The geometry of non-distributive logics

Journal of Symbolic Logic

Volumn 70, Issue 4, 2005, Pages 1108-1126

  Restall, Greg ^a   Paoli, Francesco ^b  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 32244437429     PISSN: 00224812     EISSN: None     Source Type: Journal    
DOI: 10.2178/jsl/1129642117     Document Type: Article

References (21)

1. G. BATTILOTTI and G. SAMBIN, Basic logic and the cube of its extensions, Logic and foundations of mathematics (A. Cantinietal., editors), Kluwer, 1999, pp. 165-185.
2. NUEL D. BELNAP, Display logic, Journal of Philosophical Logic, vol. 11 (1982), pp. 375-417.
3. GARRETT BIRKHOFF, Lattice theory, American Mathematical Society Colloquium Publications, Rhode Island, 1973.
4. A. CARBONE, Duplication of directed graphs and exponential blow up of proofs, Annals of Pure and Applied Logic, vol. 100 (1999), pp. 1-67.
5. J. R. B. COCKETT and R. A. G. SEELY, Finite sum-product logic, Theory and Applications of Categories, vol. 8 (2001), no. 5, pp. 63-99.
6. M. L. DALLA CHIARA and R. GIUNTINI, Paraconsistent quantum logics, Foundations of Physics, vol. 19 (1989), pp. 891-904.
7. _, Quantum logics, Handbook of philosophical logic (D. Gabbay and F. Guenthner, editors), vol. 6, Kluwer, 2002.
8. VINCENT DANOS and LAURENT REIGNIER, The structure of multiplicatives, Archive of Mathematical Logic, vol. 28 (1989), pp. 181-203.
9. B. A. DAVEY and H. A. PRIESTLEY, Introduction to lattices and order, Cambridge University Press, Cambridge, 1990.
10. REINHARD DIESTEL, Graph theory, second ed., Graduate Texts in Mathematics, vol. 173, Springer Verlag, 2000, Text available at http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/.
11. J. MICHAEL DUNN and GARY M. HARDEGREE, Algebraic methods in philosophical logic, Clarendon Press, Oxford, 2001.
12. JEAN-YVES GIRARD, Linear logic, Theoretical Computer Science, vol. 50 (1987), pp. 1-101.
13. _, Proof-nets: the parallel syntax for proof theory, Logic and algebra (New York), Dekker, 1996, pp. 97-124.
14. GEORGE GRÄTZER, General lattice theory, Academic Press, 1978.
15. D. J. D. HUGHES and R. J. VAN GLABBEEK, Proof nets for unit-free multiplicative-additive linear logic, Proceedings of the 18th Annual IEEE Symposium on Logic and Computer Science (Ottawa), June 2003, extended abstract, pp. 1-10.
16. H. NISHIMURA, Sequential method in quantum logic, this JOURNAL, vol. 45 (1980), pp. 339-352.
17. A. G. OLIVEIRA and R. J. G. B. DE QUEIROZ, Geometry of deduction via graphs of proof, Logic for concurrency and synchronization (R. J. G. B. de Queiroz, editor), Kluwer, 2003, pp. 3-88.
18. GREG RESTALL, An introduction to substructural logics, Routledge, 2000.
19. J. SCHÜLTE MONTING, Cut elimination and word problem for varieties of lattices, Algebra Universalis, vol. 12 (1981), pp. 290-321.
20. L. TORTORA DE FALCO, The additive multiboxes, Annals of Pure and Applied Logic, vol. 120 (2003), pp. 65-102.
21. _, Additives of linear logic and normalization, Part I: A (restricted) Church-Rosser property, Theoretical Computer Science, vol. 294 (2003), pp. 489-524.