Traditional Logic Research Articles

Semantic Model for Fragment of Hindi (Part 2)

This paper proposes a formal model for semantic analysis of a fragment of the Hindi language. This paper uses referential noun phrases, transitive and intransitive verb phrases and logical constants to compute the meaning of its sentences generated from the Hindi part-of-speech-tagged corpus features. The paper presents cases of conjunction and negation enriched with idempotent laws that provide semantic computation of simple and complex well-formed formulas. Our system works for any model, with one such model described in our glossary. It deals with the set-theoretic study of essential syntactic categories of Hindi, suggesting the suitability of our rule-based syntactic arrangement and model-based semantic computation by implementing them through an in-house software tool.

Direct Reduction of Syllogisms with Byzantine Diagrams

The paper explores the potential of Byzantine diagrams in syllogistic logic. Byzantine diagrams are originated by Byzantine scholars in the early modern period to use as tools for teaching and studying Aristotelian logic. This paper presents pioneering work on employing Byzantine diagrams for checking syllogistic validity through reduction.

Security and Privacy Column

Cryptographic protocols are really hard to design: they mix difficulties stemming from distributed systems, rely on cryptographic primitives and need to provide complex guarantees in the presence of an arbitrary attacker running in parallel. Rigorous security proofs are basically the only hope to avoid design flaws as witnessed by numerous examples. This has been recognized since the early 80's and two main approaches have been actively developed since. The computational model is rooted in complexity theory and relies on a reduction of the security of the protocol to a security assumption of a cryptographic primitive which itself may rely on the hardness of a computational problem. Attackers are any probabilistic polynomial time Turing Machines (PPTMs). A security proof in this model provides strong guarantees. However, getting proofs in such a detailed model correct is challenging. The symbolic model takes a different approach: messages are modeled as first-order logic terms and cryptographic primitives such as encryption schemes are idealized. Typically, only the intended functionality of an encryption is modeled by an equation such as dec(enc(m,k),k) = m to state that decryption and encryption cancel out when the same key k is used. Crucially, only the properties that are explicitly stated hold and the adversary actions are restricted to those. At the cost of being more abstract this approach is amenable to automation and tools nowadays succeed in proving industrial protocols, such as TLS or Signal.

Атеология Жоржа Батая и негативная суверенность

The article presents a brief essay on the analysis of three key concepts in the philosophy of Georges Bataille – heterology as the logic of exclusion, (a-)theology as an atheistic understanding of the death of God and the concept of ‘negative’ or ‘sacrificial’ Sovereignty. It seems that the key to understanding the various and heterogeneous philosophical, literary-poetic, cultural-anthropological and socio-economic concepts of the French thinker is the prism of the heterological logic of exclusion, which opposes the internalization of the dominant ontological discourse. The heterology or ‘logic of exclusion’ used by Georges Bataille, is not so much a negative version of the traditional logic of ‘inclusion’, but is a logic of alternative extremes. It is precisely by striving to overcome the dominant metaphysical universalism of the general order of being (embodied, according to Bataille, in the concept of ‘being’ / ‘die Existenz’ in the philosophy of Martin Heidegger). In an effort to overcome the dominant metaphysical universalism of the general order of being, Bataille turns to various kinds of ‘denials’ and extremes – the left sacred or the sanctity of ‘foulness’, the metaphorical of the disgusting, erotic and violent forms of transgression, the cultivation of the experience of inner abandonment and ultimate despair, and, also, to his own concept of ‘sacrifice’, serving as a guide to the world of sovereign domination. Thus, developing his concept of metaphysical ‘sovereignty’, Bataille turns not only to the existential, but also to the political sphere, largely contrasting his ‘metaphysics of sacrifice’ with the concept of ‘metaphysical domination’ of the German political and legal theorist Carl Schmitt. The nihilistic energy drawn from Friedrich Nietzsche and the ‘metaphysical negation’ taken from Hegel’s dialectic through the interpretation of Alexander Kozhev is used by Bataille for the purposes of his own ‘heterological’ logic of exclusion, desubjectivization and dissolution. However, negation for Bataille is not a target for itself, but a methodological tool on the way to the ‘Other’ excluded from any ontosemantic order.

THE GLOBAL INTERNAL AUDIT STANDARDS – OLD WINE IN NEW BOTTLES?

