  Convolution is a ubiquitous operation in mathematics and computing. The
Kripke semantics for substructural and interval logics motivates its study for
quantale-valued functions relative to ternary relations. The resulting notion
of relational convolution leads to generalised binary and unary modal operators
for qualitative and quantitative models, and to more conventional variants,
when ternary relations arise from identities over partial semigroups.
Convolution-based semantics for fragments of categorial, linear and incidence
(segment or interval) logics are provided as qualitative applications.
Quantitative examples include algebras of durations and mean values in the
duration calculus.
