Logical Foundations Research Articles

Computing the fuzzy partition corresponding to the greatest fuzzy auto-bisimulation of a fuzzy graph-based structure under the Gödel semantics

The similarity measure based on fuzzy bisimulation has the Hennessy-Milner property as a strong logical foundation. It is useful for classification and clustering. In this work, we design an efficient algorithm with the complexity O((mlog⁡l+n)log⁡n) for computing the fuzzy partition corresponding to the greatest fuzzy auto-bisimulation of a finite fuzzy labeled graph G under the Gödel semantics, where n, m and l are the number of vertices, the number of non-zero edges and the number of different fuzzy degrees of edges of G, respectively. Our notion of fuzzy partition is novel, defined for finite sets with respect to the Gödel t-norm, with the aim to facilitate the computation of the greatest fuzzy auto-bisimulation. By using that algorithm, we also provide an algorithm with the complexity O(m⋅log⁡l⋅log⁡n+n2) for computing the greatest fuzzy bisimulation between two finite fuzzy labeled graphs under the Gödel semantics. This latter algorithm is better (has a lower complexity order) than the previously known algorithms for the considered problem. Our algorithms can be restated for other fuzzy graph-based structures such as fuzzy automata, fuzzy labeled transition systems, fuzzy Kripke models, fuzzy social networks and fuzzy interpretations in fuzzy description logics.

Contrary to T. Hirai, Ramsey’s Critiques of Keynes in 1922 and 1926 Were Completely Wrong

This paper covers Harai’s analysis, contained in his section, titled “Keynes as a philosopher”, of Keynes’s logical theory of probability. Harai spends too much of his time repeating Ramsey’s claims about having uncovered serious errors in the structure of Keynes’s relational propositional theory. .For 100 years, Keynes’s logical theory has been interpreted and misevaluated through the eyes of an ignorant 18 year old teenager. The result has been the proliferation and spread of what can be called the “Ramsey myth”.The “Ramsey myth” is that an 18 year old teenager appeared at Cambridge University in 1921.This 18 year old teenager was a genius who wrote a three page review in the Jan., 1922 issue of Cambridge Magazine, which supposedly destroyed, devastated and demolished the logical foundations of Keynes’s A Treatise on Probability, which was his relational, propositional logic founded on Boole’s relational, propositional logic. Russell countered this in his review, but was ignored (See Brady, 2016a). In 1931, it is further supposed that Keynes then capitulated to Ramsey and repudiated his own logical theory of probability, accepting some version of Ramsey’s subjectivist theory. This myth is what Hirai’s paper is based on. It was false in 1921 and it is false today in 2022.

Beyond the nexus family – business: introducing the family business service ecosystem

PurposeExtant family business research focuses on the understanding of value creation through the binary interactions between the family and its business (the family – business nexus). This article addresses this issue by expanding the understanding of value creation beyond the family-business nexus to that of value creation among a wider set of stakeholders (the family business service ecosystem). It recognizes the multi-faceted nature of family businesses and conceptualizes a value creation process through a broader scope of internal and external stakeholders.Design/methodology/approachThis research theoretically connects Business Model Innovation (BMI) and Service dominant logic (SDL) as foundations of an ecosystem approach of value creation established through collaboration, coproduction and co-creation based on Value in Use (ViU). The authors then present the FB Service Ecosystem BM.FindingsThis research generates an overarching model of value creation and integration that reflects and enacts the purpose of the family firm’s project through interactions with ad hoc internal and external actors as possible Third Avenue of value creation, transcending the family versus business paradox. Termed FB Service Ecosystem, this overarching model can be at the forefront of economic, ecological and societal transition, by tacitly transmitting such BMs through their networks of stakeholders. The FB Service Ecosystem is important because it can support the transition of economies and societies based on service, collaboration and meeting multiple stakeholder needs.Originality/valueThis research addresses the dichotomy between financial and non-financial outcomes and between agency and stewardship. It transcends this paradox to offer an inclusive value creation perspective considering a wider set of internal and external stakeholders based on reciprocal service provision and co-creation of mutual value, foundations of service dominant logic, among actors of a service ecosystem federated by and around the family business, termed Family Business Service Ecosystem.

