Abstract
This note describes three formalized logics of context and their mathematical inter-relationships. It also proposes a Natural Deduction formulation for a constructive logic of contexts, which is what the described logics have in common.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
V. Akman and M. Surav. Steps Toward Formalizing Context. AI Magazine.
N. Alechina, M. Mendler, V. de Paiva and E. Ritter. Categorical and Kripke Semantics for Constructive Modal Logics. In Computer Science Logic (CSL’01), Paris, September 2001.
D. Basin, S. Matthews and L Vigano. Natural Deduction for Non-Classical Logics. Studia Logica, 60(1): 119–160, 1998.
G. Bellin A system of natural deduction for GL. Theoria, 2: 89–114, 1985.
G. Bellin, V. de Paiva and E. Ritter. Extended Curry-Howard Correspondence for a Basic Constructive Modal Logic. In Proceedings of Methods for Modalities II, November 2001.
G. M. Bierman and V. de Paiva. On an Intuitionistic Modal Logic. Studia Logica, 65: 383–416, 2000.
P. Bouquet and L. Serafini. Comparing Formal Theories of Context in AI. Submitted to Artificial Intelligence.
R. Bull and K. Sergerberg. Basic Modal Logic In Handbook of Philophical Logic, eds Gabbay and Guenthner, vol II, 1984.
S. Buvac, V. Buvac, and I. Mason. Metamathematics of Contexts. Fundamenta Informaticae, 23(3), 1995.
T. Costello and A. Paterson Quantifiers over Contexts. Common-Sense’98.
D. Crouch, C. Condoravdi, R. Stolle, T. King, V. de Paiva, J. O. Everett and D. Bobrow Scalability of redundancy detection in focused document collections. Proceedings First International Workshop on Scalable Natural Language Understanding (ScaNaLU-2002), Heidelberg, Germany, May 2002.
F. Fitch Symbolic Logic.
M. Fitting Proof Methods for Modal and Intuitionistic Logic. 1983.
R. Guha. Contexts: A Formalization and Some applications. Ph.D Thesis, Stanford University, 1995.
J. McCarthy. Notes on Formalizing Context. In Proc. of the 13th Joint Conference on Artificial Intelligence (IJCAI-93), 555–560, 1993.
J. McCarthy and S. Buvac. Formalizing Context (Expanded Notes). Available from http://www-formal.stanford.edu/jmc/
J. McCarthy. A Logical AI Approach to Context. Available from http://www-formal.stanford.edu/jmc/
F. Massacci. Strongly Analytic Tableaux for Normal Modal Logics. In Proceedings 12th CADE, 1994, vol 814, LNAI 723–737.
F. Massacci. Superficial Tableaux for Contextual Reasoning. In Proceedings of the AAAI-95 Fall symposium on “Formalizing context”, 60–66, 1995.
F. Massacci. Contextual Reasoning is NP-complete. In Proceedings 13th AAAI 1996, pages 621–626. AAAI Press.
P. Nayak. Representing Multiple Theories. In Proceedings of the Eleventh National Conference on Artificial Intelligence (AAAI’94), 1994.
V. de Paiva Natural Deduction Systems for Contexts, manuscript, 2003.
D. Prawitz. Natural Deduction: A Proof-Theoretic Study. Almqvist and Wiksell, 1965.
L. Serafini and F. Giunchiglia. ML systems: A Proof Theory for Contexts. To appear in the Journal of Logic Language and Information, July 2001. ITC-IRST Technical Report 0006-01.
L. Serafini. Personal communication, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Paiva, V. (2003). Natural Deduction and Context as (Constructive) Modality. In: Blackburn, P., Ghidini, C., Turner, R.M., Giunchiglia, F. (eds) Modeling and Using Context. CONTEXT 2003. Lecture Notes in Computer Science(), vol 2680. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44958-2_10
Download citation
DOI: https://doi.org/10.1007/3-540-44958-2_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40380-7
Online ISBN: 978-3-540-44958-4
eBook Packages: Springer Book Archive