Substructural logics are usually described as logics that lack some members of the usual triple of structural rules: contraction, weakening, or exchange. From this descripion alone it is clear that substructural logics are intimately connected with sequent calculi. Indeed their origin is rooted in proof theory and Gentzen-style systems. Four broad families of logics immediately answer the description:
- relevant logics
- BCK logics, or logics without contraction
- linear logic and its extensions
- Lambek calculus
It was realised early on that substructural logics share a common algebraic characteristic. Namely, all the algebraic semantics for substructural logics are (embeddable in) residuated structures. Hence the slogan “Substructural logics are logics of residuated structures''. This shift of focus brings forth a fruitful connection with more traditional areas of mathematical research, such as lattice-ordered groups, as well as encompassing two families of logics that the proof-theoretical description misses:
- fuzzy logics (where the sequent presentation is not obvious)
- intuitionistic and intermediate logics, including classical logic (where all structural rules are present)
Thus, a carefully stated proof-theoretical description of substructural logics could perhaps read: axiomatic extensions of any logic that, if presented as a sequent calculus, lacks zero or more structural rules. A phrase worthy of a logician, without a doubt.
We welcome submissions of papers on topics from (but possibly also outside of) the following list:
- Proof theory of substructural logics;
- Substructural logics from the viewpoint of abstract algebraic logic;
- Residuated lattices;
- Individual classes of residuated lattices (l-groups, MV algebras, etc.);
- Reducts and expansions of residuated lattices (BCK algebras, equivalential algebras, modal FL-algebras, etc.)
- Relationships between substructural logics and other non-classical logics (modal, paraconsistent, quantum logics, etc.);
- Applications of substructural logic
Special Session
Organized by Francesco Paoli and Tomasz Kowalski
University of Cagliari, Sardinia
Abstracts for this special session should be submitted by email
to paoli@unica.it by November 15 2009
