Abstract
System BV is an extension of multiplicative linear logic with a non-commutative self-dual operator. In this paper, we present systems equivalent to system BV where equalities for unit are oriented from left to right and new structural rules are introduced to preserve completeness. While the first system allows units to appear in the structures, the second system makes it possible to completely remove the units from the language of BV by proving the normal forms of the structures that are provable in BV. The resulting systems provide a better performance in automated proof search by disabling redundant applications of inference rules due to the unit. As evidence, we provide a comparison of the performance of these systems in a Maude implementation.
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References
Brünnler, K.: Deep inference and symmetry in classical proofs. PhD. Thesis, Technische Universität Dresden (2003)
Bruscoli, P.: A purely logical account of sequentiality in proof search. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 302–316. Springer, Heidelberg (2002)
Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: The Maude 2.0 system. In: Nieuwenhuis, R. (ed.) Rewriting Techniques and Applications, Proceedings of the 14th International Conference (2003)
Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: Maude 2.1 manual. Technical Report, Computer Science Laboratory, SRI International (2004), http://maude.cs.uiuc.edu/manual/
Clavel, M., Durán, F., Eker, S., Meseguer, J., Stehr, M.-O.: Maude as a formal meta-tool. In: Woodcock, J.C.P., Davies, J., Wing, J.M. (eds.) FM 1999. LNCS, vol. 1709, pp. 1684–1703. Springer, Heidelberg (1999)
Gugliealmi, A.: A system of interaction and structure. Technical Report, WV-02-10, TU Dresden (2002)
Guglielmi, A., Straßburger, L.: A non-commutative extension of MELL. In: Baaz, M., Voronkov, A. (eds.) LPAR 2002. LNCS (LNAI), vol. 2514, pp. 231–246. Springer, Heidelberg (2002)
Hölldobler, S., Kahramanoğulları, O.: From the calculus of structures to term rewriting systems. Technical Report, WV-04-03, TU Dresden (2004)
Kahramanoğulları, O.: Implementing system BV of the calculus of structures in Maude. In: Proceedings of the ESSLLI-2004 Student Session, Université Henri Poincaré, Nancy, France (2004)
Kahramanoğulları, O.: Plans as formulae with a non-commutative operator. Technical Report, TU Dresden (2004)
Miller, D., Nadathur, G., Pfenning, F., Scedrov, A.: Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51, 125–157 (1991)
Straßburger, L.: Linear logic and noncommutativity in the calculus of structures. PhD. Thesis, TU Dresden (2003)
Straßburger, L.: System NEL is undecidable. In: De Queiroz, R., Pimentel, E., Figueiredo, L. (eds.) 10th Workshop on Logic, Language, Information and Computation (WoLLIC). Electronic Notes in Theoretical Computer Science, vol. 84 (2003)
Tiu, A.F.: Properties of a logical system in the calculus of structures. Technical Report, WV-01-06, TU Dresden (2001)
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Kahramanoğulları, O. (2004). System BV without the Equalities for Unit. In: Aykanat, C., Dayar, T., Körpeoğlu, İ. (eds) Computer and Information Sciences - ISCIS 2004. ISCIS 2004. Lecture Notes in Computer Science, vol 3280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30182-0_99
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DOI: https://doi.org/10.1007/978-3-540-30182-0_99
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