Formal Logical System Research Articles

Mülahizələr hesabında deduksiya metodunun tətbiqinin elmi-nəzəri metodoloji problemləri

The issue of the emergence of formal axiomatic logical systems due to the emergence of logical antinomies in formal axiomatic systems, specifically the issue of developing formal logical axiomatics in the calculus of considerations was investigated in the considered research. At the same time, in order to determine the characteristics of the implementation of the logical-methodological principles and provisions of the deductive reasoning obviously, conceptual-logical foundations of the calculus of considerations was studied and the main propositions of the calculus of considerations and the analysis of the initial logical operations on them were given in the study. The basic laws of logic and the expression of one logical act with another one were also explained in the research work by giving the concepst of proportional form and tautology in the calculus of considerations. At the same time, main properties and the procedure of setting of the formal deductive theory in the calculus of considerations were studied in the article. In order to provide an adequate characterization of the conceptual and methodological bases of the calculus of considerations in the research work, the basic logical laws of the calculus of considerations developed by the German mathematician and thinker P. Hilbert were also given. In addition, the main principles and methodological provisions of the deductive method were investigated, and the rules of deriving new conclusions from the axioms were interpreted. At the end of the reviewed article, the main principles and methods of the formal axiomatic mathematical systems built on a deductive basis, specifically the calculus of considerations, were studied and a logical-methodological analysis of the calculus of considerations was carried out on this basis. In this framework, the syntactic and semantic analysis of formalized language in formal axiomatic logical systems was carried out separately, the constituent parts of those systems, including the construction scheme, were given.

The procedural aspects of postmortem defense of non-material goods of patient

The protection of privacy of patient that is applying for medical care, diagnostics and treatment is one of the main pillars of implementation of medical activities. However, despite sufficient volume of legal regulation of lifetime respect of privacy of examination, observation and facts of medical intervention, in practice occur situations when privacy ceases to be such after death of the patient. The article is based on results of content-analysis of normative legal acts (n = 11), scientific publications (n = 52), cases of judicial practice (n = 8). The problem of non-observance of privacy becomes especially actual after death of person whose name is widely known. Having no possibility to impact on causes and modes of obtaining and propagating such specific information, the deceased, one's illness, stages of treatment, struggle for life, resources spent, clinics and specialists involved become object of close attention of various subjects (mas media, Internet communities) that use obtained information for speculative purposes at the expense of fixation of inhumane public replicas and increase of number of browsing. Despite prohibition provided for by law of dissemination of information constituting privacy of applying for medical care, after death of patient and application of measures of legal liability for fact of such a disclosure, information leak occurs regularly and information that got into common access frequently discredit good name of the deceased or develop other problems that are subjects to legal protection, for family members and legal successors. Yet, circumstances of transfer of information of limited access by medical organization (data leakage) or by intent of medical worker are difficult to be proved. Therefore, in judicial practice there are practically no such cases. At that, after death of famous people, juristic community regularly faces problems of protecting personal rights and non-material values from the side of relatives, legal successors and other interested persons. On the basis of formal logical method and system analysis method of disputable situations, possible perspectives of applying for judicial protection, procedural characteristics of procedure of applying for protection and possible composition of participants are presented.

Logic-Based Reverse Analysis: A Covid-19 Surveillance Data Set Classification Problem

This study focuses on the application of formal logic systems to real-world problem-solving, specifically in the classification of the COVID-19 Surveillance Data Set (CSDS). The research introduces the integration of a random three satisfiability problem of Boolean logic into a Hopfield Neural Network (HNN) to obtain an optimal representation of Random kSatisfiability for CSDS classification. The primary goal is to utilize the optimization capabilities of the Lyapunov energy function in the HNN to extract logical relationships and identify significant features contributing to COVID-19 detection. The CSDS used in this study is sourced from the reputable UCI dataset, and the HNN's energy minimization mechanism is employed for logical mining. Computational simulations are performed with varying numbers of clauses to validate the efficacy of the proposed model in training the CSDS for classification purposes. The results showcase the efficiency and robustness of employing reverse analysis using k-satisfiability in conjunction with a Hopfield Neural Network. This approach successfully extracts dominant features related to the logical framework underlying the CSDS. By combining formal logic systems with the power of neural networks, this research offers insights into the correlation between logical rules and COVID-19 detection. The findings contribute to our understanding of how the HNN can effectively learn and classify data, opening avenues for enhanced classification techniques in the healthcare sector and other domains.

