One of the traditional ways mathematical ideas and even new areas of mathematics are created is from experiments. One of the best-known examples is that of the Fermat hypothesis, which was conjectured by Fermat in his attempts to find integer solutions for the famous Fermat equation. This hypothesis led to the creation of a whole field of knowledge, but it was proved only after several hundred years. This book, based on the author's lectures, presents several new directions of mathematical research. (...) All of these directions are based on numerical experiments conducted by the author, which led to new hypotheses that currently remain open, i.e., are neither proved nor disproved. The hypotheses range from geometry and topology (statistics of plane curves and smooth functions) to combinatorics (combinatorial complexity and random permutations) to algebra and number theory (continuous fractions and Galois groups). For each subject, the author describes the problem and presents numerical results that led him to a particular conjecture. In the majority of cases there is an indication of how the readers can approach the formulated conjectures (at least by conducting more numerical experiments). Written in Arnold's unique style, the book is intended for a wide range of mathematicians, from high school students interested in exploring unusual areas of mathematics on their own, to college and graduate students, to researchers interested in gaining a new, somewhat nontraditional perspective on doing mathematics. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. Titles in this series are co-published with the Mathematical Sciences Research Institute (MSRI). (shrink)

Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The (...) tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area. (shrink)

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially in formal argumentation, (...) (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. (shrink)

We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first two authors in (...) a previous paper. (shrink)

Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computational model for argumentation and (ii) neural networks can be used (...) to combine argumentation, quantitative reasoning and statistical learning. At the same time, non-standard logic models of argumentation started to emerge. In this paper, we propose a connectionist cognitive model of argumentation that accounts for both standard and non-standard forms of argumentation. The model is shown to be an adequate framework for dealing with standard and non-standard argumentation, including joint-attacks, argument support, ordered attacks, disjunctive attacks, meta-level attacks, self-defeating attacks, argument accrual and uncertainty. We show that the neural cognitive approach offers an adequate way of modelling all of these different aspects of argumentation. We have applied the framework to the modelling of a public prosecution charging decision as part of a real legal decision making case study containing many of the above aspects of argumentation. The results show that the model can be a useful tool in the analysis of legal decision making, including the analysis of what-if questions and the analysis of alternative conclusions. The approach opens up two new perspectives in the short-term: the use of neural networks for computing prevailing arguments efficiently through the propagation in parallel of neuronal activations, and the use of the same networks to evolve the structure of the argumentation network through learning (e.g. to learn the strength of arguments from data). (shrink)

In this paper we explore a generalization of traditional abduction which can simultaneously perform two different tasks: given an unprovable sequent Γ ⊢ G, find a sentence H such that Γ, H ⊢ G is provable ; given a provable sequent Γ ⊢ G, find a sentence H such that Γ ⊢ H and the proof of Γ, H ⊢ G is simpler than the proof of Γ ⊢ G . We argue that the two tasks should not be distinguished, (...) and present a general procedure for finding suitable hypotheses or lemmas. When the original sequent is provable, the abduced formula can be seen as a cut formula with respect to Gentzen's sequent calculus, so the abduction method is cut-based. Our method is based on the tableau-like system KE and we argue for its advantages over existing abduction methods based on traditional Smullyan-style Tableaux. (shrink)

This paper studies methodologically robust options for giving logical contents to nodes in abstract argumentation networks. It defines a variety of notions of attack in terms of the logical contents of the nodes in a network. General properties of logics are refined both in the object level and in the metalevel to suit the needs of the application. The network-based system improves upon some of the attempts in the literature to define attacks in terms of defeasible proofs, the so-called rule-based (...) systems. We also provide a number of examples and consider a rigorous case study, which indicate that our system does not suffer from anomalies. We define consequence relations based on a notion of defeat, consider rationality postulates, and prove that one such consequence relation is consistent. (shrink)

