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  1. A. H. Louie (2013). Explications of Functional Entailment in Relational Pathophysiology. Axiomathes 23 (1):81-107.
    I explicate how various relational interactions between (M,R)-systems may have realizations in pathophysiology, and how the possible reversals of the effects of these interactions then become therapeutic models. Functional entailment receives a rigorous category-theoretic treatment, and plays a crucial role in this continuing saga of relational biology.
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  2. A. H. Louie (2010). Relational Biology of Symbiosis. Axiomathes 20 (4):495-509.
    I formulate in relational terms the ubiquitous biological interaction of symbiosis. I explicate the topology of the different modes of relational interactions of (M, R)-networks, the entailment diagrams that model the host and the symbiont. These modes all have biological realizations as various categories of symbiotic relationships, ranging from mutualism to parasitism to infection.
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  3. A. H. Louie (2008). Functional Entailment and Immanent Causation in Relational Biology. Axiomathes 18 (3):289-302.
    I explicate the crucial role played by efficient cause in Robert Rosen’s characterization of life, by elaborating on the topic of Aristotelian causality, and exploring the many alternate descriptions of causal and inferential entailments. In particular, I discuss the concepts of functional entailment and immanent causation, and examine how they fit into Robert Rosen’s relational-biology universe of living, anticipatory, and complex systems.
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  4. A. H. Louie & Stephen W. Kercel (2007). Topology and Life Redux: Robert Rosen's Relational Diagrams of Living Systems. [REVIEW] Axiomathes 17 (2):109-136.
    Algebraic/topological descriptions of living processes are indispensable to the understanding of both biological and cognitive functions. This paper presents a fundamental algebraic description of living/cognitive processes and exposes its inherent ambiguity. Since ambiguity is forbidden to computation, no computational description can lend insight to inherently ambiguous processes. The impredicativity of these models is not a flaw, but is, rather, their strength. It enables us to reason with ambiguous mathematical representations of ambiguous natural processes. The noncomputability of these structures means computerized (...)
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  5. A. H. Louie (2006). (M,R)-Systems and Their Realizations. Axiomathes 16 (1-2):35-64.
    Robert Rosen’s (M,R)-systems are a class of relational models that define organisms. The realization of relational models plays a central role in his study of life, itself. Biology becomes identified with the class of material realizations of a certain kind of relational organization, exhibited in (M,R)-systems. In this paper I describe several realizations of (M,R)-systems, and in particular alternate realizations of the replication component.
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  6. A. H. Louie & I. W. Richardson (2006). A Phenomenological Calculus for Anisotropic Systems. Axiomathes 16 (1-2):215-243.
    The phenomenological calculus is a relational paradigm for complex systems, closely related in substance and spirit to Robert Rosen’s own approach. Its mathematical language is multilinear algebra. The epistemological exploration continues in this paper, with the expansion of the phenomenological calculus into the realm of anisotropy.
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