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Minimal and complete axiomatization of closed quasi-stratified acyclic structures

Determine a minimal and complete axiomatization, without redundancy, for the class of closed quasi-stratified acyclic structures (denoted QSAS^closed and equivalently characterized as QSCS) introduced in the paper.

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Background

In Section 6 the authors introduce quasi-stratified closed structures (QSCS) and prove that these coincide with the closure QSASclosed of quasi-stratified acyclic structures, providing an algebraic characterization via axioms.

They note that the presented axiomatization contains redundant axioms and explicitly state that identifying a minimal and complete axiomatization remains unresolved. This motivates further work to refine the axiom system for QSASclosed.

References

Although it is an open problem what might constitute a minimal and complete axiomatisation, the next result can be seen as a precursor for the development of a minimal complete axiomatisation of closed qsa-structures.

— Quasi-stratified Order Semantics of Concurrency (2407.13406 - Koutny et al., 18 Jul 2024) in Section 6 (Closed QS-structures), paragraph preceding Proposition \ref{prop-nevnr}