Three-way decisions with evaluative linguistic expressions

The theory of three-way decisions (3WD) requires dividing a finite, non-empty universe into three disjoint sets called positive, negative, and boundary regions. Three types of decisions are then made on the objects in each region: acceptance, rejection, and abstention (or non-commitment), respectively. Until today, a large number of 3WD extensions and applications have been proposed; some of the most recent ones also include aspects of linguistics. In this article, we first propose an innovative linguistic interpretation of three-way decisions, where the positive, negative, and boundary regions are constructed by means of the so-called evaluative linguistic expressions. These are expressions of natural language, such as small, medium, very short, quite roughly strong, extremely good, etc., and they are described within a logical theory based on the formal system of higher-order fuzzy logic. Furthermore, in line with our linguistic 3WD approach, we introduce the novel notion of linguistic rough sets, thus contributing to the development of Rough Set Theory. Finally, we connect the theory of linguistic three-way decisions with the standard 3WD model based on probabilistic rough sets, establishing conditions under which the two approaches coincide. Our results highlight connections between two different research areas: three-way decisions and the theory of evaluative linguistic expressions.

Logics for Strategic Reasoning of Socially Interacting Rational Agents: An Overview and Perspectives

This paper is an overview of some recent and ongoing developments of formal logical systems designed for reasoning about systems of rational agents who act in pursuit of their individual and collective goals, explicitly specified in the language as arguments of the strategic operators, in a socially interactive context of collective objectives and attitudes which guide and constrain the agents’ behavior.

Simple and Flexible Way to Integrate Heterogeneous Information Systems and Their Services into the World Data System

The approach to applications integration for World Data Center (WDC) interdisciplinary scientific investigations is developed in the article. The integration is based on mathematical logic and artificial intelligence. Key elements of the approach - a multilevel system architecture, formal logical system, implementation - are based on intelligent agents' interaction. The formal logical system is proposed. The inference method and mechanism of solution tree recovery are elaborated. The implementation of application integration for interdisciplinary scientific research is based on a stack of modern protocols, enabling communication of business processes over the transport layer of the OSI model. Application integration is also based on coordinated models of business processes, for which an integrated set of business applications are designed and realized.

A semiotic analysis of multiple systems of logic: using tagmemic theory to assess the usefulness and limitations of formal logics, and to produce a mathematical lattice model including multiple systems of logic

Abstract Tagmemic theory as a semiotic theory can be used to analyze multiple systems of logic and to assess their strengths and weaknesses. This analysis constitutes an application of semiotics and also a contribution to understanding of the nature of logic within the context of human meaning. Each system of logic is best adapted to represent one portion of human rationality. Acknowledging this correlation between systems and their targets helps explain the usefulness of more than one system. Among these systems, the two-valued system of classical logic takes its place. All the systems of logic can be incorporated into a complex mathematical model that has a place for each system and that represents a larger whole in human reasoning. The model can represent why tight formal systems of logic can be applied in some contexts with great success, but in other contexts are not directly applicable. The result suggests that human reasoning is innately richer than any one formal system of logic.

