In this paper, I propose a populational schema of modeling that consists of: (a) a linear AFSV schema (with four basic stages of abstraction, formalization, simplification, and verification), and (b) a higher-level schema employing the genetic algorithm (with partially random procedures of mutation, crossover, and selection). The basic ideas of the proposed solution are as follows: (1) whole populations of models are considered at subsequent stages of the modeling process, (2) successive populations are subjected to the activity of genetic operators and undergo selection procedures, (3) the basis for selection is the evaluation function of the genetic algorithm (this function corresponds to the model verification criterion and reflects the goal of the model). The schema can be applied to automate the modeling of the mind/brain by means of artificial neural networks: the structure of each network is modified by genetic operators, modified networks undergo a learning cycle, and successive populations of networks are verified during the selection procedure. The whole process can be automated only partially, because it is the researcher who defines the evaluation function of the genetic algorithm.
This article treats about modeling different phenomena by means of concepts and tools elaborated in the computer science framework, mainly in that of Artificial Intelligence (AI). After having presented the notion of formalized computer science model (CSMd), we described general interactive modeling procedure (which consists of four stages: abstraction, formalization, simplification and verification). Then we characterize this procedure in the context limited to computer science. While discussing different types of CSMd, we focus on the domain of AI, e.g. we distinguish between rule-based models (often implemented as expert systems), network-based models (often implemented as artificial neural networks) and evolutionary models (often based using genetic algorithms). But, most importantly, we believe that machine learning tools (as part of the AI domain) could and, as the matter of fact, should be used in order to automate each of the stages of the proposed interactive modeling procedure.
Two different types of analog computations are discussed in the paper: 1)analog-continuous computations (performed physically upon continuous signals),2) analog-analogical computations (performed naturally by means of socalled natural analogons of mathematical operations). They are analyzed withregard to such questions like: a) are continuous computations physically implementable?b) what is the actual computational power of different analogtechniques? c) can natural (empirical) computations be such reliable as digital?d) is it possible to develop universal analog computers (assuming that theyshould be functionally similar to universal Turing machine)? Presented analysesare rather methodological than formal.
Some new, philosophically inspired, methods of teaching mathematics are discussed in this paper. These methods are implemented and embedded in the virtual environment of learning and exploring mathematics, called officially Archipelago of Mathematics (available at www.archipelagmatematyki.pl). They seem to be effective due to different interconnections between mathematics and philosophy (both historical and contemporary).After describing methodological assumptions, goals, methods and the structure of Archipelago, I present two, designed by me, examples of its contents: (1) quasi-internet chat with the ghost of G.W. Leibniz (on metaphysics, philosophical aspects of calculus, and artificial intelligence); and (2) radio-style interview with a farmer on the mathematical theory of sets and infinity. Presented materials show such a relationships between mathematics and philosophy like: philosophical origin of some mathematical concepts, philosophical implications of some math. ideas and theorems, heuristic function of philosophical discussions in mathematics.
According to the methodology of cognitive science we consider a hypothesis (justified partially by cognitive applications of computer science), that the mind functions similarly to a computer. Philosophical consequences of this thesis are as follows: (1) there exists a mental code (similar to the code of computer program); (2) this code can be represented as one unique number; (3) this number can be computable or non-computable. If the number representing mental code is computable (by Turing machine), then it is theoretically possible to implement the mind (all cognitive processes) by means of digital techniques of data processing (because digital computers are equivalent in a theory to Turing machines). If the „mental number” belongs to a class of noncomputable numbers, however, it is highly possible that only other techniques (for example, analog or partially random ones) can guarantee an overall computer implementation of human cognition.
In this paper we show how formal computer science concepts-such as encoding, algorithm or computability-can be interpreted philosophically, including ontologically and epistemologically. Such interpretations lead to questions and problems, the working solutions of which constitute some form of pre-philosophical worldview. In this work we focus on questions inspired by the IT distinction between digitality and analogicity, which has its mathematical origin in the mathematical distinction between discreteness and continuity. These include the following questions: 1) Is the deep structure of physical reality digital or analog, 2) does the human mind resemble a more digital or analog computational system, 3) does the answer to the second question give us a cognitively fruitful insight into the cognitive limitations of the mind? As a particularly important basis for the above questions, we consider the fact that the computational power (i.e., the range of solvable problems) of some types of analog computations is greater than that of digital computations.
