Labeled Sequent Calculus for Orthologic
| dc.contributor.author | Kawano, Tomoaki | |
| dc.date.accessioned | 2019-05-24T07:15:56Z | |
| dc.date.available | 2019-05-24T07:15:56Z | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/28480 | |
| dc.description.abstract | Orthologic (OL) is non-classical logic and has been studied as a part of quantumlogic. OL is based on an ortholattice and is also called minimal quantum logic.Sequent calculus is used as a tool for proof in logic and has been examinedfor several decades. Although there are many studies on sequent calculus forOL, these sequent calculi have some problems. In particular, they do not includeimplication connective and they are mostly incompatible with the cut-eliminationtheorem. In this paper, we introduce new labeled sequent calculus called LGOI,and show that this sequent calculus solve the above problems. It is alreadyknown that OL is decidable. We prove that decidability is preserved when theimplication connective is added to OL. | en_GB |
| dc.language.iso | en | en_GB |
| dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | en_GB |
| dc.relation.ispartofseries | Bulletin of the Section of Logic; 4 | |
| dc.rights | This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. | en_GB |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0 | en_GB |
| dc.subject | Quantum logic | en_GB |
| dc.subject | Sequent calculus | en_GB |
| dc.subject | cut-elimination theorem | en_GB |
| dc.subject | Decidability | en_GB |
| dc.subject | Kripke Model | en_GB |
| dc.title | Labeled Sequent Calculus for Orthologic | en_GB |
| dc.type | Article | en_GB |
| dc.page.number | 217-232 | |
| dc.contributor.authorAffiliation | Tokyo Institute of Technology, School of Computing, Department of Mathematical and Computing Science | |
| dc.identifier.eissn | 2449-836X | |
| dc.references | [1] M. L. D. Chiara and R. Giuntini, Quantum Logics, Handbook of Philosophical Logic 2nd Edition 6 (2001), pp. 129–228. | en_GB |
| dc.references | [2] C. Faggian and G. Sambin, From Basic Logic to Quantum Logics with Cut-Elimination, International Journal of Theoretical Physics 37(1) (1998), pp. 31–37. | en_GB |
| dc.references | [3] G. M. Hardegree, Material Implication in Orthomodular (and Boolean) Lattices, Notre Dame Journal of Formal Logic 22(2) (1981), pp. 163–182. | en_GB |
| dc.references | [4] Z. Hou, A. Tiu and R. Gore, A Labelled Sequent Calculus for BBI: Proof Theory and Proof Search, TABLEAUX 2013 (2013), pp. 172–187. | en_GB |
| dc.references | [5] S. Negri, Proof Analysis in Modal Logic, Journal of Philosophical Logic 34 (2005), pp. 507–544. | en_GB |
| dc.references | [6] S. Negri, Proof theory for modal logic, Philosophy Compass 6(8) (2011), pp. 523–538. | en_GB |
| dc.references | [7] H. Nishimura, Sequential Method in Quantum Logic, The Journal of Symbolic Logic 45(2) (1980), pp. 339–352. | en_GB |
| dc.references | [8] H. Nishimura, Proof Theory for Minimal Quantum Logic I, International Journal of Theoretical Physics 33(1) (1994), pp. 103–113. | en_GB |
| dc.references | [9] H. Nishimura, Proof Theory for Minimal Quantum Logic II, International Journal of Theoretical Physics 33(7) (1994), pp. 1427–1443. | en_GB |
| dc.contributor.authorEmail | kawano.t.af@m.titech.ac.jp | |
| dc.identifier.doi | 10.18778/0138-0680.47.4.01 | |
| dc.relation.volume | 47 | en_GB |
Pliki tej pozycji
Pozycja umieszczona jest w następujących kolekcjach
Poza zaznaczonymi wyjątkami, licencja tej pozycji opisana jest jako This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.