Abstract
An inevitability operator (L) is defined within the Peircean semantic approach to temporal logic. This operator can be seen as a kind of meta-linear operator that allows to incorporate within a branching Peircean logic the underlying linear logic. Its semantic definition involves the change of frame. The semantic properties of the operator L are analyzed and a sound axiomatization is provided for this operator. The relationships that this operator introduces between the resulting branching logic and the underlying linear logic are also analyzed, semantically and axiomatically. Although the completeness of the proposed axiomatization is not provided herein, some comments are made on how to extend the usual Henkin contruction in order to obtain that result. Dynamic model structures are also used in order to define what we call herein "branching logics with a pure linear past", and sound axiomatizations are also provided for these logics.
uucp:mcvax!inesc!jcc.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Boolos, G., The Unprovability of Consistency. An Essay in Modal Logic, Cambridge University Press, 1979.
Burgess, J.P., "The Unreal Future", Theoria, XLIV, 157–174, 1978.
Carmo, J., "The Infolog Branching Logic of Events", in: Sernadas, A., Bubenko, J. and Olivé, A. (eds.), Theoretical and Formal Aspects of Information Systems 1985, North-Holland, 159–174, 1985.
Carmo, J., "Lógicas Temporais para a Especificação e Verificação de Sistemas de Informação", Ph. D. thesis, IST (the Lisbon Institute of Technology, Technical University of Lisbon), 1988.
Carmo, J. and Sernadas, A., "Branching versus Linear Logics Yet Again", internal report, IST/INESC, 1988.
Emerson, E.A. and Halpern, J.Y., ""Sometimes" and "Not Never" Revisited: On Branching versus Linear Time Temporal Logic", Journal ACM 33 (1), 151–178, 1986.
Gabbay, D.M., "Tense Systems with Discrete Moments of Time: Part I", Journal of Philosophical Logic 1, 35–44, 1972.
Hamilton, A.G., Logic for Mathematicians, Cambridge University Press, 1978.
Hughes, G.E. e Cresswell, M.J., A Companion to Modal Logic, Methuen, 1984.
McArthur, R.P., Tense Logic, D. Reidel Publishing Company, 1976.
McCall, S., "The Strong Future Tense", Notre Dame Journal of Formal Logic XX (3), 489–504, 1979.
Prior, A., Past, Present and Future, Oxford, 1967.
Rescher, N. e Urquhart, A., Temporal Logic, Springer-Verlag, 1971.
Thomason, R.H., "Indeterministic Time and Truth-Value Gaps", Theoria 36, 264–281, 1970.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1989 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carmo, J., Sernadas, A. (1989). Inevitability in branching time. In: Meyer, A.R., Taitslin, M.A. (eds) Logic at Botik '89. Logic at Botik 1989. Lecture Notes in Computer Science, vol 363. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51237-3_5
Download citation
DOI: https://doi.org/10.1007/3-540-51237-3_5
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51237-0
Online ISBN: 978-3-540-46180-7
eBook Packages: Springer Book Archive