A Hierarchy of Composition Procedures for Logic-Based Workflow Patterns

Logic-based workflow patterns capture recurring behavioural structures together with reusable temporal specifications. Their composition raises distinct problems as workflow structures become richer, including instantiation, nesting, conditional execution, repeated occurrences, and traceability of generated formulae. This paper proposes a hierarchy of Pattern Composition ($ΠC$) procedures, from $ΠC_0$ to $ΠC_4$, that organizes these requirements as progressively richer compositional capabilities. The hierarchy separates compositional complexity from the expressive power of the temporal-logic fragment, represented by $TL_j$, yielding a framework $ΠC_i[TL_j]$ for developing logical workflow specifications. We develop activation-aware Pattern Composition ($ΠC_2$), which distinguishes the structural presence of a nested pattern from its execution in a particular workflow context. We formalise its recursive procedure, analyse its properties, and define an evaluation protocol for conditional activation, conservativity under mandatory composition, and specification growth. The hierarchy also characterizes selective occurrence qualification for iterative patterns ($ΠC_3$) and provenance for tracing generated formulae to their sources ($ΠC_4$). Finally, we outline $ΠC_{\mathrm{Assist}}$, an orthogonal mode in which AI proposes and refines pattern expressions subject to the hierarchy's compositional checks.