Logic and groups

Francesco Paoli

DOI: http://dx.doi.org/10.12775/LLP.2001.007


Abelian group logic (AGL) — in other words, the logic which is sound and complete w.r.t. Abelian groups — is a non-trivial inconsistent logic, i.e. what some paraconsistent logicians call a “dialethic” logic.

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Anderson, A.R., N.D. Belnap, J.M. Dunn (1992), Entailment, vol. II, Princeton Univ. Press, Princeton, NJ.

Blute, R.F., P.J. Scott (1996), “Linear Läuchli semantics”, Annals of Pure and Applied Logic 77, 101–142.

Casari, E. (1989), “Comparative logics and Abelian l-groups”, in R. Ferro et al. (eds.), Logic Colloquium ’88, North Holland, Amsterdam, pp. 161–190.

Casari, E. (1990), “Logics on pregroups”, in Aa.Vv., Nuovi problemi della logica e della filosofia della scienza, vol. II, Clueb, Bologna, pp. 39–58.

Casari, E. (1997), “Conjoining and disjoining on different levels”, in M.L. Dalla Chiara et al. (eds.), Logic and Scientific Methods, Kluwer, Dordrecht, pp. 261–288.

Dunn, J.M. (1986), “Relevance logic and entailment”, in D. Gabbay and F. Guenthner (Eds.), Handbook of Philosophical Logic, vol. III, Reidel, Dordrecht, pp. 117–224.

Girard, J.Y. (1987), “Linear logic”, Theoretical Computer Science 50, 1–102.

Lafont, Y. (1997), “The finite model property for various fragments of linear logic”, Journal of Symbolic Logic 62, 4, 1202–1208.

Meyer, R.K., J.K. Slaney (1989), “Abelian Logic (from A to Z)”, in G. Priest, R. Routley and J. Norman (eds.), Paraconsistent Logic, Philosophia, Münich, pp. 245–288.

Restall, G. (1993), “How to be really contraction free”, Studia Logica 52, 381–392.

Routley, R., R.K. Meyer (1972), “The semantics of entailment. III”, Journal of Philosophical Logic 1, 192–208.

Troelstra, A.S. (1992), Lectures on Linear Logic, CSLI, Stanford, CA.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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