Substructural Fuzzy-Relevance Logic

Fuzzy Logics and Sub-structural Logics without Exchange

This report treats the relation between substructural logics and fuzzy logics, especially focuses on the noncommutativity of conjunctive operators i.e. substructural logics without the exchange rule. As the results, the authors show that fuzzy logics based on the left continuous pseudo-t-norms are the extensions of FLw. Also, we introduce the definition of pseudouninorms and give some methods t...

Substructural fuzzy logics

Modalities in Substructural Logics

This paper generalises Girard's results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a single modality whichèncodes' the new structural rules. Logics 1 1. Logics Logic is about valid deduction. One central result in logic is the deduction theorem. A; ` B if and only if`A ! B This result t...

Practical Programming with Substructural Types

Substructural logics remove from classical logic rules for reordering, duplication, or dropping of assumptions. Because propositions in such a logic may no longer be freely copied or ignored, this suggests understanding propositions in substructural logics as representing resources rather than truth. For the programming language designer, substructural logics thus provide a framework for consid...

Modal translations in substructural logics

Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic, It is proved that first-order variants of these logics with an intuitionistic negation cm be embedded by modal translations into M-type extensions of these logics with...