A formalization of the Lewis system S1 without rules of substitution.

Stochastica (1979)

• Volume: 3, Issue: 1, page 39-45
• ISSN: 0210-7821

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Abstract

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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.

How to cite

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Pla Carrera, Josep. "A formalization of the Lewis system S1 without rules of substitution.." Stochastica 3.1 (1979): 39-45. <http://eudml.org/doc/38805>.

@article{PlaCarrera1979,
abstract = {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.},
author = {Pla Carrera, Josep},
journal = {Stochastica},
keywords = {Lógica modal; Lógica simbólica; Sistemas lógicos de Lewis; formalization of the system S1 without substitution rule; weak Becker's equivalence},
language = {eng},
number = {1},
pages = {39-45},
title = {A formalization of the Lewis system S1 without rules of substitution.},
url = {http://eudml.org/doc/38805},
volume = {3},
year = {1979},
}

TY - JOUR
AU - Pla Carrera, Josep
TI - A formalization of the Lewis system S1 without rules of substitution.
JO - Stochastica
PY - 1979
VL - 3
IS - 1
SP - 39
EP - 45
AB - 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.
LA - eng
KW - Lógica modal; Lógica simbólica; Sistemas lógicos de Lewis; formalization of the system S1 without substitution rule; weak Becker's equivalence
UR - http://eudml.org/doc/38805
ER -

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