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.
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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.
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© 2000 Springer Science+Business Media Dordrecht
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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
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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
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