Abduction is or subsumes a process of inference. It entertains possible hypotheses and it chooses hypotheses for further scrutiny. There is a large literature on various aspects of non-symbolic, subconscious abduction. There is also a very active research community working on the symbolic (logical) characterisation of abduction, which typically treats it as a form of hypothetico-deductive reasoning. In this paper we start to bridge the gap between the symbolic and sub-symbolic approaches to abduction. We are interested in benefiting from developments (...) made by each community. In particular, we are interested in the ability of non-symbolic systems (neural networks) to learn from experience using efficient algorithms and to perform massively parallel computations of alternative abductive explanations. At the same time, we would like to benefit from the rigour and semantic clarity of symbolic logic. We present two approaches to dealing with abduction in neural networks. One of them uses Connectionist Modal Logic and a translation of Horn clauses into modal clauses to come up with a neural network ensemble that computes abductive explanations in a top-down fashion. The other combines neural-symbolic systems and abductive logic programming and proposes a neural architecture which performs a more systematic, bottom-up computation of alternative abductive explanations. Both approaches employ standard neural network architectures which are already known to be highly effective in practical learning applications. Differently from previous work in the area, our aim is to promote the integration of reasoning and learning in a way that the neural network provides the machinery for cognitive computation, inductive learning and hypothetical reasoning, while logic provides the rigour and explanation capability to the systems, facilitating the interaction with the outside world. Although it is left as future work to determine whether the structure of one of the proposed approaches is more amenable to learning than the other, we hope to have contributed to the development of the area by approaching it from the perspective of symbolic and sub-symbolic integration. (shrink)

Humans are often extraordinary at performing practical reasoning. There are cases where the human computer, slow as it is, is faster than any artificial intelligence system. Are we faster because of the way we perceive knowledge as opposed to the way we represent it? -/- The authors address this question by presenting neural network models that integrate the two most fundamental phenomena of cognition: our ability to learn from experience, and our ability to reason from what has been learned. This (...) book is the first to offer a self-contained presentation of neural network models for a number of computer science logics, including modal, temporal, and epistemic logics. By using a graphical presentation, it explains neural networks through a sound neural-symbolic integration methodology, and it focuses on the benefits of integrating effective robust learning with expressive reasoning capabilities. -/- The book will be invaluable reading for academic researchers, graduate students, and senior undergraduates in computer science, artificial intelligence, machine learning, cognitive science and engineering. It will also be of interest to computational logicians, and professional specialists on applications of cognitive, hybrid and artificial intelligence systems. (shrink)

This book explores why, regarding practical reasoning, humans are sometimes still faster than artificial intelligence systems. It is the first to offer a self-contained presentation of neural network models for many computer science logics.

The great leader Heydar Aliyev at both stages of his political leadership through his titanic activity proved that he is the patron of science and education in Azerbaijan. Independent Azerbaijan and its achievements in the field of science and education are the crowning achievement of the great leader. Heydar Aliyev, whose life and work are an example for history and for the people, always paid special attention to the development of science and education and took care of these areas as (...) a priority policy of the state. Although science and education are two independent fields of development, it is impossible to isolate one from the other, and from this point of view, the problems of science and education should be approached comprehensively - as both areas are part of the overall state policy and are of a strategic nature, their integration is inevitable. The national leader repeatedly emphasized that the future of each nation depends on the development of its science and education, and also considered the development of science and education one of the important conditions for the development of an independent state. Against the background of the integration of independent Azerbaijan into the world community, the need to integrate Azerbaijani science and education into world science and education was one of the main priorities in the activities of the world famous politician. To destroy a nation, it is enough to destroy its science and education - in this context, Heydar Aliyev saved the Azerbaijani people from destruction - he repeatedly mentioned that any progress depends on the development of science and education. Having chosen the path of integration into secular education, Azerbaijan paid special attention to this strategic area as one of the important factors of national security after the restoration of independence. (shrink)

In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics (of extensions) to such networks. We offer three different approaches to obtaining semantics. 1. The (...) translation approach This uses the methodology of ' Logic by translation'. We translate faithfully the new networks into ordinary Dung networks with more nodes and extract the semantics from the translation. 2. The labelling approach This method regards the arrows as additional entities to be attacked and to mount attacks and applies a variation of the usual machinery of Camindada like labelling to the network. The new concept we need to employ here is that of 'joint attacks'. 3. The logic programming approach We translate the higher level network into a logic program and obtain semantics for it through known semantics for logic programs. We then compare our methods with those of S. Modgil and P. M. Dung et al. (shrink)

