Abstract
This book presents a uniform goal-directed algorithmic proof theory for a variety of logics. The logics involved have a wide range, and small variations in the goal-directed algorithm can take us from one logic to a completely different one.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
As a preliminary result, in [Gabbay et al., 1999] it is shown that a straightforward refinement of the goal-directed procedure gives an O(n logn)-space procedure for intuitionistic implication/negation fragment, the optimal space upper bound found so far.
In [1999] Galmiche and Pym discuss extensively proof search for type-theoretic languages, including goal-directed search and possible extensions of logic programming.
A (partial) list of works is: [Gabbay and Reyle, 1984; Miller, 1989; McCarty, 1988a; Bollen, 1991; Miller et al., 1991; Hodas and Miller, 1994; Harland and Pym, 1991; Gabbay, 1987; Giordano et al., 1992; Baldoni et al., 19981. More references are given in the previous chapters.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Gabbay, D.M., Olivetti, N. (2000). Conclusions and Further Work. In: Goal-Directed Proof Theory. Applied Logic Series, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1713-7_6
Download citation
DOI: https://doi.org/10.1007/978-94-017-1713-7_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5526-2
Online ISBN: 978-94-017-1713-7
eBook Packages: Springer Book Archive