×

Linear logic and Łukasiewicz \(\aleph_0\)-valued logic: A logico-algebraic study. (English) Zbl 1032.03054

Summary: A new characterization of all the MV-algebras embedded in a CL-algebra is presented. A new sequent calculus for Łukasiewicz \(\aleph_0\)-valued logic is introduced. Some links between this calculus and the sequent calculus for multiplicative additive linear logic are established. It is shown that Łukasiewicz \(\aleph_0\)-valued logic can be embedded in a suitable extension of MALL.

MSC:

03G25 Other algebras related to logic
03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
03B50 Many-valued logic
06D35 MV-algebras
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1023/A:1008311022292 · Zbl 0951.03024 · doi:10.1023/A:1008311022292
[2] DOI: 10.1016/S0888-613X(98)00007-3 · Zbl 0937.06011 · doi:10.1016/S0888-613X(98)00007-3
[3] DOI: 10.1090/S0002-9947-1958-0094302-9 · doi:10.1090/S0002-9947-1958-0094302-9
[4] Ciabattoni A., of the Conference KGC ’97 1289 pp 128–
[5] DOI: 10.1007/978-94-015-9480-6 · doi:10.1007/978-94-015-9480-6
[6] DOI: 10.1016/0304-3975(87)90045-4 · Zbl 0625.03037 · doi:10.1016/0304-3975(87)90045-4
[7] Girard J.-Y., London Math. Soc. L.N 222 (1995)
[8] DOI: 10.1007/978-94-011-0215-5_5 · doi:10.1007/978-94-011-0215-5_5
[9] DOI: 10.2307/2275915 · Zbl 0814.03038 · doi:10.2307/2275915
[10] DOI: 10.1016/0022-1236(86)90015-7 · Zbl 0597.46059 · doi:10.1016/0022-1236(86)90015-7
[11] Ono , H. 1990. Structural rules and a logical hierarchy, Mathematical Logic, Edited by: Petkov , P. P. 95–104. New York: Plenum Press. London · Zbl 0790.03007
[12] DOI: 10.1007/BF00370844 · Zbl 0865.03015 · doi:10.1007/BF00370844
[13] Troelstra A. S., Lectures on linear logic (1992) · Zbl 0942.03535
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.