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach (...) This uses the methodology of ' Logic by translation'. We translate faithfully the new networks into ordinary Dung networks with more nodes and extract the semantics from the translation. 2. The labelling approach This method regards the arrows as additional entities to be attacked and to mount attacks and applies a variation of the usual machinery of Camindada like labelling to the network. The new concept we need to employ here is that of 'joint attacks'. 3. The logic programming approach We translate the higher level network into a logic program and obtain semantics for it through known semantics for logic programs. We then compare our methods with those of S. Modgil and P. M. Dung et al. (shrink)

From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be (...) of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics. (shrink)

Buchman et al.'s (2024) paper illuminates a pressing issue concerning the utilization of machine learning (ML) in psychiatric care, shedding light on its potential to exacerbate stigma and social d...

Être et temps dote de moyens de penser supposés nous libérer d’une voie sans issue: du rapport kantien au monde et de ce qu’Heidegger considère comme une erreur métaphysique générale. Sein und Zeit sera pourtant interrompu avant son achèvement et, rétrospectivement, Heidegger mettra certains de ses paramètres en question. Comme si Heidegger aussi ne s’était pas donné les moyens nécessaires à son projet, au moment voulu, et que, suggérerons-nous, pris dans son propre combat avec le christianisme, il avait répété et (...) déplacé, à son insu, en 1927, ce dont il voulait se séparer, engageant par là une impasse et un tournant, la richesse d’un combat et d’un débat. (shrink)

Résumé La thématique du retrait traverse l’œuvre de Heidegger : elle est inséparable de sa quête de l’être (qui se dévoile en se voilant), de ses conceptions de la vérité et de la terre. Mais cette multi-présence du rapport entre don et rétraction n’est pas seulement inscrite dans la manière de penser de Heidegger. Elle concerne aussi le développement de Sein und Zeit, inachevé. La question qui s’impose est alors celle de savoir si et dans quelle mesure cette thématique ne (...) relève que d’une dimension philosophique ou bien si elle n’a pas aussi à voir, chez Heidegger, avec une dimension biographique. (shrink)

Résumé La thématique du retrait traverse l’œuvre de Heidegger : elle est inséparable de sa quête de l’être (qui se dévoile en se voilant), de ses conceptions de la vérité et de la terre. Mais cette multi-présence du rapport entre don et rétraction n’est pas seulement inscrite dans la manière de penser de Heidegger. Elle concerne aussi le développement de Sein und Zeit, inachevé. La question qui s’impose est alors celle de savoir si et dans quelle mesure cette thématique ne (...) relève que d’une dimension philosophique ou bien si elle n’a pas aussi à voir, chez Heidegger, avec une dimension biographique. (shrink)

Le débat sur la légitimité de la philosophie en Provence au début du XIVe siècle s’ouvrit par une attaque des fondamentalistes contre la magie astrale et les tentatives des rationalistes d’apprivoiser les puissances des corps célestes et des maladies par l’emploi d’images de planètes ou de signes du zodiaque. L’article décrit et analyse les positions rationalistes sur le degré de réalité et le statut halachique de la magie astrale. On peut en distinguer trois : la magie astrale est a) illusoire (...) et interdite, b) illusoire mais psychologiquement efficace, et interdite, c) réelle et permise. Cette dernière opinion était celle de penseurs comme Levi ben Abraham et l’école de Prat Maïmon. La magie astrale acquit en fin de compte sa légitimité dans le contexte de l’herméneutique biblique. (shrink)

Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y and x ↛ y . Given a diagram D, one can ask the formal question of “is there a valid path between node x and node y?” Depending on the existence of a valid path we can answer the question “x is a y” or “x is not a y”. The answer to the above question is determined through a complex inductive algorithm on paths (...) between arbitrary pairs of points in the graph. This paper aims to simplify and interpret such diagrams and their algorithms. We approach the area on two fronts. Suggest reactive arrows to simplify the algorithms for the winning paths. We give a conceptual analysis of inheritance diagrams, and compare our analysis to the “small” and “big sets” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as information channels and comparisons of truth values. This results in an upward chaining, split validity, off-path preclusion inheritance formalism of a particularly simple type. We show that the small and big sets of preferential reasoning have to be relativized if we want them to conform to inheritance theory, resulting in a more cautious approach, perhaps closer to actual human reasoning. We will also interpret inheritance diagrams as theories of prototypical reasoning, based on two distances: set difference, and information difference. We will see that some of the major distinctions between inheritance formalisms are consequences of deeper and more general problems of treating conflicting information. It is easily seen that inheritance diagrams can also be analysed in terms of reactive diagrams - as can all argumentation systems. AMS Classification: 68T27, 68T30. (shrink)

