On the Formalization of Hegel’s Dialectical Logic

A Fresh Look: The Social Competence of Information Science

BackgroundSignaling systems typically involve large, structured molecules each consisting of a large number of subunits called molecule domains. In modeling such systems these domains can be considered as the main players. In order to handle the resulting combinatorial complexity, rule-based modeling has been established as the tool of choice. In contrast to the detailed quantitative rule-based modeling, qualitative modeling approaches like logical modeling rely solely on the network structure and are particularly useful for analyzing structural and functional properties of signaling systems.ResultsWe introduce the Process-Interaction-Model (PIM) concept. It defines a common representation (or basis) of rule-based models and site-specific logical models, and, furthermore, includes methods to derive models of both types from a given PIM. A PIM is based on directed graphs with nodes representing processes like post-translational modifications or binding processes and edges representing the interactions among processes. The applicability of the concept has been demonstrated by applying it to a model describing EGF insulin crosstalk. A prototypic implementation of the PIM concept has been integrated in the modeling software ProMoT.ConclusionsThe PIM concept provides a common basis for two modeling formalisms tailored to the study of signaling systems: a quantitative (rule-based) and a qualitative (logical) modeling formalism. Every PIM is a compact specification of a rule-based model and facilitates the systematic set-up of a rule-based model, while at the same time facilitating the automatic generation of a site-specific logical model. Consequently, modifications can be made on the underlying basis and then be propagated into the different model specifications – ensuring consistency of all models, regardless of the modeling formalism. This facilitates the analysis of a system on different levels of detail as it guarantees the application of established simulation and analysis methods to consistent descriptions (rule-based and logical) of a particular signaling system.

Formal executable models provide a means to gain insights into the behavior of complex distributed systems. Ideas can be prototyped and assurance gained by carrying out analyses at different levels of fidelity: searching for desirable or undesirable behaviors, determining effects of perturbing the system, and eventually investing effort to carry out formal proofs of key properties. This modeling approach applies to a wide range of systems, including a variety of protocols and networked cyber-physical systems. It is also emerging as an important tool in understanding many different aspects of biological systems. Rewriting logic (RWL) is a formalism that is well-suited to developing and working with formal executable models. In RWL term rewriting is used to represent both structure (equational properties and functions) and transformation / behavior. Logics and inference systems can be naturally represented in RWL, as can the structure and behavior of distributed systems both engineered and natural. Maude is a high performance realization of Rewriting Logic. Maude specifications are naturally executable and the Maude environment provides a variety analysis tools to reason about properties of models. These include reachability analysis, symbolic execution (narrowing), and model-checking. In addition, Maude is reflective. This provides a powerful mechanism for extension. The talk will present a sampling of executable specifications using Maude and its extensions.

The idea at the basis of this special issue is that reopening the old debate about the logical status of Hegel's dialectics is extremely interesting, for various reasons. The first reason is that a new Hegel is circulating, nowadays, in the philosophical literature, with specific reference to Hegel's dialectical logic and its relation to the history and philosophy of logic. This development deserves to be accounted for. Secondly, new research about the connection between contradictory logical systems and Hegel's dialectics is also being developed, and this too deserves to be acknowledged. Finally there are, recently, confirmations that the concept of dialectics is of general interest, and that the usual perplexities about the Hegelian triadic and fairly mechanic device of ‘yes, not, and not not’ are in remission.

The feature interaction problem is prominent in telephone service development. Many of the problems which arise when features combine are due to badly developed requirements models for individual features. With sufficiently good requirements models, in which each feature is formally modelled and validated against customer understanding, the feature interaction problem is much more tractable. Through a number of case studies, we have discovered that no one semantic framework is suitable for the synthesis and analysis of formal feature requirements models. Consequently we advocate a mixed-model approach. Firstly, we have an operational model, written in LOTOS using an object-based style, which is useful for constructing an executablemodel for validation. Secondly,we have a logical model (based on the B method) which is used to verify the state invariant properties of our system. Finally, we use TLA to provide semantics for a static analysis of liveness and fairness properties. No one model can treat each of these aspects, yet each of these aspects of the conceptualisation are necessary in the formal development of features. A simple example, in which we combine call forwarding and call screening features, illustrates the roles played by each of the models.

