Some remarks on linear logic

Abstract

Linear logic and its variants, often called substructural logics, have shed light on various new aspects of traditional logic. In this note we shall discuss some of them.

A related version of this paper was published as (Okada 2004). A different earlier version may be found in (Benoist et al. 2006), although the earlier standpoint of the author is different from that in this paper. For a technical introduction to linear logic, J.-Y. Girard’s (Girard 1987) and his other writings are always most suggestive and informative, although some philosophical standpoints are not the same as those of the present paper. A minimal technical introduction for nonexperts may be found in (Okada 1999). In particular, the reader can see some concrete examples of the use of the non-modal state description of linear logic on the state-description level, which is a lower level that the truth-falsehood level of the traditional logics.