L'ébranlement d'une relation naturelle et fusionnelle entre Perséphone et sa mère, la déesse des moissons Déméter, est l'occasion d'une réflexion sur une problématique centrale à tout processus d'émergence : la confrontation à la séparation. L'enlèvement de la jeune fille par son oncle, le roi des morts, le refus de la Korê de s'unir à lui, le compromis trouvé entre la volonté d'Hadès et les incessantes résistances de la mère et de la fille face à la séparation, nous conduisent à une (...) interrogation sur le travail du négatif, plus précisément sur la tension entre séparation nécessaire et séparation impossible et sur le sens de cette tension pour le processus créateur. (shrink)

HANDBOOK OF DEFEASIBLE REASONING AND UNCERTAINTY MANAGEMENT SYSTEMS EDITORS: DOV M. ... and A. Hunter Volume 3: Belief Change Edited by D. Dubois and H. Prade HANDBOOK OF DEFEASIBLE REASONING AND ...

In lieu of an abstract, here is a brief excerpt of the content:April 3, 2010 (11:17 am) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE2902\russell 29,2 050 red.wpd 1 Gabbay and Woods, eds., The Rise of Modern Logic from Leibniz to Frege, Vol. 3 of the Handbook of the History of Logic (Amsterdam, etc.: North-Holland, 2004). russell: the Journal of Bertrand Russell Studies n.s. 29 (winter 2009–10): 167–90 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 eviews BERTRAND RUSSELL IN RECENT (...) BOOKS ON LOGIC HISTORY Irving Anellis Peirce Edition / Indiana U.–Purdue U. Indianapolis, in 46202–5157, usa [email protected] Dov M. Gabbay and John Woods, eds. Logic from Russell to Church. Vol. 5 of The Handbook of the History of Logic. Amsterdam, etc.: North-Holland, 2009. Pp. xii + 1056. us$260; £157.99; ¤185.95. Leila Haaparanta, ed. The Development of Modern Logic. Oxford and New York: Oxford U. P., 2009. Pp. x + 904. us$150.00. The essay “Bertrand Russell’s Logic” by Andrew D. Irvine in Volume 5 of the Handbook of the History of Logic is one of the shortest in the volume (pp. 1–28). But something of Russell pervades many of the other essays as well, as we might expect given the centrality that Principia Mathematica has occupied in the historiography of logic through much of the twentieth century. This is especially evident in the lengthiest of the essays, Andrea Cantini’s “Paradoxes, Self-reference and Truth in the 20th Century” (pp. 875–1013), and more than tangentially in Dale Jacquette’s “Logic for Meinongian Object Theory Semantics” (pp. 29–76) and Michael Potter’s “The Logic of the Tractatusz” (pp. 255–304). In their preface, the editors of the Handbook explain (p. vii) the rationale for treating Frege and Russell in separate volumes.1 One reason is that it was a matter of simple conveniencez—zto keep the volume covering logic from Leibniz to Frege of manageable size. The other is historical: while admitting that Frege and Russell shared important goals and the philosophical position of logicism, it is noted that Frege’s most important work in logic and foundations was carried out prior to his learning of Russell’s paradox, whereas the entire corpus of Russell’s work, Principiaz included, was designed to a considerable extent in eTorts to deal with the paradox, as was much of the work in logic, set theory, and philosophy of logic that came as a consequence of the discovery of that paradox. Gabbay April 3, 2010 (11:17 am) C:\Users\Milt\Desktop\backup copy of Ken's G\WPData\TYPE2902\russell 29,2 050 red.wpd 168 Reviews and Woods also make explicit the philosophical diTerences between Frege and Russell regarding the epistemological status of axioms as one of the signiWcant diTerences between these two. More particularly, the editors assert (p. viii) that, in the very brief period between publication of the second volume of Frege’s Grundgesetze (1903) and Russell’s Principles of Mathematics (1903), there was a pronounced shift initiated in the goals of mathematical logic, away from naïve apriority of axiom systems, towards study of the limits and properties of formal systems.Thecontributors to these metalogical concerns, Herbrand, Hilbert, and Gödel, among others, are the subject of the bulk of the essays included in Volume 5 of the Handbook. The task that Irvine undertakes is initiated by the eTort to understand the unity of Russell’s technical body of work in mathematics, logic, metaphysics, and epistemology. Thus the discrepancy between the neo-Hegelian concept of relations, inherited from Bradley, with certain types of relationsz—zlogical, spatial, temporal, for examplez—zwith the mathematical understanding of relations, is given as the ground for Russell’s abandonment of idealism in favour of realism (pp. 4–5). For example, there is nothing inherent in two relata, say Abelard and Héloise, which contributes to the relation of love between the pair; rather, its root is found in the mental states of one or the other of the lovers, so that the relation itself is not an intrinsic property of one of the pair. Likewise, Russell reaches this position... (shrink)

