2025 year, volume 29, issue 1 (PDF)

A.V. Chechkin Mathematical Foundations of Theoretical Computer Science (Informatics). The Theory of Fuzzy Semantic Information About a Point. Semantics of Natural Language

Introduction. In cybernetics, they deal with information for managing a single object, that is, with information related to only one point, which, due to its uniqueness, does not require a unique semantic pointer. Cybernetics serves automatic control systems. Computer science(Informatics) uses information about fundamentally different points, which requires fundamentally different, autonomous, unique semantic pointers for these points. In humans, cybernetics is responsible for the unconditioned reflexes of the first signaling system, for the subconscious regulation of human life support biomechanisms. Computer science in humans is responsible for conscious cognitive behavior of humans, for conditioned (acquired) reflexes associated primarily with natural language, with learning and with the second human signaling system (with language), [1-2]. Computer science deals with intelligent systems that use information about various points. The concept of “clear semantic information about a point” was introduced and studied in [3-4]. This concept is based on the theory of filters and ultrafilters by A. Cartan and only within the framework of the theory of classical distinct sets. Whereas the concept of “fuzzy semantic information about a point” requires special formalization, which will be discussed in this article. Сonclusion. Let’s draw general semantic conclusions. Let us clarify the concept of “natural language semantics”. In philosophy, in semiotics, within the framework of the concept of the “Frege triangle”, the semantics of a word (sign) is called content (signification, meaning) and is opposed to its denotation (the referent). In theoretical computer science, the semantics of information about a point is understood as the information about a point brought by this information. Let us single out two methodological principles for describing the semantics of dictionary words-concepts. The principle of non-uniqueness of descriptions (Semantics taken from different dictionaries) and the principle of additional descriptions (Semantics of additions from different dictionaries). The terms “stable phrase or stable word-concept” emphasize only their broad, universally recognized semantics. Note that humans have two sensory signaling systems in their central nervous system. The first system is when his sensory receptors perceive signals from natural objects or natural processes, and then subconscious reactive life–sustaining behavior occurs. The second system is when his sensory receptors perceive signals from artificial symbols, language symbols, and the semantics of these language symbols are perceived as a subconscious sensory image of a point in the primary signaling system, followed by cognitive purposeful human behavior that requires the use of a variety of information and knowledge about different points (objects and processes). At the same time, the subconscious images of the first signaling system (primary sensorium) are the leading ones in the semantics of words and phrases of natural language, for which the generally recognized clear or fuzzy semantics of stable words-concepts and stable phrases of natural language is used, for example, a private relative to an expert group (explicit or imaginary). In both human signaling systems, specific neurons play a leading role - attractors (collectors) of information about only one point. For example, the so-called neurons of “My grandmother”, “My house”, etc. [1-2]. Note the important special role of the semantic pointer of a point or the unique proper name of a point (x0) in the cognitive properties of natural language. It is thanks to the dot pointer that the process of highlighting the holistic perception of an entity (some object or some process) takes place. The details are assembled into a single whole. This highlights the objective systemic structure of the natural world.

Keywords: almost complete predicting, predicting machine, prediction of superwords by a machine, criterion for predicting.

Koldoba E.V. Reconciliation of Wilson formulas and the equation of state for calculating the phase equilibrium of oil and gas

Iterative methods are used to compute phase equilibrium in multicomponent hydrocarbon solutions. Wilson’s formula is taken to calculate initial approximations, and the equation of state is taken to calculate chemical potentials or volatility. The paper proposes a method for adjusting Wilson’s formula to the equation of state used. It is shown that the consistent coeficients for heavy components are greater than for light ones. The approach allows one to construct a thermodynamically consistent system and eliminate some non-physical solutions and numerical instabilities.

Keywords: equations of state, Wilson’s formula, compution of phase equilibrium, multicomponent solutions, oil, numerical modeling.

Xinghao Niu Empirical study of manifold learning techniques on forecasting stock price trend

In this work, five popular manifold learning techniques, PCA, ISOMAP, Locally Linear Embedding, Laplacian Eigenmaps and t-SNE, are examined on improving prediction accuracy of stock price trend. Effect of examined manifold learning techniques on classification and clustering task is proved to be different. Examined techniques tend to often worsen performance in clustering task. In classification task, observed improvement by all methods is slight, usually less than 1 percent. And only Laplacian Eigenmaps can more often stably improve classification accuracy at all number of components while other methods can’t. Experiment results also suggest that there is no general effective technique for different stock price data set.

Keywords: dimension reduction, manifold learning, stock.

Galatenko A.V. Bounds on the number of proper families of k-valued functions

Proper families of functions are a convenient apparatus for memory-eficient specification of large parametric families of quasigroups and d-quasigroups. K.D. Tsaregorodtsev proved that there exists a natural one-to-one correspondence between proper families of functions and unique sink orientations of a Boolean cube. The cardinality of such orientations was estimated by J. Matousek. In our paper we extend Matousek’s lower bound to the case of \[k\]-valued logics for arbitrary \[k > 2\], present a number of corollaries and prove that properness is a rare property, namely, the fraction of proper families of the size n in the class of all families of n-ary functions \[(f_1,...,f_n)\] such that \[x_i\] is dummy for \[f_i(x_1,...,x_n)\] tends to \[0\] as \[n \rightarrow \infty \].

Keywords: proper families of functions, \[k\]-valued functions, hypergraph, matching.

Kapustin I.S. On algebraic system created from set algebra by adding the set power indicator

This paper concerns the properties of the functional system \[C_n\]. This system has the domain \[2^{\mathbb{Z}}\], and is generated by functions \[2^{\mathbb{Z}} \setminus x \], \[x \cup y\], \[x \cap x\] and power indicators \[card_0(x)...card_n(x)\].

Keywords: functional system, precomplete class, set algebra, completion criteria.

Nosov M.V. Implementation of algorithms by schemes of functional elements

In this paper, a scheme of functional elements for a Turing machine is constructed while maintaining the polynomial condition, if the machine possessed such a property.

Keywords: Turing machine, a scheme of functional elements.