Strategi Berargumentasi dalam Menyelesaikan Masalah Hukum

Legal argumentation is the reason for a clear description of the explanation, in the form of a series of logical statements, to strengthen or reject an opinion, stance or idea, relating to the principles of law, legal norms and concrete legal regulations, as well as legal systems and legal discoveries. The study of legal arguments is carried out using normative juridical methods, namely reviewing secondary data in the form of primary, secondary and tertier legal materials. The question that will be studied is how the strategy of argumentation in solving legal problems. The results of the study concluded that actions must be taken to find strong legal arguments in resolving or finding solutions to legal problems, namely by doing: a) Fact Gathering; b) Classification of Legal Issues; c) Identification and Selection of Relevant Legal Issues; d) Legal discoveries relating to Legal Issues; e) Application of the Law. In the application of the law there are often obstacles, including overlapping authorities and conflicts of interest that occur due to differences in interests and differences in how to interpret laws and regulations. In this regard, interpretation, reasoning and legal argumentation are carried out to prevent and overcome overlapping authorities and conflicts of interest and turn it into an arena of cooperation between governments, entrepreneurs, and society. The conclusion of this study is that legal argumentation is a scientific skill in finding legal solutions, a form of analysis to reach a solution is by the existence of legal opinions. A meaningful argument is built only on logic. In other words, a "conditio sine qua non" decision may be accepted, if based on a process of reason, in accordance with the formal system of logic which is an absolute condition for argumentation. In order for an argument to have meaning, a basic material and an appropriate way are needed. The basic material needed to conduct legal agumentation is an understanding of a matter about law related to legal science. The ability to understand basic materials alone is not enough if it is not presented in the right way. For this reason, a mastery of parables is needed in carrying out the thought process to facilitate using legal arguments

Use of the PVS formal logic system in the method of formal proof of security in the construction of information security systems

The object of research is the information and telecommunication system (ITS) and ensuring the protection of information stored, processed and circulating in it. One of the most problematic areas in the creation of secure ITS is the logical inconsistency and incompleteness of the information security policy. That is, a set of laws, rules, restrictions, recommendations, etc., which regulate the procedure for processing information and are aimed at protecting information from a certain set of threats. The reason for such problems is usually the absence of pre-design modeling of the information security system as a component of the information and telecommunications system, which in the end causes the latter to be vulnerable. An important prerequisite for the creation of a secure ITS is the construction of a subject-object model of the system, which makes it possible to determine the connections between objects, their features, to model information flows and types of access to information and infrastructure resources. According to the existing clear, complete and consistent subject-object model of the ITS, it becomes possible to apply mathematical methods to modeling the processes of its functioning, including for solving the problem of formal proof of security. The paper considers the main idea of the method of formal proof of security, which can be used when building information security systems or assessing the security of the created information and telecommunications system. It is shown that for its implementation it is possible to use the methodology of automatic theorem proving. One of the ways to solve this problem, which is proposed in the work, is the use of the PVS (Prototype Verification System) formal logic system, which is widely used for writing specifications and constructing proofs. The main components of this system are considered, as well as the possibilities of its use for automatic proof of statements about the impossibility of unauthorized access under the conditions of a certain security policy. An example of the use of the PVS system for the formal proof of the security of the system in the framework of the Bella-LaPadula security policy is given.

Formalisation of Bayesian concealment

In order to assure the concealment by cryptographic protocols, it is an effective measure to prove the concealment in a formal logical system. In the contemporary context of cryptographic protocol, the concealment has to be proved by using probability theory. There are several concepts of concealment in probability theory. One of them is Bayesian concealment. This study proposes a formal logical system to prove the Bayesian concealment of a secret sharing scheme.

On achieving human-level knowledge representation by developing a natural language of thought

What is the nature of knowledge representation needed for human-level artificial intelligence? This position paper contends that to achieve human-level AI, a system architecture for human-level knowledge representation would benefit from a neuro-symbolic approach combining deep neural networks with a ‘natural language of thought’ and would be greatly handicapped if relying only on formal logic systems.

