Meeting a Modality?
Substructural logics are logics one can give by a Gentzen-style derivation system lacking some or all of the structural rules like associativity, permutation, weakening or contraction. Such logics have received a lot of attention in recent years, partly because of their interest for applications in e.g. computer science (linear logic, cf. Girard (1987)) or linguistics (Lambek Calculus, cf. Lambek (1961) for the original article, or Moortgat (1988), van Benthem (1991) or Morrill (1992) for recent developments). There is a bewildering variety of substructural logics, as we may drop any subset of structural rules from a standard derivation system for let’s say intuitionistic logic. Of this landscape, Wansing (1993) draws a partial map in the form of a lattice, set-inclusion of the derivable sequents being the ordering.
KeywordsRelative Clause Atomic Formula Intuitionistic Logic Linear Logic Logical Rule
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