От логики к бессмысленности: философия языка Людвига Витгенштейна в повести Томаса Бернхарда «Хождение»

The article attempts to reveal the scale of influence of Ludwig Wittgenstein’s Tractatus Logico-Philosophicus on the subject matter and writing method of Thomas Bernhard. On the basis of the novella Walking, published in 1970, we demonstrate that the issues raised by Wittgenstein at the beginning of the 20th century were of primary importance for Bernhard. The Austrian writer was interested not only in establishing the relationship between the world and language, but also in extrapolating this metaphysical problem to an understanding of the nature of literary creativity. Wittgenstein in his work asked the critical question about the possibility of adequate transmission of events by means of language and sought to explore its ontological and logical foundations. However, this idea of the philosopher receives an unusual refraction in the novella Walking. On the one hand, Bernhard casts doubt on Wittgenstein’s assumption about the initial isomorphism of words and objects and condemns his characters to endless wandering in the closed space of speech. On the other hand, in such a negative way he confirms the ideological core of the “linguistic turn”, and, in fact, that human existence is determined by language. Thus, literary exploration of themes of madness, suicide, the deceptiveness of reality, which in the logical continuum of the Tractatus are declared nonsensical, leads Bernhard’s narrative to an existential level.

Semantic 3D city interfaces—Intelligent interactions on dynamic geospatial knowledge graphs

Abstract This article presents a system architecture and a set of interfaces that can build scalable information systems capable of large city modeling based on dynamic geospatial knowledge graphs to avoid pitfalls of Web 2.0 applications while blending artificial and human intelligence during the knowledge enhancement processes. We designed and developed a GeoSpatial Processor, an SQL2SPARQL Transformer, and a geospatial tiles ordering tasks and integrated them into a City Export Agent to visualize and interact with city models on an augmented 3D web client. We designed a Thematic Surface Discovery Agent to automatically upgrade the model’s level of detail to interact with thematic parts of city objects by other agents. We developed a City Information Agent to help retrieve contextual information, provide data concerning city regulations, and work with a City Energy Analyst Agent that automatically estimates the energy demands for city model members. We designed a Distance Agent to track the interactions with the model members on the web, calculate distances between objects of interest, and add new knowledge to the Cities Knowledge Graph. The logical foundations and CityGML-based conceptual schema used to describe cities in terms of the OntoCityGML ontology, together with the system of intelligent autonomous agents based on the J-Park Simulator Agent Framework, make such systems capable of assessing and maintaining ground truths with certainty. This new era of GeoWeb 2.5 systems lowers the risk of deliberate misinformation within geography web systems used for modeling critical infrastructures.

The reemergence of the language-of-thought hypothesis: Consequences for the development of the logic of thought.

Quilty-Dunn et al. defended the reemergence of language-of-thought hypothesis (LoTH). My commentary builds up implications for the study of the development of our logical capacities. Empirical support for logically augmented LoT systems calls for the investigation of their logical primitives and developmental origin. Furthermore, Quilty-Dunn et al.'s characterization of LoT helps the quest for the foundation of logic by dissociating logical cognition from natural language.

Preparing students to form customized education programs for their future

Current trends including globalization, digitalization, informatization, computerization, etc., dictate new requirements for the forms, content and delivery methods of education. Education in the form of acquiring knowledge is replaced by the form of acquisition of competences. The actual principle of the quality and level of education is the competence approach, and in the field of providing educational services - the student-centered approach. The purpose of this work is to share the discussion regarding the trajectory of student's education with the necessary competencies for future professional activity, taking into account the student-centered approach to the educational process systems thinking required to solve complex problems, and dynamic optimization methods. The formation of the student's educational trajectory is based on the development of methodological, ontological and logical foundations of knowledge construction. Ontologies play a decisive role in the description model of the formation of such trajectories when a system of ontological descriptions of various training programs is created, which simultaneously becomes a means of methodology for the formation of new trajectories of knowledge. The use of the proposed principles of formation of the student's educational trajectories allows to make this process, on the one hand, more personalized, and on the other hand, transdisciplinary - which ensures the unification of students into study groups by courses, departments and faculties. The practical implementation of the step-by-step principles of building and installing educational programs takes place in the format of "Prism of Knowledge" based on the "Web-Software Complex – Editor of Learning Trajectory Scenarios". It provides the user with a toolkit with dynamic optimization methods for building various scenarios of the optimal learning trajectory taking into account innovations and future professional activities. Therefore, the given system of formation of knowledge trajectories allows building both personal knowledge bases and unification of groups of students, which in the future will contribute to the development of student-oriented education.