Scalable optimization in grid, cloud, and intelligent network computing – foreword

This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of three-valued and four-valued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structural rules of contraction, cut and identity feature in paradoxical derivations. It then introduces model theoretic treatments of the paradoxes, including a simple fixed-point model construction which generates three-valued models for theories of truth, which can provide models for a range of different non-classical logics. The Element closes with a discussion of the relationship between proofs and models, arguing that both have their place in the philosophers' and logicians' toolkits.

Logic algebra is important to establish the basis of mathematical logic, so in this paper, complete continuous-valued logic algebra is proposed, the definitions of seven kinds of integrity cluster of logical operation model that may exist in continuous-valued propositional logic are given, which can directly include and deal with the four uncertainties that may exist in continuous-valued propositional logical operator model. They are the uncertainty of propositional true degree arising from true /false contradictions, the uncertainty of logical operator model arising from enemy / friends contradictions, the uncertainty of logical operator model arising from loose/strict contradictions, the uncertainty of logical operator model arising from familiar/unfamiliar contradictions. Continuous-valued logic algebra is the important basis for further establishment of continuous-valued of dialectical logic.

Fractional-order PID control is a landmark in the development of fractional-order control theory. It can improve the control precision and accuracy of systems and achieve more robust control results. As a theorem-proving formal verification method, it can be applied to an arbitrary system represented by a mathematical model. It is the ideal verification method because it is not subject to limits on state numbers. This paper presents the higher-order logic (HOL) formal verification and modeling of fractional-order PID controller systems. Firstly, a fractional-order PID controller was designed. The accuracy of fractional-order PID control can be supported by simulation, comparing integral-order PID controls. Secondly, the superior property of fractional-order PID control is validated via higher-order logic theorem proofs. An important basic property, the relationship between fractional-order differential calculus and integral-order differential calculus, was analyzed via a higher-order logic theorem proof. Then, the relations between the fractional-order PID controller and integral-order PID controller were verified based on the fractional-order Grünwald–Letnikov definition for higher-order logic theorem proofs. Formalization models of the fractional-order PID controller and the fractional-order closed-loop control system were established. Finally, the stability of the fractional-order control systems was verified based on established formal models and theorems. The results show that the fractional-order PID controllers can be conducive to the control performance of control systems, and the higher-order logic formal verification method can ensure the reliability and security of fractional-order control systems.

This chapter discusses the development of Wittgenstein’s philosophy of logic with reference to the color-exclusion problem, relating to propositions in the case of which the attribution of a property excludes the simultaneous attribution of a property of the same kind to the same object. This led Wittgenstein, first, to consider the possibility of logic as a phenomenological investigation that would establish which properties have this character of mutual exclusion. While this would have saved the Tractatus’ assumption of the independence of elementary propositions and the associated account of truth-functions, however, it would have compromised its conception of the non-substantiality and formality of logic. Recognizing this, Wittgenstein rejected elementary propositions and introduced the notion of propositional systems to account for relevant kinds of cases. But this soon revealed further problems concerning logic, pertaining to logical generality, the universality and topic-neutrality of logic, the status of logical languages and models, and the conception of logic as a rigorous non-empirical investigation. Eventually, dealing with these problems led Wittgenstein to develop his mature philosophy of logic. I conclude with comments on the new life that can be given to Wittgenstein’s propositional systems in the context of his mature philosophy of logic.

A central goal of systems biology is the construction of predictive models of bio-molecular networks. Cellular networks of moderate size have been modeled successfully in a quantitative way based on differential equations. However, in large-scale networks, knowledge of mechanistic details and kinetic parameters is often too limited to allow for the set-up of predictive quantitative models.Here, we review methodologies for qualitative and semi-quantitative modeling of cellular signal transduction networks. In particular, we focus on three different but related formalisms facilitating modeling of signaling processes with different levels of detail: interaction graphs, logical/Boolean networks, and logic-based ordinary differential equations (ODEs). Albeit the simplest models possible, interaction graphs allow the identification of important network properties such as signaling paths, feedback loops, or global interdependencies. Logical or Boolean models can be derived from interaction graphs by constraining the logical combination of edges. Logical models can be used to study the basic input–output behavior of the system under investigation and to analyze its qualitative dynamic properties by discrete simulations. They also provide a suitable framework to identify proper intervention strategies enforcing or repressing certain behaviors. Finally, as a third formalism, Boolean networks can be transformed into logic-based ODEs enabling studies on essential quantitative and dynamic features of a signaling network, where time and states are continuous.We describe and illustrate key methods and applications of the different modeling formalisms and discuss their relationships. In particular, as one important aspect for model reuse, we will show how these three modeling approaches can be combined to a modeling pipeline (or model hierarchy) allowing one to start with the simplest representation of a signaling network (interaction graph), which can later be refined to logical and eventually to logic-based ODE models. Importantly, systems and network properties determined in the rougher representation are conserved during these transformations.

