Abstract
The results presented in this paper wereobtained in the framework of basic logic, a new logicaiming at the unification of several logical systems.The first result is a sequent formulation for orthologic which allows the use of methods of proof theoryin quantum logic. Such a formulation admits a verysimple procedure of cut-elimination and hence, becauseof the subformula property, also a method of proof search and an effective decision procedure. Byusing the framework of basic logic, we also obtain acut-free formulation for orthologic with implication,for linear orthologic, and, more in generally for a wide range of new quantum-like logics. Theselogics meet some requirements expressed by physicistsand computer scientists. In particular, we propose agood candidate for a linear quantum logic withimplication.
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Faggian, C., Sambin, G. From Basic Logic to Quantum Logics with Cut-Elimination. International Journal of Theoretical Physics 37, 31–37 (1998). https://doi.org/10.1023/A:1026652903971
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DOI: https://doi.org/10.1023/A:1026652903971