From basic logic to quantum logics with cut-elimination

International Journal of Theoretical Physics

Volumn 37, Issue 1, 1998, Pages 31-37

  Faggian, Claudia ^a   Sambin, Giovanni ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032394961     PISSN: 00207748     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1026652903971     Document Type: Article

References (15)

1. Battilotti, G., and Sambin, G. (1996). Basic logic and the cube of its extensions, in Logic and Scientific Methods, M. L. Dalla Chiara, K. Doets, D. Mundici, and J. van Benthem, eds., Kluver, Dordrecht, to appear.
2. Battilotti, G., Faggian, C., and Sambin, G. (1996). Basic logic: reflection, symmetry, visibility, to appear.
3. Cutland, N. J., and Gibbins, P. F. (1982). A regular sequent calculus for quantum logic in which ∧ and ∨ are dual, Logique et Analyse Nouvelle Serie, 25, 221-248.
4. Dalla Chiara, M. L., and Giuntini, R. (1989). Paraconsistent quantum logics, Foundations of Physics, 19, 891-904.
5. Dummett, M. (1976). Introduction to quantum logic, unpublished notes.
6. Faggian, C. (1996). Basic logic and Girard's negation: A new approach to orthologic, to be submitted.
7. Gentzen, G. (1935). Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, 39, 176-210. English translation in The Collected Papers of Gerhard Gentzen, M. E. Szabo, ed., North-Holland, Amsterdam (1969), pp. 68-131.
8. Gentzen, G. (1935). Untersuchungen über das logische Schliessen, Mathematische Zeitschrift, 39, 176-210. English translation in The Collected Papers of Gerhard Gentzen, M. E. Szabo, ed., North-Holland, Amsterdam (1969), pp. 68-131.
9. Girard, J.-Y. (1987), Linear logic, Theoretical Computer Science, 50, 1-102.
10. Lincoln, P. D., Mitchell, J., Scedrov, A., and Shankar, N. (1990). Decision problems for propositional linear logic, in Proceedings 31st Annual IEEE Symposium on Foundations of Computer Science, pp. 239-311.
11. Nishimura, H. (1980). Sequential method in quantum logic, Journal of Symbolic Logic, 45, 339-352.
12. Nishimura, H. (1994). Proof theory for minimal quantum logic. I, II, International Journal of Theoretical Physics, 33, 103-113, 1427-1443.
13. Pratt, V. (1993). Linear logic for generalized quantum mechanics, in Proceedings Workshop on Physics and Computation (PhysComp'92), Dallas, IEEE, pp. 166-180.
14. Takano, M. (1995). Proof theory for minimal quantum logic: A remark. International Journal of Theoretical Physics, 34, 649-654.
15. Tamura, S. (1988). A Gentzen formulation without the cut rule for ortholattices, Kobe Journal of Mathematics, 5, 133-150.