Theoretical-probablic approach to the modeling of uncertainty in economic activity from the perspective of the historical path of its development

The article is devoted to the problem of modeling uncertainty in the field of economics and business based on probability theory. Specifically, the purpose of the study was to review the features, potential and limitations of probability theory as a means of quantitative analysis and modeling of uncertainty in economic activity from the point of view of the historical path of its formation and development. As part of this, the key events of the origin and development of probability theory, key aspects of substantiating its logical foundations and building it as a purely mathematical discipline were considered. Particular attention was paid to the issue of distinguishing between stochastic and non-stochastic uncertainty in the plane of practical situations of economic decision-making. As one of the important methodological emphases of the work, the thesis that when the situation of making an economic decision is burdened by non-stochastic uncertainty of one or another origin, it is justified and useful to turn to an expert approach. At the same time, the theory of subjective probabilities, the theory of fuzzy sets, and interval analysis stand out as the system-forming components of the theoretical basis of the latter.

Economic planning must be polycentric, not monocentric: Introduction to a symposium on Mises and Hayek on socialism and knowledge

AbstractThe roaring (20‐) 20s are a decade of anniversaries and milestones. 2020 was the 100th anniversary of Ludwig von Mises's seminal article “Economic Calculation in the Socialist Commonwealth” and the 75th anniversary of F.A. Hayek's seminal article “The Use of Knowledge in Society.” 2022 brought a series of significant anniversaries: the 100th anniversary of Mises's Socialism: An Economic and Sociological Analysis as well as the 60th anniversary of James M. Buchanan and Gordon Tullock's The Calculus of Consent: Logical Foundations of Constitutional Democracy, Milton Friedman's Capitalism and Freedom, and Murray Rothbard's Man, Economy, and State. It was also the 20th anniversary of Vernon Smith's Nobel Prize. The works and milestones celebrating anniversaries in 2022 owe much to Mises's and Hayek's pathbreaking contributions. This paper summarizes and contextualizes Mises's and Hayek's arguments about socialism and knowledge and introduces a Southern Economic Journal symposium on the anniversaries of “Economic Calculation in the Socialist Commonwealth” and “The Use of Knowledge in Society.”

Multi-Query Optimization Revisited: A Full-Query Algebraic Method.

Sharing data and computation among concurrent queries has been an active research topic in database systems. While work in this area developed algorithms and systems that are shown to be effective, there is a lack of logical foundation for query processing and optimization. In this paper, we present PsiDB, a system model for processing a large number of database queries in a batch. The key idea is to generate a single query expression that returns a global relation containing all the data needed for individual queries. For that, we propose the use of a type of relational operators called -operators in combining the individual queries into the global expression. We tackle the algebraic optimization problem in PsiDB by developing equivalence rules to transform concurrent queries with the purpose of revealing query optimization opportunities. Centering around the -operator, our rules not only cover many optimization techniques adopted in existing batch processing systems, but also revealed new optimization opportunities. Experiments conducted on an early prototype of PsiDB show a performance improvement of up to 36X over a mainstream commercial DBMS.

Познаёт ли сознание само себя в когнитивных науках?

The paper critically examines some theses from A.V. Smirnov’s monograph ‘The Logic of Meaning as a Philosophy of Consciousness: An Invitation to Reflection’. In particular, the statement about the inability of cognitive sciences to exhaustively explain conscious­ness because of its de-subjectivation within their framework. It is shown that cognitive sciences are generally able to cope with the intellectual and controlling aspects of con­sciousness. Only its phenomenal aspect remains in question, but this is clearly not what the author of the monograph means. Further, he argues that understanding the workings of consciousness underlies the philosophical foundations of any subject. The analysis shows that if we exclude consciousness as control and the phenomenal consciousness, which are obviously irrelevant here, then the philosophical foundations of anything within this understanding are reduced either to normative requirements in the form of the logical foundations of theories, or to empirical data in the form of cognitive limita­tions of real subjects. Attributing rationalism and universalism to the Western philosophy as its essential properties, the author of the monograph does not take into account that ra­tionalism as anti-empiricism has long been a kind of abandoned trend, and rationalism as a commitment to inferential procedures has also been recently challenged by some strong alternatives. Similarly, the author’s opinion of the Western philosophy of mind as the exe­cution of the Cartesian program, which he reduces to cogito ergo sum, is disputed. This methodological tool – and the metaphysical principle as well – of Descartes is subjected to incessant attacks from representatives of various schools of Western philosophy. More­over, it underlies not the philosophy of mind, but the epistemology of the great philoso­pher. Finally, the author’s concept of ‘unfolding the folded’ comes down to a kind of di­alectical deduction of the empirical features of various cultures from a priori predeter­mined ‘subject-predicate gluings’ and ‘intuitions of integrity’, which paradoxically brings us back to Hegelian-type rationalism.

