2015/09/26 by Nick Bezhanishvili, Bezhanishvili, Nick, Galatos, Nick +2
Computer Science · #03B20 #03B47 #03C05 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1509.07980
openalex publication_date 2015/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Canonical formulas are a powerful tool for studying intuitionistic and modal\nlogics. Actually, they provide a uniform and semantic way to axiomatise all\nextensions of intuitionistic logic and all modal logics above K4. Although the\nmethod originally hinged on the relational semantics of those logics, recently\nit has been completely recast in algebraic terms. In this new perspective\ncanonical formulas are built from a finite subdirectly irreducible algebra by\ndescribing completely the behaviour of some operations and only partially the\nbehaviour of some others. In this paper we export the machinery of canonical\nformulas to substructural logics by introducing canonical formulas for\nk-potent, commutative, integral, residuated lattices (k-\CIRL).\nWe show that any subvariety of k-\CIRL is axiomatised by canonical\nformulas. The paper ends with some applications and examples.\n