Prijatelj, Andreja Free algebras corresponding to multiplicative classical linear logic and some of its extensions. (English) Zbl 0862.03042 Notre Dame J. Formal Logic 37, No. 1, 53-70 (1996). From the abstract: In this paper, constructions of free algebras corresponding to multiplicative classical linear logic, its affine variant, and their extensions with \(n\)-contraction \((n\geq 2)\) are given. As an application, the cardinality problem of some one-variable linear fragments with \(n\)-contraction is solved. Reviewer: M.Abad (Bahia Blanca) Cited in 1 ReviewCited in 1 Document MSC: 03G25 Other algebras related to logic 03B20 Subsystems of classical logic (including intuitionistic logic) Keywords:free algebras; multiplicative classical linear logic; extensions with \(n\)-contraction; cardinality problem; one-variable linear fragments × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Birkhoff, G., Lattice Theory , American Mathematical Society, Colloquium Publications, vol. XXV, New York, 1967. · Zbl 0153.02501 [2] Došen, K., and P. Schröder-Heister, Substructural Logics , Studies in Logic and Computation, Clarendon Press, Oxford, 1993. · Zbl 0811.68056 [3] Girard, J. Y., “Linear logic,” Theoretical Computer Science , vol. 50 (1987), pp. 1–101. · Zbl 0625.03037 · doi:10.1016/0304-3975(87)90045-4 [4] Hori, R., H. Ono and H. Schellinx, “Extending intuitionistic linear logic with knotted structural rules,” Notre Dame Journal of Formal Logic , vol. 35 (1994), pp. 219–242. · Zbl 0812.03008 · doi:10.1305/ndjfl/1094061862 [5] De Jongh, D., L. Hendriks, and G. Renardel de Lavalette, “Computations in fragments of intuitionistic propositional logic,” Journal of Automatic Reasoning , vol. 7 (1991), pp. 537–561. · Zbl 0743.03007 · doi:10.1007/BF01880328 [6] Prijatelj, A., “Connectification for \(n\)-contraction,” Studia Logica , vol. 54 (1995), pp. 149–171. · Zbl 0823.03003 · doi:10.1007/BF01063150 [7] Prijatelj, A., “Bounded contraction and Gentzen-style formulation of Łukasiewicz logics,” forthcoming in Studia Logica . · Zbl 0865.03015 · doi:10.1007/BF00370844 [8] Slaney, J., “Sentential constants in systems near \(\mathbf R\),” Studia Logica , vol. 52 (1993), pp. 443–455. · Zbl 0796.03031 · doi:10.1007/BF01057657 [9] Troelstra, A. S., Lectures on Linear Logic , CSLI Lecture Notes, No. 29, Center for the Study of Language and Information, Stanford, 1992. · Zbl 0942.03535 [10] Troelstra, A. S., and D. van Dalen, Constructivism in Mathematics , (two volumes), North-Holland, Amsterdam, 1988. Mathematical Reviews (MathSciNet): Zentralblatt MATH: 0661.03047 · Zbl 0653.03040 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.