In this paper the authors suggest that the Global Internal Audit Standards (the IIA’s Standards) issued in January 2024 resemble the placing of old wine in new bottles, insofar as they represent a missed opportunity to truly transform rules-driven Standards into principles-based Standards. This co-authored essay provides two perspectives on the revised Standards: although written independently, and originating from different premises, they both arrive at similar conclusions in favor of principles-based Standards. The authors suggest that the prescriptiveness of the IIA’s Standards continues to petrify individual judgment and critical reasoning, narrowing intellectual and moral horizons in modern internal auditing. By following rules, the focus of internal auditors is misguided toward form over substance, encouraging a checklist-based mind-set that diminishes moral agency. The authors therefore advocate principles-based Standards because they tend to encourage the internal auditor to apply abstract concepts to concrete examples. The authors see unexploited potential inherent in the encouragement of individual judgment, especially when entering the pioneering zone of the pragmatic implementation of the IIA’s Standards – a zone characterized by complexity, chaos, ambiguity, and trade-offs, in which internal auditors are compelled to address WHAT IF types of question. Although the two authors converge in their overall conclusion, they offer alternative reasons for their views, and differing (though perhaps not entirely irreconcilable) suggestions for the future. Lenz draws our attention, in our VUCA and BANI world, and in the age of artificial intelligence, to rethink what it means to be human, and to rethink the skills that make internal auditors strong, influential, and effective. He presents the Trust Triangle that places authenticity as an anchor term to the discourse. Effective internal auditors must have strong human skills: he therefore suggests a model with five competence blocks of the most important skills of the effective internal auditor. There is no need for humans who behave like robots. The refined leitmotif of “The Gardener of Governance: Our nature is Nurture” is suggested as purposeful for internal auditing. O’Regan proposes a future focus on the rigorous application of traditional logic to internal auditing. He suggests that such an emphasis on logic might offset the socially-constructed, slippery, and ever-changing knowledge base of internal auditing, thereby facilitating the development of principles-based standard-setting.

Gudina Tumsa’s Approach to Human Rights: a Dialogue between Anthropology and Christology

I shall present Rev. Gudina’s approach to the crucial issue of human rights. Put rightly, the very phenomenon that marks that particular period in Ethiopian history was the Marxist [-Leninist] ideology. Marxism emphasized social and economic issues more than anything to the extent of seeing human beings but in terms of this internal logic. Knowing the dangers of this socio-economic view of human beings, Rev. Gudina developed an approach to understanding of human nature from an informed [theological] anthropological perspective. Based on his theological-anthropological analysis of human nature he developed a stance on human rights. But theological anthropology was not the only starting point of Rev. Gudina’s perspective on human rights. In this paper, I shall discuss that Rev. Gudina’s approach to human rights was the result of his creative holding of a dialog between theological anthropology and Christology.

Thinking Scripts

Chinese traditional characters share with Peirce’s existential graphs the fact of being endowed with an object-language that they describe through a nonlinear syntax and in an iconic way. Here iconicity is not restricted to images and perceptive similarity since diagrams and graphic metaphors are iconic too. The graphs are shown to be a borderland between Western traditional logic and Chinese traditional writing and culture, so the écart (Jullien’s concept for cultural distance) between characters and graphs is preserved even though graphs break with the Western prejudice in favor of conventionality at the expense of iconicity in logical systems. The take-home lesson for the study of writing systems is to substitute the orality-writing duality with the interplay among orality, writing, and pictures thus shifting from a linguistic typology to a semiotic one.

The Art of Conjecture: A Window into the Heart

In 1561, Francesco Casoni published De arte, ac ratione in criminum causis disserendi, a dialogue that offered judges a rigorous method of investigation in criminal cases in which eyewitness testimony or a confession was lacking. Typically, in such cases, judges relied on their own personal arbitrium (discretion) in deciding whether to remand defendants to torture or sentence them to the gallows. Drawing not only on Aristotelian logic and classical rhetorical theory but also on the works of contemporary philosophers, Casoni used his dialogue to lay out a rigorous interpretative methodology. To Casoni, the careful elaboration of inferences, along with the proper use of loci, and a reasoned interpretation of signs (both natural signs and signs of conscience) enabled judges to read, through the opaque surfaces of the body, the interior states of those brought into their courts on suspicion of crimes—and to do so without resorting to torture.

Особенности толкования термина «следование» у И. Канта

Modern formal logic, which is based on Kant’s logical project, interprets logical consequence as formal, which leads to substantive paradoxes that combine any thoughts at all and so to the loss of consequence as such. Beginning with A. Tarski, modern history of logic brings the problem of logical consequence into the realmof search for the relation of consequence, or grounding. In his doctoral dissertation on the nature of logical formality J. MacFarlane claims that the paradoxes of formal theories of logical consequence stem from the loss of grounding by the transcendental system of logic in the post­Kantian logical tradition. Arguably, analysis of logical terminology of consequence in Kant’s seminal works — Critique of Pure Reason, Critique of the Power of Judgment — in comparison with the terminology of earlier works, Prolegomena and lectures on logic attributed to him will clarify the question of the relation oflogical consequence in the formal and non­formal sense. The key concept of consequence in Kant’s terminology is Folgerung, which denotes ‘following’ in logical and non­logical contexts. I have also analysed related concepts: Folge, Abfolge, folglich etc., established dif- ferences between logical terms with similar meaning ‘inference’ (Schluss) and ‘conclusion’ (Konklusion). Finally, I make an attempt to formulate the problem of logical consequence in formal logic through the logical terms Schlussfolge, Folgerung and Konsequenz. On the strength of my analysis I propose to consider Kant’s consequence (Folgerung) to be a concept of transcendental logic that reflects the relation of consequence and grounds formal consequence.

