Compositionality and Emergence in Holonic Neuro-Symbolic Multi-Agent Systems: A Learnable Variant of Kautz's Topology 2

Holonic multi-agent systems promise emergent collective behaviour through hierarchical composition, yet the formal conditions under which sub-holon intentions yield well-defined holon-level intentions remain under-specified. Building on Bratman's planning theory of intention and Koestler's holonic principle, this paper introduces Topology 2', a learnable variant of Kautz's Symbolic[Neuro] paradigm in which the symbolic-neural interface is itself an object of agent learning rather than a fixed coupling. The paper provides six theorems characterising: (i) the conditions under which sub-holon intentions mesh into a coherent holon-level intention; (ii) the persistence of intentions under hierarchical embedding; (iii) the irreducibility of certain emergent holonic properties to any individual sub-holon, instantiated as a topology jump in the Kautz hierarchy; (iv) the closure of Topology 6 under well-defined composition; (v) a bounded-reconsideration result over typed event spaces, with concentration bounds and a quantitative informed-blind separation linking the holon's event-filtering policy to Bratman's resource-bounded rationality; and (vi) an arbitrated composition result extending the formalism to sub-holons whose intentions do not fully mesh, mediated by a structural tribunal. Two auxiliary structural abstractions — sensors, formalising the perception layer that produces typed events, and tribunals, formalising intention arbitration — round out the model. The framework is instantiated in the MINERVA reference architecture, with preliminary feasibility evidence from a heterogeneous-holon deployment on consumer-grade hardware. Formal validation of the theorems is deferred to forthcoming work as supercomputing resources become available. The contribution bridges the planning theory of intention, holonic systems theory, and contemporary neuro-symbolic AI under a single compositional formalism. Keywords: holonic multi-agent systems; BDI agents; compositionality; emergence; neuro-symbolic AI; Kautz taxonomy; shared cooperative activity; Bratman; bounded rationality; topology jump Additional notes: Theoretical paper. Empirical validation deferred to companion work. Intellectual property of the formalism, theorems, and architectural contributions is retained by Alejandro Jaime as stated in the paper.