Twenty Significant Problems in AI Research, with Potential Solutions via the SP Theory of Intelligence and Its Realisation in the SP Computer Model

This paper highlights 20 significant problems in AI research, with potential solutions via the SP Theory of Intelligence (SPTI) and its realisation in the SP Computer Model. With other evidence referenced in the paper, this is strong evidence in support of the SPTI as a promising foundation for the development of human-level broad AI, aka artificial general intelligence. The 20 problems include: the tendency of deep neural networks to make major errors in recognition; the need for a coherent account of generalisation, over- and under-generalisation, and minimising the corrupting effect of ‘dirty data’; how to achieve one-trial learning; how to achieve transfer learning; the need for transparency in the representation and processing of knowledge; and how to eliminate the problem of catastrophic forgetting. In addition to its promise as a foundation for the development of AGI, the SPTI has potential as a foundation for the study of human learning, perception, and cognition. And it has potential as a foundation for mathematics, logic, and computing.

Boosting human Insight by Cooperative AI: Foundations of Shannon-Neumann Logic

We present the logical foundation of an artificial intelligence (AI) capable of dealing with complex dynamic challenges, that would be very hard to handled using traditional approaches (e.g. predicate logic and deep learning). The AI is based on a cooperative questioning game, to boost insight. Insight gains are measured by information, probability, uncertainty (Shannon), as well as utility (von Neumann). The framework is a two-person cooperative iterated Q&A game, in which both players (human, AI agent) benefit (positive-sum): the human player gains insight and the AI player learns to improve its suggestions. Generally speaking, valuable insight is typically gained by asking ’good’ questions about the ’right’ topic, at the ’appropriate’ time and place: by posing insightful questions. In this study, we propose a logical and mathematical framework, for the meanings of ’good, right, appropriate’, within clearly-defined classes of human intentions.

A bunch of sessions: a propositions-as-sessions interpretation of bunched implications in channel-based concurrency

The emergence of propositions-as-sessions, a Curry-Howard correspondence between propositions of Linear Logic and session types for concurrent processes, has settled the logical foundations of message-passing concurrency. Central to this approach is the resource consumption paradigm heralded by Linear Logic. In this paper, we investigate a new point in the design space of session type systems for message-passing concurrent programs. We identify O’Hearn and Pym’s Logic of Bunched Implications (BI) as a fruitful basis for an interpretation of the logic as a concurrent programming language. This leads to a treatment of non-linear resources that is radically different from existing approaches based on Linear Logic. We introduce a new π-calculus with sessions, called πBI; its most salient feature is a construct called spawn, which expresses new forms of sharing that are induced by structural principles in BI. We illustrate the expressiveness of πBI and lay out its fundamental theory: type preservation, deadlock-freedom, and weak normalization results for well-typed processes; an operationally sound and complete typed encoding of an affine λ-calculus; and a non-interference result for access of resources.

Public Value in Public Service Ecosystems

ABSTRACT This article conceptualizes public value and develops a conceptual framework for understanding the nature of public value in public service ecosystems. So far, the conceptualization and research of public value, and its nature in the context of public service ecosystems is incoherent and scant. The theoretical development of this article occurs within the theoretical foundations of service ecosystems, public value, service-dominant logic, and public service dominant logic. It bridges the theoretical domains of value and service ecosystem research between the public and private sector research. It proposes a framework for characterizing the nature of public value at different levels of a public service ecosystem. The main theoretical contribution of this paper is the further conceptualization of public value and its characterization in the context of public service ecosystems. The article makes articulated propositions and provides novel theories for understanding and analyzing public value and public service ecosystems relevant for researchers, public managers, and policymakers of this field.

