期刊
STUDIA LOGICA
卷 106, 期 3, 页码 453-480出版社
SPRINGER
DOI: 10.1007/s11225-017-9749-5
关键词
Connexivity; Necessity; Normal modal logics; Contraposition; Conditionals
The first section of the paper establishes the minimal properties of so-called consequential implication and shows that they are satisfied by at least two different operators of decreasing strength (symbolized by -> and double right arrow). Only the former has been analyzed in recent literature, so the paper focuses essentially on the latter. Both operators may be axiomatized in systems which are shown to be translatable into standard systems of normal modal logic. The central result of the paper is that the minimal consequential system for double right arrow, CI double right arrow, is definitionally equivalent to the deontic system KD and is intertranslatable with the minimal consequential system for ->, CI. The main drawback ot the weaker operator double right arrow is that it lacks unrestricted contraposition, but the final section of the paper argues that double right arrow has some properties which make it a valuable alternative to ->, turning out especially plausible as a basis for the definition of operators representing synthetic (i.e. context-dependent) conditionals.
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