О вечной ценности идей в сиюминутных воплощеньях

Opinions have degrees of epistemic “value”, measured in the framework of a given culture. These degrees do not necessarily coincide with degrees of momentary actuality in the society and in the cultural environment. Parameters of social-cultural evaluation vary with time gaining and/or losing actuality. They even depend on whether those who pronounce these opinions are acquainted with those whom these opinions are ascribed to or with “certified” authors of the ideas. This social dimension of opin-ion evaluation may be manipulatively used in mass media so that even openly fake news and fake ‘truths’ are taken for granted by addressees. Two approaches are extensively discussed in the literature on such “quotational” view of language use: the “semantic” approach and the “formal” approach. The for-mer takes the content of propositions not to depend on the sentence forms presented to the audience. For the second approach, the propositions taken as ideas wholly de-pend on the form of presentation, even on syntactical details of formal realizations of ideas in discourse, being socially adapted to the cultural environment. This view im-plies that evaluation of ideas depends even on “syntactic vagaries” of a given lan-guage, such as Russian or English additionally to the ways they present propositions and propositional attitudes in formal logical systems.

How do students promote mathematical argumentation through guide-redirecting warrant construction?

Argumentation is a mathematical discourse that is currently widely studied by researchers as a stepping stone in constructing mathematical evidence. A variety of argumentation studies display different formats and constructs ranging from Toulmin’s argumentation with a formal logic system to a general discourse that presents justifications and explanations for informal arguments with an inductive approach. It is based on the student’s difficulties in preparing a search warrant until later gave rise to the idea of reconstruction of the warrant and the importance of guide-redirecting warrant construction (GWC). The results showed that GWC could guide students in constructing statements and reasons or explanations towards the expected evidence. Students also realize that statements are related to reason and explanation in building whole arguments. Even so, the presentation of the statement is still aligned with the evidence submitted, so for reasons that display the axiomatic system, it still faces problems.

The Barcan formulas and necessary existence: the view from Quarc

The Modal Predicate Calculus gives rise to issues surrounding the Barcan formulas, their converses, and necessary existence. I examine these issues by means of the Quantified Argument Calculus (Quarc), a recently developed, powerful formal logic system. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, a fact that lends additional interest to this examination, as Quarc might offer a better representation of our modal concepts. The validity of the Barcan formulas and their converses is shown by Quarc to be a result of the specific incorporation of quantification in the Predicate Calculus, and not as reflecting a feature of the interaction of quantification and modality more generally. Necessary existence is shown to follow from the identification, in the Predicate Calculus on its canonical interpretation, of particular quantification, ascription of existence and the ‘there is’ construction, three constructions which are distinguished in both Quarc and Natural Language. The issues surrounding the Barcan formulas, their converses and necessary existence are thus shown to be an artefact of a specific logic system, not an essential feature of our relevant modal concepts or of formal logic.

On the logic of the unconscious

ABSTRACT Freud argues that the laws of classical logic do not hold true with regard to the unconscious. The aim of this paper is to provide an alternative logic that is consistent with Freud’s conception of the unconscious. This aim is achieved in two steps. First, I argue that most Freudian features of the unconscious are consequences of the fact that unconscious thoughts in the Freudian sense are negationless. Then I suggest a formal logical system that lacks the negation symbol, and is known as negationless-logic, with which to formulate the logic of the unconscious. I demonstrate that this suggestion provides a better understanding of various psychological phenomena, such as projection, reaction-formation, delusion and the misconstrual of the empty set in childhood. Finally, I argue that negationless-logic provides solutions to certain shortcomings in Matte-Blanco’s formulation of the logic of the unconscious.

Cut elimination and complexity bounds for intuitionistic epistemic logic

Abstract The formal system of intuitionistic epistemic logic (IEL) was proposed by S. Artemov and T. Protopopescu. It provides the formal foundation for the study of knowledge from an intuitionistic point of view based on Brouwer–Heyting–Kolmogorov semantics of intuitionism. We construct a cut-free sequent calculus for IEL and establish that polynomial space is sufficient for the proof search in it. We prove that IEL is PSPACE-complete.

