TL;DR
This paper demonstrates that all axiomatic extensions of the full Lambek calculus with exchange can be characterized by formulas at a specific level of the substructural hierarchy, clarifying the structure of these logical systems.
Contribution
It establishes that formulas at the level of the substructural hierarchy suffice to axiomatize all extensions of the full Lambek calculus with exchange.
Findings
All axiomatic extensions are axiomatized by -level formulas.
Clarifies the substructural hierarchy's role in logical axiomatizations.
Provides a foundation for further classification of substructural logics.
Abstract
We prove that all axiomatic extensions of the full Lambek calculus with exchange can be axiomatized by formulas on the level of the substructural hierarchy.
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