Logics for algorithmic chemistries
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Logics for algorithmic chemistries Ceth Lightfield1 Accepted: 31 October 2020 © Springer Nature B.V. 2020
Abstract Algorithmic chemistries are often based on a fixed formalism which limits the fragment of chemistry expressible in the domain of the models. This results in limited applicability of the models in contemporary mathematical chemistry and is due to the poor fit between the logic used for model construction and the system being modeled. In this paper, I propose a system-oriented methodology which selects a formalism through a mapping of chemical transformation rules to proof-theoretic structural rules. Using a formal specification framework from the field of artificial chemistry, expressive adequacy is ensured by the choice of logic being based on the system properties to be modeled. To illustrate the methodology, a case study is provided that shows how the proposed approach selects linear logic for modeling resource sensitivity and the proof-theoretic interpretation facilitates translation to a programming language. Since the method results in a plurality of models, I conclude with a discussion on how the proposal contributes to multi-model paradigms in computational pharmacology. Keywords Artificial chemistry · Biochemical modeling · Computational pharmacology · Lambda calculus · Linear logic Building models for constructive dynamical systems requires nonclassical formalisms since such systems cannot be analyzed using classical modeling techniques (Harmer et al. 2010). For complex systems, modeling through explicit enumeration of the governing equations is impractical and is an area where research on rule-based modeling frameworks is making progress (Chylek et al. 2015). An early example is Walter Fontana’s (1991a, b) algorithmic chemistry (AlChemy) models in which 𝜆-expressions are used to represent molecules and chemical transformations are represented as functionally analogous to 𝜆-application. However, the complex dynamics of systems under investigation by practicing chemists exceeds the expressibility of 𝜆-calculus and thus limited the adoption of the framework in practice (Fontana and Buss 1996, 66). Since this early work, research has primarily proceeded by incrementally amending the modeling formalism to increase its expressive limits. Some frameworks, for instance, “Chemlambda” (Buliga and Kauffman 2014), are still based on 𝜆-calculus, while Fontana * Ceth Lightfield [email protected] 1
California, USA
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transitioned to the construction of Kappa models which employ 𝜅-calculus (Boutillier et al. 2018). A significant challenge introduced by this fragmentation is that it inhibits progress for modeling cases in which a change in formalism results in incompatible models. Thus, rather than amending the formalism to increase its expressive limits, I advocate for a methodological shift in which the choice of an expressively adequate formalism is guided by the nature of the modeling target. In this paper I present a system-oriented approach to formalism
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