Projectivity and unification in substructural logics of generalized rotations

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...

Relevant and substructural logics

This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods.

Substructural fuzzy logics

Substructural Logics on Display

Substructural logics are traditionally obtained by dropping some or all of the structural rules from Gentzen’s sequent calculi LK or LJ. It is well known that the usual logical connectives then split into more than one connective. Alternatively, one can start with the (intuitionistic) Lambek calculus, which contains these multiple connectives, and obtain numerous logics like: exponential-free l...

Displaying and Deciding Substructural Logics

Many logics in the relevant family can be given a proof theory in the style of Belnap's display logic (Belnap 1982). However, as originally given, the proof theory is essentially more expressive than the logics they seek to model. In this paper, we consider a modiied proof theory which more closely models relevant logics. In addition, we use this proof theory to provide decidability proofs for ...