Начиная с начала 2000 года осуществляется внедрение GHIS в здравоохранении, в рамках принятого проекта о реформирование информ Mathematical Problems of Computer Science 50, 35--51, 2018. Constructing Adequate Mental Models Edward M. Pogossian Institute for Informatics and Automation Problems of NAS RA e-mail:epogossi@aua.am Abstract Mental systems represent realities, have varying effectiveness with respect to our goals and are processed to support utilization and gain benefits from utilities. Classifiers induced by mental systems are effective with respect to the goals insofar as regularly provide utilities and enhance effectiveness of modeling of those utilities constructively and adequately. In the paper we discuss ontological, constructive and systemic models of mental systems, mentals, comparable by expressiveness with algorithms and natural languages, provide arguments of their adequacy for explaining, understanding and human-computer interactions as well as convince to follow the ideas of inventors of algorithms in adequate modeling of mental behavior. To consist functional and connectivity mental models and recalling that artificial neuron nets are systems of classifiers, we provide evidence that mentals can be reduced to systems of classifiers as well. Keywords: Mental models, Regularization, Adequate, Constructive, Explaining, Human-computer interactions, Neuron nets. 1. Introduction 1.1.1. We, humans, are somewhat able to represent the causers of imprints in us and the imprints themselves by classifiers of those imprints. And since imprints can follow only certain doings of their causers (either external, internal, or both), the classifiers represent the causers representing, in fact, the doings of the causers. 1.1.2.We process classifiers to preserve or provide our utilities. We enhance effectiveness of that process, particularly, enhancing the quality of classifiers as well as uniting the efforts of members of communities for the utilities by communicatives (cms) of the classifiers, i.e., by IDs of classifiers or classified samples , as, for example, we communicate now by IDs, English words, in this paper. 1.1.3. Classifying the causers of imprints and imprints themselves as realities and their totality as our universe we assume that effectiveness of preservation of our identity is to the extent to which we, particularly, adequately represent the universe by constructive classifiers and effectively process them. In other words, as comprehensively and adequately classifiers cover the diversity of realities as powerful we become. 35 Constructing Adequate Mental Models 36 For example, each of us enhances his effectiveness in the universe growing up his language skills. Then, communities, say speaking English with more than 300 thousand of highly constructive classifiers, are incomparably powerful than tribes with languages in a few thousand words representing mainly not constructive classifiers. And whether the first assertion of the Bible “...It was the Word in the Beginning and the Word is the God” doesn’t remind that the classifiers and their cms in languages, i.e., the words, either acquired from genomes or from communities are one of fundamentals of our power… 1.2.1.In the diversity of classifiers we identify ourselves as originated and formed by communities, then as a type of cellular realities, cellulars, which, in turn, identify as an intersection of a type of not entropic, negentropic, realities [6], negs, with a type of durables, refers, i.e., realities able to preserve the identity of caused in them imprints. Consequently, humans and representations of humans, say by their doings, are, at least, dependent while mainly predetermined by fundamentals of communities, cellulars and negs. 1.2.2.Particularly, mental doings of humans are essentially predetermined by genomes and cultures of their communities implying communality of members of communities not only in innate means of representing realities by sensors and classifiers, in types of processing of those representations for variety of utilities including enhancement of effectiveness of themselves but also, in general, in commonality of particular lines of reasoning, counting, expressing them in languages, etc. That is why the novelty of mental doings of humans, usually, is in enlightening lines of cause effect reasoning between already known communal utilities and representations of realities. And only occasionally that novelty is in discovering of new utilities or case effect reasoning why those novelties become so sound in communities up to becoming granted by Nobel Prizes. 1.2.3. Thus, reflecting the above assumptions to this research we classify it as an attempt to enlighten then generalize already known and successfully applied expertise of mental modeling by the founders of algorithms, namely, the expertise of transition from classifiers of computability to their models, algorithms. And, apparently, in that modeling we cannot but have to heavily relay on the fundamentals of communities, cellulars and negs stated, particularly, by the following assumptions. 1.3.1.1. Ad1. Durables are realities that in contrast with others ,temporals, have somewhat, kernel of durables (Kd), that can be properly identified in the time. . Ad2. Refers are durables with kernels including the imprints of their causers. Ad3. Refers able to identify classes of imprints are classifying refers. 