:19.312Z Has data issue: false hasContentIssue false

Modulated fibring and the collapsing problem

Published online by Cambridge University Press:  12 March 2014

Cristina Sernadas
Affiliation:
Center For Logic and Computation - CLC, Department of Mathematics IST UTL, AV. Rovisco Pais, 1049-001 Lisboa, Portugal, E-mail: css@math.ist.utl.pt URL: http://www.cs.math.ist.utl.pt/s84.www/cs/css.html
João Rasga
Affiliation:
Center for Logic and Computation - CLC, Department of Mathematics 1ST UTL, AV. Rovisco Pais, 1049-001 Lisboa, Portugal, E-mail: jfr@math.ist.utl.pt URL: http://www.cs.math.ist.utl.pt/s84.www/cs/jfr.html
Walter A. Carnielli
Affiliation:
Center For Logic, Epistemology and the History of Science - CLE, Department of Philosophy IFCH Unicamp, P.O. Box 6133, 13083-970 Campinas - SP -, Brazil, E-mail: carniell@cle.unicamp.br URL: http://www.cle.unicamp.br/prof/carnielli/

Abstract

Fibring is recognized as one of the main mechanisms in combining logics, with great significance in the theory and applications of mathematical logic. However, an open challenge to fibring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that fibring imposes unwanted interconnections between the given logics. Modulated fibring allows a finer control of the combination, solving the collapsing problem both at the semantic and deductive levels. Main properties like soundness and completeness are shown to be preserved, comparison with fibring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Blackburn, P. and de Rijke, M., Why combine logics?, Studia Logica, vol. 59 (1997), no. 1, pp. 527.CrossRefGoogle Scholar
[2]Bolc, L. and Borowik, P., Many-Valued Logics I, Springer Verlag, 1992.CrossRefGoogle Scholar
[3]Caleiro, C., Carnielli, W. A., Coniglio, M. E., Sernadas, A., and Sernadas, C., Fibringnon-truth-functional logics: Completeness preservation, Journal of Logic, Language and Information, (in print).Google Scholar
[4]Carnielli, W. A., Systematization of finite many-valued logics through the method of tableaux, this Journal, vol. 52 (1987), no. 2, pp. 473493.Google Scholar
[5]Carnielli, W. A. and Marcos, J., Limits for paraconsistency calculi, Notre Dame Journal of Formal Logic, vol. 40 (1999), no. 3, pp. 375390.CrossRefGoogle Scholar
[6]Carnielli, W. A. and Marcos, J., Tableau systems for logics of formal inconsistency, Proceedings of the International Conference on Artificial Intelligence (IC-AI'2001) (Arabnia, H. R., editor), CSREA Press, Athens, GA, USA, 2001, pp. 848852.Google Scholar
[7]Carnielli, W. A. and Marcos, J., A taxonomy of C-systems, Proceedings of the 2nd World Congress on Paraconsistency 2000 (Carnielli, W. A., Coniglio, M. E., and D' Ottaviano, I. M. L., editors), Marcel Dekker, 2002, pp. 194.Google Scholar
[8]Del Cerro, L. Fariñas and Herzig, A., Combining classical and intuitionistic logic, Frontiers of Combining Systems (Baader, F. and Schulz, K., editors), Kluwer Academic Publishers, 1996, pp. 93102.CrossRefGoogle Scholar
[9]Gabbay, D., Fibred semantics and the weaving of logics: Part 1, this Journal, vol. 61 (1996), no. 4, pp. 10571120.Google Scholar
[10]Gabbay, D., An overview of fibred semantics and the combination of logics, Frontiers of combining systems (Baader, F. and Schulz, K., editors), Kluwer Academic Publishers, 1996, pp. 155.Google Scholar
[11]Gabbay, D., Fibring logics, Oxford University Press, 1999.Google Scholar
[12]Goodman, N., The logic of contradiction, Zeitschrift för Mathematische Logik and Grundlagen der Mathematik, vol. 27 (1981), no. 2, pp. 119126.CrossRefGoogle Scholar
[13]Gottwald, S., A Treatise on Many-Valued Logics, Research Studies Press, 2001.Google Scholar
[14]Rasga, J., Sernadas, A., Sernadas, C., and Viganò, L., Fibring labelled deduction systems, Journal of Logic and Computation, (in print).Google Scholar
[15]Reyes, G. and Zolfaghari, H., Bi-Heyting algebras, toposes and modalities, Journal of Philosophical Logic, vol. 25 (1996), no. 1, pp. 2543.CrossRefGoogle Scholar
[16]Sernadas, A., Sernadas, C., and Caleiro, C., Fibring of logics as a categorial construction, Journal of Logic and Computation, vol. 9 (1999), no. 2, pp. 149179.CrossRefGoogle Scholar
[17]Sernadas, A., Sernadas, C., and Zanardo, A., Fibring modal first-order logics: Completeness preservation, Preprint, Section of Computer Science, Department of Mathematics, Instituto Superior Técnico, 1049-001 Lisboa, Portugal, 2001, Submitted for publication.Google Scholar
[18]Zanardo, A., Sernadas, A., and Sernadas, C., Fibring: Completeness Preservation, this Journal, vol. 66 (2001), no. 1, pp. 414439.Google Scholar