This paper is devoted to actin filament networks as a computation medium. The point is that actin filaments are sensitive to outer cellular stimuli (attractants as well as repellents) and they appear and disappear at different places of the cell to change the cell structure, e.g. its shape. Due to a
Classical mechanics implicitly use Archimedes' axiom, according to that everything may be measured by a rigid scale. Uncertainty in quantum mechanics shows the limits of applying Archimedes' axiom. The negation of Archimedes' axiom is derivative from the negation of the set‐theoretic axiom of foundation. The latter postulates that the set‐membership relation is well‐founded: for every set there exists no infinitely descending chain. Denying the foundation axiom in number systems implies setting a non‐Archimedean ordering structure. The main claim of our paper is that physical reality may be regarded as non‐well‐founded in the framework of probabilities distributed on non‐Archimedean ordering structures, in particular, distributed on p‐adic numbers.
In the paper, we show that timed transition system models can be used as a high-level model of behavior of Physarum machines. A Physarum machine is a programmable amorphous biological computer experimentally implemented in the vegetative state of Physarum polycephalum. Timed transition system models have been used in our new object-oriented programming language for Physarum polycephalum computing.
Abstract In this paper, I show that we can find some foundations of logic and legal argumentation in the tablets of Mesopotamia at least since the dynasty of Ur III. In these texts, we see the oldest correct application of logical inference rules (e.g. modus ponens ). As concerns the legal argumentation established in Mesopotamia, we can reconstruct on the basis of the tablets the following rules of dispute resolutions during trials: (1) There are two parties of disputants: (i) a protagonist who formulates a standpoint and (ii) an antagonist who disagrees with the protagonist’s standpoint and formulates an alternative statement. (2) There is a rational judge represented by high-ranking citizens who should follow only logical conclusions from facts and law articles as premises.
In the article, we aim to understand the responses of living organisms, exemplified by mycelium, to external stimuli through the lens of a Turing machine with an oracle (oTM). To facilitate our exploration, we show that a variant of an oTM is a cellular automaton with an oracle, which aptly captures the intricate behaviours observed in organisms such as fungi, shedding light on their dynamic interactions with their environment. This interaction reveals forms of reflection that can be interpreted as a minimum volume of consciousness. Thus, in our study, we interpret consciousness as a mathematical phenomenon when an arithmetic function is arbitrarily modified. We call these modifications the hybridization of behaviour. oTMs are the mathematical language of this hybridization.
The question arises whether logic was given to us by God or whether it is the result of human evolution. I believe that at least the modus ponens rule ( A and if A then B implies B) is inherent in humans, but probably many other modern systems (e.g., resource logic, non - monotonic logic etc.) are the result of humans adapating to the environment. It is therefore of interest to study and compare the way logic is used in ancient cultures as well as the way logic is going to be used in our 21st century. This welcome book studies and compares the way formation of logic in three cultures: Ancient Greek (4th century B.C.), Judaic (1st century B.C. – 1st century A.D.) and Indo-Buddhist (2nd century A.D.) The book notes that logic became especially popular during the period of late antiquity in countries covered by the international trade of the Silk Road. This study makes a valuable contribution to the history of logic and to the very understanding of the origions and nature of logical thinking. -Prof. Dov Gabbay, King's College London, UK Andrew Schumann in his book demonsrates that logic step-by-step arose in different places and cultural circles. He argues that if we apply a structural-genealogical method, as well as turn to various sources, particularly, religious, philosophical, linguistic, etc., then we can obtain a more general and more adequate picture of emengence and development of logic. This book is a new and very valuable contribution to the history of logic as a manifestation of the human mind. - Prof. Jan Wolenski, Jagiellonian University, Poland The author of the Archaeology of Logic defends the claim, calling it "logic is aftter all", which sees logical competence as a practical skill that people began to learn in antiquity, as soom as they realized that avoiding cognitive biases in their reasoning would make their daily activities more successful. The in-depth reading of the book with its diving into the comparative quotations in the long dead or hardly known to most of us languages like Sumerian-Akkadian, Aramatic, Hebrew and etc, will be rewarded by the response that the logical competence is diverse and it can be trained, despite the inevitabilitiy of the reasoning fallacies; and that critical discussions and agaonal character of the social lide are the necessary tools for that. - Prof. Elena Lisanyuk
In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert's style, sequent, and hypersequent. We present a general way that allows to construct systematically analytic calculi for a large family of non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and p-adic valued logics characterized by a special format of semantics with an appropriate rejection of Archimedes' axiom. These logics are built as different extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's, Product, and Post's logics). The informal sense of Archimedes' axiom is that anything can be measured by a ruler. Also logical multiple-validity without Archimedes' axiom consists in that the set of truth values is infinite and it is not well-founded and well-ordered. On the base of non-Archimedean valued logics, we construct non-Archimedean valued interval neutrosophic logic INL by which we can describe neutrality phenomena.
Research in unconventional, or nature-inspired, computing aims to uncover novel principles of efficient information processing and computation in physical, chemical and biological systems, to develop novel non-standard algorithms and computing architectures, and also to implement conventional algorithms in non-silicon, or wet, substrates. This emerging field of science and engineering is predominantly occupied by theoretical research, e.g. quantum computation, membrane computing and dynamical systems computing. Despite the profound potential offered by unconventional computing, only a handful of experimental prototypes are reported so far, for example gasdischarge analog path finders; maze-solving micro-fluidic circuits; geometrically constrained universal chemical computers; specialized and universal chemical reaction--diffusion processors; universal extended analog computers; maze-solving chemo-tactic droplets; enzyme-based logical circuits; spatially extended crystallization computers for optimization and computational geometry; molecular logical gates and circuits.
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