Multi-Domain Propagation Algebra (MDPA)

The Multi-Domain Propagation Algebra (MDPA 2.0) is a relational, multi-sorted algebra for modeling propagation, reachability, and influence flow across typed domains. Unlike classical Kleene algebra, MDPA 2.0 does not assume a general star operation. Instead, it introduces a globally coupled propagation operator TTT and a closure T∗T^{\ast}T∗ defined as the least fixed point of a monotone functional over a product of hom-sets. This construction provides a mathematically rigorous foundation for heterogeneous reachability, using tools from lattice theory, domain theory, and Rel-enriched category theory. MDPA 2.0 supports both theoretical analysis (fixed-point semantics, categorical structure) and efficient computation in the finite case via a typed Boolean block–Warshall algorithm. This version (v2.0) is the first fully formal specification of the MDPA framework.