In a recent paper del Valle-Inclan and Schlöder argue that bilateral calculi call for their own notion of proof-theoretic harmony, distinct from the usual (or ‘unilateral’) ones. They then put forward a specifically bilateral criterion of harmony, and present a harmonious bilateral calculus for classical logic. In this paper, I show how del Valle-Inclan and Schlöder’s criterion of harmony suggests a notion of normal form for bilateral systems, and prove normalisation for two (harmonious) bilateral calculi for classical logic, HB1 and (...) HB2. The resulting normal derivations have the usual desirable features, like the separation and subformula properties. HB1-normal form turns out to be strictly stronger that the notion of normal form proposed by Nils Kürbis, and HB2-normal form is neither stronger nor weaker than a similar proposal by Marcello D’Agostino, Dov Gabbay, and Sanjay Modgyl. (shrink)

Principia (Book 1, Sect. 6), Newton's Lemma 28 on the algebraic nonintegrability of ovals has had an unusually mixed reception. Beginning in 1691 with Jakob Bernoulli (who accepted the lemma) and Huygens and Leibniz (who rejected it and offered counterexamples), Lemma 28 has a history of eliciting seemingly contradictory reactions. In more recent times, D.T. Whiteside in 1974 gave an “unchallengeable counterexample,” while the mathematician V.I. Arnol'd in 1987 sided with Bernoulli and called Newton's argument an “astonishingly modern topological (...) proof.” This disagreement mostly stems, we argue, from Newton's vague statement of the lemma. Indeed, we identify several different interpretations of Lemma 28, any one of which Newton may have been intending to assert, and we then test a number of proposed counterexamples to see which, if any, are true counterexamples to one or more of these versions of the lemma. Following this, we study Newton's argument for the lemma to see whether and where it fails to be convincing. In the end, our study of Newton's Lemma 28 provides an answer to the question, Who is right: Huygens, Leibniz, Whiteside and the others who reject the lemma, or Bernoulli, Arnol'd, and the others who accept it? (shrink)

We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.

Füzuli Qurbanovun “Heydər Əliyev və yeni liderlik: fəlsəfi-elmi təhlil” kitabı AMEA Fəlsəfə və Sosiologiya İnstitutunun Elmi Şurasının 05.04.2023-cü il tarixli, 02 saylı iclasının qərarı ilə çapa məsləhət görülmüşdür. Əsərin elmi redaktorları prof. İlham Məmmədzadə və t.e.d. Eynulla Mədətli, rəyçiləri prof. Etibar Nəcəfov, prof. Cahangir Məmmədov və redaktoru Qabil Camalovdur. Müəllif kitaba “Ön söz”lə başlayır. Burada Heydər Əliyevin şəxsiyyət kimi davranışları, bir vətəndaş olaraq mövqeyi, başçı-lider vəhdətində dövlət xadimi kimi Azərbaycana olan böyük sevgisindən söhbət açılır. Sonra isə Heydər Əliyevi dövlət başçısı (...) və lider kimi doğru anlamaq üçün Azərbaycanın müstəqilliyini ürəkdən sevmənin zəruri olduğu vurğulanır. (shrink)