Unary-Determined Distributive ℓ-Magmas and Bunched Implication Algebras
Published research
Research Summary
A distributive lattice-ordered magma combines a distributive lattice with a multiplication that preserves joins in each argument. In the unary-determined case, multiplication can be expressed through two join-preserving unary operations:
x · y = (p(x) ∧ y) ∨ (x ∧ q(y)).
We identify conditions on these operations that make multiplication associative, commutative, idempotent, or unital. The results give structural descriptions of algebraic models of bunched implication logic and support more efficient construction of finite models.
Publication Details
- N. Alpay, P. Jipsen, and M. Sugimoto. Varieties of unary-determined distributive ℓ-magmas and bunched implication algebras. Logical Methods in Computer Science 20 (2024), no. 1, article 12.