Simulation of certain oscillatory biological processes (original) (raw)

The Logic of Dynamical Systems is Relevant - Mind

Mind, 2025

Lots of things are usefully modelled in science as dynamical systems: growing populations, flocking birds, engineering apparatus, cognitive agents, distant galaxies, Turing machines, neural networks. We argue that relevant logic is ideal for reasoning about dynamical systems, including interactions with the system through perturbations. Thus, dynamical systems provide a new applied interpretation of the abstract Routley-Meyer semantics for relevant logic: the worlds in the model are the states of the system, while the (in)famous ternary relation is a combination of perturbation and evolution in the system. Conversely, the logic of the relevant conditional provides sound and complete laws of dynamical systems.

Towards universality of growth grammars: Models of Bell, Pag�s, and Takenaka revisited

Annals of Forest Science, 2000

Growth grammars" are extended parametric Lindenmayer systems, enriched by some novel features (expand operator, global sensitivity, interpretive rules, arithmetical-structural operators). They can serve as a formal basis for describing functionalstructural plant models from the literature. This is demonstrated on three well-known models having in common that they were originally developed without using any formal grammars: an early, but quite general structural plant simulator by Bell, a root model by Pagès and Kervella, and an above-ground tree model (involving competition for light) by Takenaka. The study considers the special extensions of L-systems necessary to rebuild some characteristic features of each of these models. The obtained degree of universality and the current limitations of the growth-grammar approach with respect to functional-structural tree models are discussed.

Emergence: logical, functional and dynamical

Synthese, 2012

Philosophical accounts of emergence have been explicated in terms of logical relationships between statements (derivation) or static properties (function and realization). Jaegwon Kim is a modern proponent. A property is emergent if it is not explainable by (or reducible to) the properties of lower level components. This approach, I will argue, is unable to make sense of the kinds of emergence that are widespread in scientific explanations of complex systems. The standard philosophical notion of emergence posits the wrong dichotomies, confuses compositional physicalism with explanatory physicalism, and is unable to represent the type of dynamic processes (self-organizing feedback) that both generate emergent properties and express downward causation. Keywords Emergence • Downward causation • Reduction • Self-organization • Chaos • Feedback 1 A better translation is "the whole is over and above its parts, and not just the sum of them all."

How quantales emerge by introducing induction within the operational approach

1998

Abstract. We formally introduce and study a notion of'soft induction'on entities with an operationally motivated logico-algebraic description, and in particular the derived notions of'induced state transition'and'induced property transition'. We study the meaningful collections of these soft inductions which all have a quantale structure due to the introduction of temporal composition and arbitrary choice on the level of these state transitions and the corresponding property transitions.

THE DYNAMICAL BASIS OF EMERGENCE IN NATURAL HIERARCHIES

Since the origins of the notion of emergence in attempts to recover the content of vitalistic anti-reductionism without its questionable metaphysics, emergence has been treated in terms of logical properties. This approach was doomed to failure, because logical properties are either sui generis or they are constructions from other logical properties. If the former, they do not explain on their own and are inevitably somewhat arbitrary (the problem with the related concept of supervenience, Collier, 1988a), but if the latter, reducibility is assured because logical constructs are reducible, by definition, to their logical components. A satisfactory account of emergence must recognise that it is a dynamical, not a logical property of property of natural systems, and that its basis is dynamical rather than logical composition. introduced the concept of cohesion as the closure of the causal relations among the dynamical parts of a dynamical particular that determine its resistance to external and internal fluctuations that might disrupt its integrity.

Modeling of Phenomena and Dynamic Logic of Phenomena

2011

Modeling a complex phenomenon such as the mind presents tremendous computational complexity challenges. Modeling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, a problem or some theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models.

Observational structures and their logic

Theoretical Computer Science, 1992

A powerful paradigm is presented for defining semantics of data types which can assign sensible semantics also to data representing processes. Processes are abstractly viewed as elements of observable sort in an algebraic structure, independently of the language used for their description. In order to define process semantics depending on the observations we introduce observational structures, essentially first-order structures where we specify how processes are observed. Processes are observationally related by means of experiments considered similar depending on a similarity law and relations over processes are propagated to relations over elements of non-observable sort by a propagation law. Thus an observational equivalence is defined, as union of all observational relations, which can be seen as a very abstract generalization of bisimulation equivalences introduced by David Park. Though being general and abstract our construction allows to extend and improve interesting classical results. For example it is shown that for finitely observable structures the observational equivalence is obtainable as a limit of a denumerable chain of iterations; our conditions, which apply to algebraic structures in general, when instantiated in the case of labelled transition systems, are more liberal than the finitely branching condition. More importantly, we show how to associate with an observational structure various modal observational logics, related to sets of experiment schemas, that we call pattern sets. The main result of the paper proves that for any family of pattern sets representing the simulation law the corresponding modal observational logic is a Hennessy-Milner logic: two observable objects are observationally equivalent if and only if they satisfy the same set of modal observational formulas. Indeed observational logics generalize to first-order structures various modal logics for labelled transition systems. Applications *Work partially funded by COMPASS-Esprit Basic Research Group No. 3264 and by CNR-PF Sistemi Informatici e Calcolo Parallelo. **David Park, the inventor of bisimulation semantics, was to the first author not just the pioneer who friendly introduced him to semantics long time ago at the University of Warwick, but especially a scientist, whose research interests were rooted in classical European culture and in a genuine concern for social life.

Morphologic for knowledge dynamics: revision, fusion, abduction

HAL (Le Centre pour la Communication Scientifique Directe), 2018

Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the typical results that can be obtained.