Abstract
The paper extends the similarity saturation calculus [8] by including flexible function symbols. The most attractive property of the similarity saturation calculus consists in that it allows to build derivations constructively both for a finitary complete and finitary incomplete first order linear temporal logic. The saturation calculus contains the so-called alternating rule and this rule splits off the logical part from the temporal one in the quasi-primary sequents. If the saturation process involves unification and flexible function symbols, then the alternating rule includes (in the temporal part of the rule) renaming of variables and a replacement of flexible function symbols by rigid ones. The employment of flexible symbols means the introduction of some kind of constraints in the saturation process.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
H. Andreka, J. Nemeti, J. Sain: On the strenghth of temporal proof, LNCS, 379, 135–144 (1989).
Ben-Ari: Mathematical Logic for Computer Science, Prentice Hall, 1993.
M. Fisher: A normal form for first order temporal formulae, LNCS, 607, 370–384 (1992).
D.M. Gabbay: The declarative past and the imperative future, LNCS, 398, 409–448 (1987).
H. Kawai: Sequential calculus for a first order infinitary temporal logic, Zeitchr. fur Math. Logic und Grundlagen der Math., 33, 423–452 (1987).
R. Pliuškevičius: On saturated calculi for a linear temporal logic, LNCS 711, 640–649 (1993).
R. Pliuškevičius: The saturated tableaux for linear miniscoped Horn-like temporal logic, Journal of Automated Reasoning, 13, 51–67 (1994).
R. Pliuškevičius: On the replacement of induction for a first order linear temporal logic, Proc. of Second World Conf. on the Fund. of Artif. Intell., 331–342 (1995).
I. Sain: Temporal logics need their clocks. Theoret. Comput. Sci., 95, 75–95(1992).
J. Sakalauskaitė: A sequent calculus for a first order linear temporal logic with equality. LNCS, 620, 430–440 (1992).
A. Szalas: Concerning the semantic consequence relation in first-order temporal logic, Theoret. Comput. Sci. 47, 329–334 (1986).
P. Wolper: The tableaux method for temporal logic: an overview, Log. et anal. 28, 119–136 (1985).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pliuškevičius, R. (1996). On saturation with flexible function symbols. In: Penczek, W., Szałas, A. (eds) Mathematical Foundations of Computer Science 1996. MFCS 1996. Lecture Notes in Computer Science, vol 1113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61550-4_172
Download citation
DOI: https://doi.org/10.1007/3-540-61550-4_172
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61550-7
Online ISBN: 978-3-540-70597-0
eBook Packages: Springer Book Archive