The advantages and disadvantages of formalization in philosophy are summarized. It is concluded that formalized philosophy is an endangered speciality that needs to be revitalized and to increase its interactions with non-formalized philosophy. The enigmatic style that is common in philosophical logic must give way to explicit discussions of the problematic relationship between formal models and the philosophical concepts and issues that motivated their development.

The purpose of the article is to analyze the relationship between the phenomenon of conscience and ideology. The work uses psychoanalytic and cultural-historical approaches, the methods of critical philosophical reflection and dialectical logic are applied. Conscience is viewed as a person’s ability to critically assess his or her thoughts and actions in accordance with personal ideas about what should be done. At the same time, attention is focused on the fact that feelings of shame and conscience are inherent in all people, since they are fundamental in the mechanisms of human consciousness and self-consciousness. Actually, their presence acts as one of the main features which distinguish humans from other animals. In turn, ideas about what is due are dynamic, since they are fixed by specific actors of the cultural and historical process, who are individuals who have determined their understanding of what is due, values and ways to achieve them, who have sufficient will to convince others that their guidelines are correct. But not all ideals set a progressive, humanistic direction. At the same time, the work emphasizes that no personal ideas about what should be done can take the form of a general ideology if they do not reflect, to one degree or another, the material interests of the most part of society. At the same time, the logic of the study leads to the conclusion that the absence of a common ideology that promotes humanistic values aggravates the moral disorientation of representatives of modern Russian society, reducing the level of self-control provided by conscience.

The purpose of the article is to analyze the prospects for the socio-economic development of Russia. The work uses a culturalhistorical approach, applies methods of critical philosophical reflection and dialectical logic. The main attention is paid to considering the most acceptable form of social organization for Russia, following the traditional features of its historical evolution. The work focuses on the importance of fostering patriotic sentiments for the successful existence of the state and society. The logic of the research shows that at present the ideas of patriotism and liberalism are the main ideological constructs, on the approval of which not only the form of social organization, but also the possibility of the existence of an independent Russia largely depends. The author believes that there is no need for Russia to create a form of public organization in the likeness of Western countries. Russia can occupy a worthy economic niche, provided that there is a public organization in which national and personal interests are harmoniously combined, where there will be no exaggeration of the importance of private property, relative to state one.

A lot of research in the field of artificial intelligence cannot be completed, or carried out at all, due to the lack of at the moment a correct theory of the human brain functioning associated with its intellectual activity, at least at a conceptual level. So far, there are no comprehensive proposals by researchers on what principles should be based on models of elementary and structured meanings processed by the brain in the course of human life, not to mention formal languages and their grammars, or, especially, formal theories designed for these purposes. The purpose of this article is to fill the gap in scientific knowledge about the human brain. Academician P.K. Anokhin in 1984 proposed the concept of a model for organizing and regulating a behavioral act, in which there is a place for all basic processes and conditions. It was called the functional system model. With such a model, it becomes possible in the same vein, using axiomatic statements, to create a logical-dialectical model of the functioning process at the physiological level of any of the higher mental functions. The dialectical logic of controlling any human body functional systems follows from the conceptual knowledge of the vital functions of these functional systems, obtained exclusively by natural experimenting. Therefore, the conceptual knowledge of the vital functions of each studied functional system of a person should precede the description of the logic essence of its control. The human psyche is one of the most important functional systems of the human body. The article presents the fundamental concepts of the vital functions of this system, which allow revealing the essence of the dialectical logic of life-supporting functions control and a formal model of the dialectic logic of the human psyche functional system control.