PL
W niniejszej pracy pokazujemy, w jaki sposób formalne pojęcia informatyczne – takie, jak kodowanie, algorytm czy obliczalność – mogą być interpretowane filozoficznie, w tym ontologicznie i epistemologicznie. Interpretacje takie prowadzą do pytań i problemów, których robocze rozwiązania składają się na jakąś formę prefilozoficznego światopoglądu. W pracy kładziemy nacisk na pytania inspirowane informatycznym rozróżnieniem cyfrowości i analogowości, które ma swój matematyczny pierwowzór w matematycznym rozróżnieniu dyskretności i ciągłości. Między innymi są to następujące pytania: 1) czy głęboka struktura fizykalnej rzeczywistości ma charakter cyfrowy, czy analogowy, 2) czy ludzki umysł przypomina bardziej informatyczny system cyfrowy czy analogowy, 3) czy odpowiedź na pytanie drugie daje nam owocny poznawczo wgląd w ograniczenia poznawcze umysłu? Za szczególnie istotną podstawę powyższych pytań uznajemy fakt, że moc obliczeniowa (tj. zakres rozwiązywalnych problemów) niektórych typów obliczeń analogowych jest większa od mocy obliczeń cyfrowych.
The subject of the paper is a contemporary interpretation of J.S. Mill’s elimination method using selected concepts of Zdzisław Pawlak’s decision logic. The aim of the interpretation is to reformulate the original rules (canons) of Mill’s induction so that they correspond more precisely to his concept of cause as a complex sufficient condition. In the first part of the paper, we turn to Mill’s writings and justify the thesis that in his understanding the cause is an aggregation of circumstances, and not a single circumstance; next, we point out that Mill’s original canons (for example the canon of agreement and the canon of difference) do not allow causes-aggregations to be singled out from empirical data. In the second part of this paper, we present such aspects of Z. Pawlak’s decision logic that serve as the basis for the formalisation of the method of eliminative induction. We describe exhaustively the schema of induction that involves a gradual - divided into three stages - simplification of a set of implications corresponding to the observed dependencies [system of potential causes, effect]. The simplification is deductive because it maintains consistency within the set of implications. We show that such schema is ideal for isolating complex causes (aggregations of circumstances), ultimately described using complex conditional formulas of decision logic.
The article deals with computer science models (CSMd), that is, formal constructions which are described theoretically in the language of computer science (the language of algorithms and data structures), and which can therefore, be implemented in the form of applications and activated on a computer. After distinguishing different kinds of CSMd (e.g. theoretical and real) and presenting some examples of CSMd (especially in the field of mental phenomena) we discuss in detail the modeling procedure. This procedure can be initiated by a metaphor (understood as an initial, informal image of a studied phenomenon), has a cyclical and open character, and – according to our methodological reconstruction – consists of four stages: abstraction, formalization, simplification and verification. We discuss these stages in the context of computer science, referring to four elements: the studied domain, a meta-theory (always formal), the constructed theory of the studied domain (formalized in the language of meta-theory), and the constructed model (always temporary). We present a simplified scheme of the whole procedure and identify three cycles of the modeling loop: small, proper and wide. Finally we claim that contemporary CSMd (especially computer science models of the mind) should be constructed using artificial intelligence tools, such as machine learning and data mining techniques.
The paper considers the problem of building trust in computational artefacts of the AGI (Artificial General Intelligence) type, which are defined from an ethical point of view as explicite moral agents. As a result of an analysis based on research of the literature and current trends in the development of AGI systems, several conditions have been presented for the construction of behavioural tests necessary to check the correctness of their functioning considered both from an ethical and social point of view. Conducting of such tests should simplify the market approval procedures of AGI systems at the level of manufacturers, the individual users and certification authorities.
PL
W artykule rozważany jest problem budowania zaufania do artefaktów obliczeniowych typu AGI (ang. Artificial General Intelligence), z etycznego punktu widzenia określanych jako podmioty moralne explicite. W wyniku analizy opartej na badaniach literatury oraz przedstawieniu aktualnych trendów w rozwoju systemów AI wskazanych jest kilka warunków skonstruowania testów behawioralnych niezbędnych do sprawdzania poprawności ich działania z etycznego punktu widzenia. Przeprowadzenie takich testów powinno ułatwić procedury etycznej aprobaty systemów AGI zarówno na poziomie wytwórców, indywidualnego użytkownika, jak i jednostek certyfikujących.
The main aim of this paper is to justify the thesis that in molecular biology - in the scope of phenomena fundamental for the functioning of the cell - a significant role is played by analog (nondiscrete) information, which can be described in computational terms. It is a methodological thesis, indicating a certain direction of advancing new biological hypotheses. This aim is realized in two stages. In sections 1 and 2 we discuss the computer-science concept of analogicity, generally describing different concepts of analog-continuous and analog-empirical computations, as well as discussing the relationship between analogicity and digitality. In sections 3 and 4 we analyze some components of the process of protein formation, emphasizing that an adequate description of this process requires taking into account information of an analog nature, which, with a certain research attitude, can be described, but also used, computationally.