6 Conclusions and Future Work 7 Related Work
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چکیده
in GG oteborg (where it was nished) for their supportive environments. We are especially thankful to Grigori Mints for proposing the subject for research and clarifying numerous questions. G. Mints has also helped with numerous suggestions and corrections concerning the earlier versions of the paper. P.Lincoln and J.Smith have helped with various suggestions and corrections regarding the previous versions of the paper. J.-M. Andreoli has helped with discussions concerning focusing. 35 unneeded repetition of labels. The number 500000000 indeed denotes 500 millions, the approximate number of subgoals generated during a 14-hour bottom-up search. formula bottom-up prover resolution prover time subgoals time derived retained In our experiments resolution method and bottom-up method usually exhibit roughly the same degree of eeciency for propositional linear logic and resolution normally surpasses bottom-up method for the nonexponential fragment of linear logic. Since in the classical case the superior eeciency of resolution when compared to the bottom-up search becomes very noticeable for predicate logic (mainly due to the possibility to use uniication), it can be hoped that resolution as a practical proof-seach tool may be superior to the bottom-up search for the predicate version of linear logic. Several strategies presented above for the bottom-up prover (a modiied rule 0 , employing invertibility of & and O, moving weakening to axioms) have been independently suggested also in 1] and 2]. Focusing is discovered in 1] and partially in 2]. Both 5] and 4] treat predicate level of linear logic, but with a severly restricted propositional structure, with the aim to devise a special linear logic programming language. The resolution method for full linear logic along the lines of a general resolution framework of 12] was rst presented in 13]. The last paper also introduces the strategy which is analogous to using implicit-weakening rules and avoiding explicit weakening applications.
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