In the Lewis and Langford formalization of system S1 (1932), besides the deduction rules, the substitution rules are as well used: the uniform substitution and the substitution of strict equivalents. They then obtain systems S2, S3, S4 and S5 adding to the axioms of S1 a new axiom, respectively, without changing the deduction rules. Lemmon (1957) gives a new formalization of systems S1-S5, calling them P1-P5. Is is worthwhile to remark that in the formalization of P2-P5 one does not use any more the substitution of equivalentsrule, although Lemmon still maintains the uniform substitution rule. Anyhow Lemmon system P1 uses the substitution of equivalents rule in addition to uniform substitution rule. Moreover these substitution rules have been used later by Feys (1965), Hughes and Cresswell (1968), Zeman (1973) to construct Lewis modal systems. This paper deals with a new formalization of S1 system, following Lemmon's ideas, without substitution rules.
@article{urn:eudml:doc:38805,
title = {A formalization of the Lewis system S1 without rules of substitution.},
journal = {Stochastica},
volume = {3},
year = {1979},
pages = {39-45},
zbl = {0426.03027},
mrnumber = {MR0562439},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38805}
}
Pla Carrera, Josep. A formalization of the Lewis system S1 without rules of substitution.. Stochastica, Tome 3 (1979) pp. 39-45. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38805/