1.3.1.2. An1. All negs are classifying refers and do in the universe to preserve certain roots which include regular energy supply for their doings and an ability to stay classifying refers.. An2.The existence of natural negentropics different from cellulars, remains open yet while some types of artificial ones humans can already construct. An3.While existence of types of durables seems tractable the origin of negs and cellulars (even though as unicells) remains a mystery yet. 1.3.2. Ac1. Cellulars do to reproduce themselves, do to benefit from utilities, i.e., realities favorable for the roots, to avoid their damagers, to utilize realities uncertain yet with respect to (wrt) the roots as well as to challenge already gained utilities and, possibly, roots themselves. Ac2.Cellulars represent realities via doings of those realities. Ac3. The vast majority of doings of cellulars are predetermined by genomes and cultures of their communities. E. Pogossian 37 Ac4. Cellulars gain effective doings, at least, by a chance search in the space of diversely replicated doings of their cells, and, possibly, by regular cognition of regularities of the universe. Ac5. Cellulars have sensors, or classifiers outputting identified imprints for certain inputs. Ac6. Mental doings of cellulars are doings over imprints of certain realities, i.e., mental doers (mdoers) and systems of mdoers (mss), aimed to support doings of cellulars by their mss representing and processing. Ac7. Mss m of members x of communities C of cellulars have IDs (mID) and comprise certain nets xN. Mss m corresponding to mIDs, or the meanings of mIDsof x, are connectivity subnets of the nets xN rooted in those mIDs, and can be activated internally or externally by their mIDs or by samples r of already classified by m realities. Subsets of those mIDs and realities r communalized in C comprise communicatives (cms) of C. 1.3.3. Commenting on the assumptions and, first of all, the negentropicity of humans let’s recall that entropics, following Schrödinger [6], comprise the vast majority of realities. They inevitably lose their energy, and therefore, any sign of durability. In opposite to entropics, negentropics, negs, comprise only a small island of realities and are able to preserve certain durables, root realities, or roots in space and time, and the premise necessary to preserve the roots is their ability in regular gaining energy from others. Roots for realities r, we assume, are any given, usually not explained yet realities, possibly constituents or doings of r, that are preserved for r regularly and with first priority wrt others. Apparently, roots of negs necessarily include doings for gaining energy and ones to preserve that ability. 1.3.4. Roots of cellulars include, at least, their genomes, doings for periodic diversified reproduction of genomes and doings for preserving realities induced as auxiliary to the roots. 1.3.4.1. Mental doings are baking other doings including themselves, are either genomic or gained in the lifetime while gained mainly by acquisition from the cultures of communities. 1.3.4.2. Mdoers do over outputs of sensors and mdoers to elaborate instructions for the effectors. While they can be represented as classifiers, particularly, relationships, rules, regularities or their compositions, algorithms, we argue that they are reducible to classifiers of n-tuples of identified, nominated realities. 1.3.4.3. Mss compose mdoers to represent, particularly, systemic classifiers, say Factories, Computers, Chess Positions. 1.3.5.1. Classifiers of roots and utilities are identified as root and induced goals why cellulars can be classified as goal oriented realities. Attributes, we assume, include classifiers of constituents of compound utilities and realities with uncertain yet utilities. Apparently, realities can be partially ordered by degrees of their utilities wrt the roots, thus, to induce corresponding ordering for the goals and attributes. 1.3.5.2. Mss as well as their constituent mdoers can be processed for a variety of goals, particularly, to learn new utilities and to enhance effectiveness of mss. 1.4.1.While the fundamentals of mss and their processing can be found for all cellulars the highest of them are unique only for humans that can be stated, particularly, by the following assumptions. Ah1. Doings of members of human communities are mainly equal implied by equality of 99% of genomes of all humans and commonality of cultures of communities of their being. Ah2. Humans adapt to the universe mainly by cognition and development of mental doings. Ah3. Humans accumulate, reproduce effective doings then transfer them in space and time not only by genomes but also by the records of the patters of those doings that are essentially depersonalized and estranged from particular members of their communities. Constructing Adequate Mental Models 38 Ah4. Meanings m of mIDs of x@C are connectivity subnets of nets xN rooted in mIDs can be scaled by their effectiveness wrt utilities of x, say constructiveness of adequate modeling of m, and wrt explanations of m in C, say completeness of m wrt intensions of x and expectations in C. Ah5.Mental doings classified by psychologists and psychiatrists including classifying, learning, prognosticating, communicating can be equally represented by adequate constructive models of mss and their nets. 1.4.2. Cognizers are, we assume, a type of mss while cognition includes doings in acquisition, accumulation as well as revelation, discovery of mss, particularly, by learning of new utilities or enhancement of effectiveness of the existing ones. 1.4.3. All over governing of mss including their cognition, activation and processing is realized, we assume, by controllers that, it is not excluded, can be the causers of our awareness or consciousness and be mss as well. Particularly, controllers govern communication between the members of communities in explaining and understanding mss of each other. 1.4.4. Being realties we can classify and explain ourselves as well. For example, controllers explain mss “Humans” of the author by resolving it into this, ongoing text, namely, corresponding English words to IDs of constituents of the mss. In general, that resolution can start from any constituents of the target mss while their IDs can be chained causally, logically or in a variety of other modes and be detailed depending, particularly, onthe goals of the author. 