One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity
| dc.contributor.author | Płaczek, Paweł | |
| dc.date.accessioned | 2021-05-05T13:58:34Z | |
| dc.date.available | 2021-05-05T13:58:34Z | |
| dc.date.issued | 2020-11-13 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/35352 | |
| dc.description.abstract | Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided (in fact, left-sided) sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTime complexity of the multiplicative fragment of NBL. | en |
| dc.language.iso | en | |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl |
| dc.relation.ispartofseries | Bulletin of the Section of Logic;1 | en |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0 | |
| dc.subject | Substructural logic | en |
| dc.subject | Lambek calculus | en |
| dc.subject | nonassociative linear logic | en |
| dc.subject | sequent system | en |
| dc.subject | PTime complexity | en |
| dc.title | One-Sided Sequent Systems for Nonassociative Bilinear Logic: Cut Elimination and Complexity | en |
| dc.type | Other | |
| dc.page.number | 55-80 | |
| dc.contributor.authorAffiliation | Adam Mickiewicz University, Faculty of Mathematics and Computer Science Uniwersytetu Poznanskiego 4, 61-614 Poznan, Poland | en |
| dc.identifier.eissn | 2449-836X | |
| dc.references | [1] V. M. Abrusci, Phase semantics and sequent calculus for pure noncommutative classical linear propositional logic, The Journal of Symbolic Logic, vol. 56(4) (1991), pp. 1403–1451, DOI: http://dx.doi.org/10.2307/2275485 | en |
| dc.references | [2] A. Bastenhof, Categorial Symmetry, Ph.D. thesis, Utrecht University (2013). | en |
| dc.references | [3] W. Buszkowski, On classical nonassociative Lambek calculus, [in:] M. Amblard, P. de Groote, S. Pogodalla, C. Retoré (eds.), Logical Aspects of Computational Linguistics, vol. 10054 of Lecture Notes in Computer Science, Springer (2016), pp. 68–84, DOI: http://dx.doi.org/10.1007/978-3-662-53826-5_5 | en |
| dc.references | [4] W. Buszkowski, Involutive nonassociative Lambek calculus: Sequent systems and complexity, Bulletin of the Section of Logic, vol. 46(1/2) (2017), DOI: http://dx.doi.org/10.18778/0138-0680.46.1.2.07 | en |
| dc.references | [5] P. De Groote, F. Lamarche, Classical non-associative Lambek calculus, Studia Logica, vol. 71(3) (2002), pp. 355–388, DOI: http://dx.doi.org/10.1023/A:1020520915016 | en |
| dc.references | [6] N. Galatos, P. Jipsen, Residuated frames with applications to decidability, Transactions of the American Mathematical Society, vol. 365(3) (2013), pp. 1219–1249, URL: https://www.jstor.org/stable/23513444 | en |
| dc.references | [7] N. Galatos, H. Ono, Cut elimination and strong separation for substructural logics: an algebraic approach, Annals of Pure and Applied Logic, vol. 161(9) (2010), pp. 1097–1133, DOI: http://dx.doi.org/0.1016/j.apal.2010.01.003 | en |
| dc.references | [8] J.-Y. Girard, Linear logic, Theoretical Computer Science, vol. 50(1) (1987), pp. 1–101, DOI: http://dx.doi.org/10.1016/0304-3975(87)90045-4 | en |
| dc.references | [9] J. Lambek, On the calculus of syntactic types, [in:] R. Jakobson (ed.), Structure of language and its mathematical aspects, vol. 12, Providence, RI: American Mathematical Society (1961), pp. 166–178, DOI: http://dx.doi.org/10.1090/psapm/012/9972 | en |
| dc.references | [10] J. Lambek, Cut elimination for classical bilinear logic, Fundamenta Informaticae, vol. 22(1, 2) (1995), pp. 53–67, DOI: http://dx.doi.org/10.3233/FI-1995-22123 | en |
| dc.references | [11] M. Pentus, Lambek calculus is NP-complete, Theoretical Computer Science, vol. 357(1-3) (2006), pp. 186–201, DOI: http://dx.doi.org/10.1016/j.tcs.2006.03.018Get. | en |
| dc.contributor.authorEmail | pawel.placzek@amu.edu.pl | |
| dc.identifier.doi | 10.18778/0138-0680.2020.25 | |
| dc.relation.volume | 50 |
Pliki tej pozycji
Pozycja umieszczona jest w następujących kolekcjach
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako https://creativecommons.org/licenses/by-nc-nd/4.0