Defining Relevant Implication in a Propositionally Quantified S4
Kremer, Philip
J. Symbolic Logic, Tome 62 (1997) no. 1, p. 1057-1069 / Harvested from Project Euclid
R. K. Meyer once gave precise form to the question of whether relevant implication can be defined in any modal system, and his answer was `no'. In the present paper, we extend $\mathbf{S4}$, first with propositional quantifiers, to the system $\mathbf{S4\pi}+$; and then with definite propositional descriptions, to the system $\mathbf{S4\pi}+^{lp}$. We show that relevant implication can in some sense be defined in the modal system $\mathbf{S4\pi}+^{lp}$, although it cannot be defined in $\mathbf{S4\pi}+$.
Publié le : 1997-12-14
Classification: 
@article{1183745365,
     author = {Kremer, Philip},
     title = {Defining Relevant Implication in a Propositionally Quantified S4},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 1057-1069},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745365}
}
Kremer, Philip. Defining Relevant Implication in a Propositionally Quantified S4. J. Symbolic Logic, Tome 62 (1997) no. 1, pp.  1057-1069. http://gdmltest.u-ga.fr/item/1183745365/