1.4.5.Mainly equal doings of members of communities C mean, particularly, that - the same any what cause equal imprints for any x,y @C , thus, x realities are equal to y realities what implies the universe UC equal for all members of C, - mental doings including classifying, learning, teaching, inference, prognostication are equal in C what let members of C to communicate doings of each other for effective collaborations. 1.5.1. A mighty way of enhancement of effectiveness of mss, and thus, cognizers, is the regularization of classifiers induced by mdoers and mss [47]. Namely, classifiers Cl of members x of communities C are regularized in C if accompanied by ontological in C methods, instructions allowing x regularly provide positive samples of inputs of Cl as well as let the members of C to do the same by communicating with x. In constructive regularization those samples can be provided deterministically and without any involvement of cellulars while, otherwise, can be grown up from a priory given prototypes like cells or crystals, be the products of services to humans or machines. 1.5.2. Regularly provided positives r of classifiers Cl and Cl themselves are interpreted as models of classifiers Cl’ if r are classified as positives of Cl` andCl are interpreted as adequate models of Cl’ if positives r meet certain additional requirements focused for positives of Cl. For example, algorithms are adequate models of deterministic methods if, following Church, to any method by certain instructions equal algorithms can be corresponded [30 ]. 1.5.3. Interpreting the aims of algorithms to enhance the effectiveness of classifiers of deterministic methods we expand them to other classifiers focusing the mental ones and state the following: S1. Algorithms are modeling and constructively regularize deterministic methods. S2. OO Languages are constructively regularized and strongly expand algorithms. S3. Mentals are constructively regularized and strongly expand OOL. S.4.For languages L of communities C allowing the members x of C to communicate, i.e., to explain and understand mss of each other expressed in L, communication algorithms LC can be E. Pogossian 39 constructed letting computers communicate mental models Mns of mssMs of C equally wrt the members of C if Mns and Ms are equal to each other. 1.6. At present adequacy of mss is questioned functionally and connectively. Functional questioning examines the equality of performances of mss and models of mss of any origin. In contrast, in connectivity modeling it is required that the units of the models mss have to be adequate models of the units of nerves systems, neurons, and, particularly, looking for adequacy of mss with artificial nets of neurons, ANN. Examining primarily functional adequacy of mentals and recalling ANN are systems of classifiers we provide an evidence that mentals can be reduced to systems of classifiers as well , thus, stating that S5. Mentlals can consist of functional and connectivity mental models. 1.7. In what follows, first, we continue to develop constructive models of mss, mentals introduced in [47], to argue later that they are modeling mss adequately. Then, refine systemic classifiers and constructive regularization of classifiers followed by overview of some ad hoc regularized classifiers. We question the ways of proving that mentals can be adequate constructive models of mss and suggest to examine equality of performances of particular mss with corresponded them mentals as well as question the consistency of performances of structural models of connectivity neuron nets, for example, artificial neuron nets, with purely functional models of mss, mentals. Ideally, equality of performances of mss and mentals have to be proven for all mss as well as Church thesis had to be examined for all deterministic methods. Realistically, we focus the proof of equality of performances of mentals and some inevitable in cognition mss, including communications, explaining, understanding [47], some types of learning , acquisition and search of mss [42, 43,50], . 1.7. Our models are based on and try to fuse findings of many outstanding researchers. We refer to some of their publications [1-35] to learn them in depth as well as refer to some works [36]-[42], which can add to understanding of our ideas and their approbations [43]-[50]. 2. Systemic vs. Do Classifiers 2.1. Doers, in general, are, we assume, realities having in- out- put parts and for available inrealities, i.e., for realities, and more, for somewhat, at the input parts, either elaborate certain output realities or stay passive. In- out- realities comprise their in- out- domains, or in- out-doms. Indomswrt outputs are split into classes of equality, thus, absence of outputs corresponds to the class (?) of uncertain inrealities. 2.2. Doers are do-classifiers Cl if indoms are split into two classes +Cl and ?Cl; otherwise they are corresponders, cors. Apparently, identifiers of do-classifiers Cl by themselves are sufficient to indicate their classes of equality, i.e., the positives +Cl, while classes of cors can be indicated by pairing those identifiers with the corresponding outputs. 2.3.Realities I{i} are identifiers, IDs, of realities R{r} and Z{z} wrt Z if - to any r,z the unique IDs i(r), i(z) correspond, - to any r,z certain classifiers are linked allowing by IDs i(r), i(z) to recall corresponding r, z, - any r can address to any z for recalling any r, z. Identified realities of given R, Z paired with their IDs are named nominals wrt Z. 2.4. Classifiers of n-tuples of nominals are n-place relationships shortly named rels for n=2. Rels (a,b) can be depended or not on the orders of their arguments. Constructing Adequate Mental Models 40 2.5.1. Systems H over nominals Nls containing rels Rls, i.e., Rls