Adorable A and the Lovelight L - Together Again

Su Rogerson

Su Rogerson (Monash) will present "Adorable A and the Lovelight L - Together Again" at 1 in Old Arts 224 on 18 October.

Abstract: Abelian logic (Left Abelian Group Logic, LAGL) was independently introduced by Meyer and Slaney [1] and Casari [3] in 1989. Further results were published by Meyer and Slaney in [2]. This paper takes the axiomization of LAGL; given by Meyer and Slaney and compares it with Right Abelian Group Logic, RAGL (refered to as the Lovelight L in [5]). The axiomizations are different [4] and when the rule of modus ponens is added to each logic in turn, different properties are observed. This paper expands on these results giving reasons as to why adding modus ponens rather than reverse modus ponens to RAGL makes RAGL, in a sense, deductively weaker than LAGL with modus ponens.

References

[1] Meyer, R.K, Slaney J.K., Abelian Logic (From A to Z), in G. Priest, R. Routley, J. Norman (eds.), Paraconsistent Logic -- Essays on the Inconsistent. Philosophia Verlag, Muenchen, 1989.

[2] Meyer, R.K, Slaney J.K., ìA, Still Adorableî, in W. Carnielli, M. Coniglio, I DíOttaviano (eds.), Paraconsistency: the logical way to the inconsistent. Proceedings of the World Congress held in Sao Paulo, Marcel Dekker, Inc., New York, Basel, 2002.

[3] Casari, E., Comparative Logics and Abelian l-Groups, in R. Ferro et al.(eds.) Logic Colloquium í88, North Holland, Amsterdam.

[4] Kalman, J. A., Substitution-and-detachment systems related to abelian groups, in J. C. Butcher, ed., A Spectrum of Mathematics: Essays presented to H. G. Forder, Auckland University Press, OUP, 1971, 22-31.

[5] Rogerson, S., Abstract 'Investigations into a class of robustly contraction free logics', Bulletin of Symbolic Logic (2001), p. 290.