ИНТЕНСИОНАЛЬНОСТЬ: ОТ ФИЛОСОФСКОЙ ЛОГИКИ К МЕТАМАТЕМАТИКЕ

The article is devoted to the study of the status of intensionality in the exact contexts of logical and mathematical theories. The emergence of intensionality in logical and mathematical discourse leads to significant obstacles in its formalization due to the appearance of indirect contexts, the uncertainty of its indication in the theoretical apparatus, as well as the presence of various kinds of difficult-to-account semantic distinctions. The refusal to consider intensionality in logic is connected with Bertrand Russell’s criticism of Alexius Meinong’s intensionality ontology, and with Willard Van Orman Quine’s criticism of the concept of meaning and quantification of modalities. It is shown that this criticism is based on a preference for the theory of indication over the theory of meaning, in terms of the distinction “Bedeutung” and “Sinn” introduced by Gottlob Frege. The extensionality thesis is explicated; by analogy with it the intensionality thesis is constructed. It is shown that complete parallelism is not possible here, and therefore we should proceed from finding cases of extensionality violation. Since the construction of formal logical systems is to a certain extent connected with the programs of the foundations of mathematics, the complex interweaving of philosophical and purely technical questions makes the question of the role of intensionality in mathematics quite confusing. However, there is one clue here: programs in the foundations of mathematics have given rise to metamathematics, which, although it stands alone, is considered a branch of mathematics. It is not by chance that, judging by the problems arising in connection with intensionality, there is a growing suspicion that intensionality can play a significant role in metamathematics. As for the question of the sense in which metamathematics results can be considered mathematical, in terms of the presence of intensional contexts in both disciplines, it is a matter of taste: for example, the autonomy of mathematical knowledge as a result of the desire of mathematicians to eliminate the influence of philosophy that took place in the case of David Hilbert may be worth considering in the context of mathematics. Thus, the rather vague concept of intensionality receives various explications in different contexts, whether it is philosophical logic or metamathematics. In any case, the detection of context intensionality is always associated with a clear narrowing of the research area. It is obvious that the creation of a more general theory of intensionality is possible within a more general framework, in which logic and mathematics must be combined. In this respect, we can hope for the resumption of a logical project, which would be a purely logical consideration made of the natural and the mathematical.

Logical Foundations and Kant's Principles of Formal Logic

The abstract status of Kant's account of his ‘general logic’ is explained in comparison with Gödel's general definition of a formal logical system and reflections on ‘abstract’ (‘absolute’) concepts. Thereafter, an informal reconstruction of Kant's general logic is given from the aspect of the principles of contradiction, of sufficient reason, and of excluded middle. It is shown that Kant's composition of logic consists in a gradual strengthening of logical principles, starting from a weak principle of contradiction that tolerates a sort of contradictions in predication, and then proceeding to the (constructive) principle of sufficient reason, and to a classical-like logic, which includes the principle of excluded middle. A first-order formalisation is applied to this reconstruction, which reveals implicit modalities in Kant's account of logic, and confirms the implementability of Kant's logic into a sound and complete formal system.

Інформаційна технологія для розробки та впровадження web-застосунків

The problem of the rapid creation of effective web-applications of one class with using formal means are considered. The conceptual approach to its solution is offered on the basis f analysis of the peculiarities of web-applications construction. The approach is based on defining the standard web application architecture and selecting its components using formal methods in accordance with user requirements. A formal logical system is used, which uses the design of web-applications as a process of outputting the formula specified according to the needs of the user, which defines the schemes of execution of the modules of the system. An important feature of the approach is the ability to 3D-visualize the process of designing the system, which creates conditions for effective interaction between developers and machine development tools. Ref. 4, pic. 2

The role of syntactic representations in set theory

In this paper, we explore the role of syntactic representations in set theory. We highlight a common inferential scheme in set theory, which we call the Syntactic Representation Inferential Scheme, in which the set theorist infers information about a concept based on the way that concept can be represented syntactically. However, the actual syntactic representation is only indicated, not explicitly provided. We consider this phenomenon in relation to the derivation indicator position that asserts that the ordinary proofs given in mathematical discourse indicate syntactic derivations in a formal logical system. In particular, we note that several of the arguments against the derivation indicator position would seem to imply that set theorists could gain no benefits from the syntactic representations of concepts indicated by their definitions, yet set theorists clearly do.