Abstract
We present two approaches to define the semantics for positive/negative conditional rewrite systems. The first — the recursive evaluation approach — is based on a well-founded ordering and leads to a perfect model semantics. The second — the built-in evaluation approach — is based on a set of predefined inequations and leads to an initial model semantics provided the inequations are interpreted in a non-standard way. Both approaches coincide if a suitable inequation covering property is satisfied.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K. R. Apt, H. Blair and A. Walker, Towards a Theory of Declarative Knowledge, in: J. Minker, ed., Foundations of Deductive Databases and Logic Programming (Morgan Kaufmann, Los Altos, 1988) pp. 89–148.
J. Avenhaus and K. Becker, Conditional rewriting modulo a built-in algebra, SEKI Report SR-92-11.
J. Avenhaus and K. Madlener, Term rewriting and equational reasoning, in: R. B. Banerji, ed., Formal Techniques in Artificial Intelligence (North-Holland, Amsterdam, 1990) pp. 1–43.
L. Bachmair and H. Ganzinger, Perfect model semantics for logic programs with equality, in: Proc. of 8th Int. Conf. on Logic Programming (MIT Press, 1991) pp. 645–659.
N. Dershowitz and J. P. Jouannaud, Rewriting systems, in: J. van Leeuwen, ed., Handbook of Theoretical Computer Science, Vol. B (Elsevier, Amsterdam, 1990) pp. 241–320.
N. Dershowitz and M. Okada, A rationale for conditional equational rewriting, Theoret. Comput. Science 75(1/2) (1990) pp. 111–137.
J.-P. Jouannaud and B. Waldmann, Reductive conditional term rewriting systems, in: Proc. Third IFIP Working Conference on Formal Description of Programming Concepts, Ebberup, Denmark (1986).
S. Kaplan, Simplifying conditional term rewriting systems: unification, termination and confluence, J. Symbolic Computation 4(3) (1987) pp. 295–334.
S. Kaplan, Positive/negative conditional rewriting, in: Conditional Term Rewriting Systems, LNCS 308 (Springer, Berlin, 1987) pp. 129–143.
T. C. Przymusinski, On the declarative semantics of deductive databases and logic programming, in: J. Minker, ed., Foundations of Deductive Databases and Logic Programming (Morgan Kaufmann, Los Altos, 1988) pp. 193–216.
C.-P. Wirth and B. Gramlich, A constructor-based approach for positive/negative conditional equational specifications, this volume.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Becker, K. (1993). Semantics for positive/negative conditional rewrite systems. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_16
Download citation
DOI: https://doi.org/10.1007/3-540-56393-8_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56393-8
Online ISBN: 978-3-540-47549-1
eBook Packages: Springer Book Archive