Волинська шляхта на Віленському сеймі 1566 р.: давні проблеми та спроби їх вирішення (за матеріалами 39-ї книги записів Литовської Метрики)

Th e purpose of the article is the analysis of a separate document from the 39th Book of Records of the Lithuanian Metricа, which concerns the participation of Volyn nobi- lity delegation at the session of Wilno Sejm (Sejm Wileński) in January 1566. Th e methodo- logical foundations of the research are based on the fundamental dogmas of historicism and objecti vity. At the same time, the principle of systematicity was used for a comprehensive study of the document content. Analytical and synthesizing methods were used to generalize the obtained information. Th e scientifi c novelty consists in conducting analytical work with the content of the presented document and its corresponding publication at the end of the article. Conclusions. A delegation from Volyn nobility arrived at Wilno Sejm which had been held early in 1566. Th e ambassadors had the authority to inform the Grand Duke of Lithuania Sigismund II Augustus about various problems in the region and to obtain appropriate solutions to them. Actually, it was structured like this: fi rst the message of the ambassadors, and then the resolution of the ruler. Th e total of 14 positions ("prozb") were presented. Currently, the principle of distri- bution of these “prozb” remains unknown from the document: arbitrary or regular. In terms of content we can establish that the raised issues were related to: military service, payment of cer- tain taxes and implementation of duties, administrative positions, criminal off enses and the stay of military mercenaries in Volyn. Th e analyzed document vividly illustrates one of the aspects of the General Sejm (Sejm Walny) functioning and its competence. Sigismund II August did not ignore any of Volyn ambassadors’ "prozb". However not all of them received an immediate solution. Th e ruler took the opposite position on some issues as for example in the case of Lutsk monitor position in the Council of Lords: Sigismund II August categorically refused to renew the historical antiquity to which the plenipotentiary ambassadors appealed.

The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics

<i>The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics</i>

E. Durkheim’s concept of sacredness

E. Durkheim’s concept of sacredness as formulated in The Elementary Forms of the Religious Life aims at explaining why and how an aggregate of people becomes ‘a single whole’ and reproduces itself. This concept is the logical foundation of Durkheim’s ‘sociological holism’ for it focuses, according to T. Parsons, on ‘the core of the social system’. The principles of this concept are opposite to the principles of ‘methodological nominalism and individualism’ of the British social anthropology as expressed in the theory of animism. Durkheim defines the sacred as an ‘impersonal force’, impersonal ‘collective being’, ‘collective soul’ created and reproduced on the religious cults. The individual principle is reduced by Durkheim to the animal and wild which can be understood only as a part of the ‘collective being’ in primitive societies. In defining the nature of religious rituals, Durkheim relied on the concept of ritual by W. Robertson-Smith, which defines the main meaning of cults as the ‘union’ of adepts with the deity and each other. By removing the deity as a transcendental principle, Durkheim reduced the meaning of religious rituals to the reproduction of social unity, solidarity. Durkheim’s theory of sacredness, like its opposite - the theory of animism, is based on the concepts of the philosophy of the Modern Time, which determined the anthropomorphization of consciousness and confusion of terms ‘person’ and ‘individuality’. The significance of Durkheim’s concept should not be identified in the positivist perspective - as an explanation of facts unexplained by alternative theories. In such an interpretation, this concept was criticized and rejected by most scholars. However, it is important as a part of ‘social engineering’ which changed the intellectual environment, including the scientific community, in a specific, ideologically leftist direction.

Logical Realism and Ezumezu Logic

This paper examines the metaphysical status of Ezumezu logic in the direction of logical realism. While presenting Ezumezu logic as a prototype of African logic, Chimakonam makes statements that somewhat entail logical monism. Using the method of critical analysis of related literature, the paper argues that presenting Ezumezu logic as one of the prototypes of African logic while at the same time making claims that elevate it to a hegemonic status, gives rise to what is regarded in the paper as the monist-pluralist paradox. Drawing lessons from Abakedi’s ID paradox, the paper argues that a monist logical foundation for African logic cannot be consistently defended without paradoxes. The paper proposes that different African philosophies should be grounded by different African logics such that one need not be trained in one particular prototype such as Ezumezu logic or argue in conformity to it to qualify as an African professional or scholar.

Mechanizing Matching Logic In Coq

Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive definitions and linear temporal logic. In addition, it serves as the logical foundation of the K semantic framework, which was used to build practical verifiers for a number of real-world languages. Despite being a fundamental formal system accommodating substantial theories, matching logic lacks a general-purpose, machine-checked formalization. Hence, we formalize matching logic using the Coq proof assistant. Specifically, we create a new representation of matching logic that uses a locally nameless encoding, and we formalize the syntax, semantics, and proof system of this representation in the Coq proof assistant. Crucially, we prove the soundness of the formalized proof system and provide a means to carry out interactive matching logic reasoning in Coq. We believe this work provides a previously unexplored avenue for reasoning about matching logic, its models, and the proof system.