Using the Five Safes to structure economic evaluations of data governance

Abstract As the world has become more digitally dependent, questions of data governance, such as ethics, institutional arrangements, and statistical protection measures, have increased in significance. Understanding the economic contribution of investments in data sharing and data governance is highly problematic: outputs and outcomes are often widely dispersed and hard to measure, and the value of those investments is very context-dependent. The “Five Safes” is a popular data governance framework. It is used to design and critique data management strategies across the world and has also been used as a performance framework to measure the effectiveness of data access operations. We report on a novel application of the Five Safes framework to structure the economic evaluation of data governance. The Five Safes was designed to allow structured investigation into data governance. Combining this with more traditional logic models can provide an evaluation methodology that is practical, reproducible, and comparable. We illustrate this by considering the application of the combined logic model-Five Safes framework to data governance for agronomy investments in Ethiopia. We demonstrate how the Five Safes was used to generate the necessary context for a more traditional quantitative study, and consider lessons learned for the wider evaluation of data and data governance investments.

О соотношении логики и философии математики Канта

For Kant’s theoretical philosophy, logic was not at all a separate or peripheral discipline. Quite the opposite, it can be argued that formal general logic became a kind of a paradigm of his transcendental philosophy, and its central ideas are due to the specific nature of Kant’s logical concept. Kant’s philosophy of mathematics is of particular interest, since one of the central questions of his Critique of Pure Reason is the question of how mathematics is possible as a science of universal and necessary truths. Kant’s theoretical philosophy cannot be understood without his mathematical concept, since the type of synthesis that, according to Kant, underlies mathematics is the same as for all other objects of perception. In addition, in his transcendental philosophy, the difference between the philosophical and mathematical methods turns out to be fundamental. Undoubtedly, Kant’s original logical concept, including the construction of a new and non-standard transcendental logic, could not but have a significant impact on the main characteristics of his philosophy of mathematics. Their mutual influence may be of interest to anyone who wants to find the key to understanding Kant’s philosophy in a more general context. The following central provisions of Kant’s philosophy of mathematics, formulated by him in “The Transcendental Aesthetic”, “The Transcendental Doctrine of Method” and other small fragments of the Critique of Pure Reason, can be distinguished: firstly, it is the idea of formality of both mathematical and any rational cognition (just as formal logic is the basis of “empty” logical forms, mathematics is formal, since it deals with pure a priori forms of intuitions); secondly, it is the doctrine of the synthetic a priori character of mathematical truths; thirdly, it is his idea that mathematical knowledge is realized through the construction of concepts, and, finally, it is the idea of the direct and necessary connection of mathematical knowledge with pure forms of intuitions, i.e. with extremely general areas of empirical experience. At the same time, the apparatus of traditional logic available to Kant had significant limitations that did not make it possible to adequately represent mathematical knowledge. On the one hand, the features of Kant’s interpretation of formal logic and the transcendental logic developed by him in his critical philosophy determine the constructive and synthetic nature of mathematical knowledge; on the other hand, the non-trivial philosophy of mathematics developed by him is a response to the limitations of traditional logic and an attempt to overcome them. The construction of mathematical concepts in pure a priori intuition allows one to go beyond the limits of these limitations in mathematical knowledge, which had exceptional consequences for the history of modern philosophy of mathematics and the history of the foundations of mathematics. It must be assumed that the key features of Kant’s logical concept and his philosophy of mathematics have not yet exhausted their heuristic possibilities for topical research in these areas of science and philosophy.

Reforestation pipeline: case for quality management of NIR-region grading of Scots pine seeds and FLR-algorithm for information processing

When controlling the process of improving the quality of seeds by separating on a spectrometric basis, the primary information about the state of Scots pine seeds is carried by the wavelengths of optical fluxes and their amplitudes. The algorithm for analyzing the required characteristics of small forest seeds in the infrared range is a corresponding sequence of logical terms that provide the ability to determine the specified seed parameters by a combination of spectral frequencies and light flux amplitudes taken from the corresponding photodetectors. At ΔС = 0.5, the efficiency of the algorithm was 77.6 %, and at ΔС = 0.9, respectively, 99.5 %. In this regard, the choice of ΔС is the result of a compromise between the cost of rejection of high-quality seeds and losses when using unrecognized low-quality seeds and it is made according to the results of relevant experiments.

On the paradoxical behavior of divergent series

This paper presents some considerations on summation method on infinite divergent series. Irrefutably divergent series don’t have a sum in the traditional logic of the term. However there are extensions, where transformed definitions apportion changed values to the same divergent series and they rarely have agreeable properties. Particularly, at beginning and manipulating these instinctively, it easily comes across nasty paradoxes. In this article for any odd prime p, the divergent series and on using this representation for further leads to a paradoxical bewildering novel formula which evidently contradicts the basic principles of arithmetic and the definition of a divergent series identical to Ramanujan paradox. Illustrations to support this illogicality result are discussed analytically and demonstrated graphically.

Aletik Bağıntılar Işığında Mantık Eklemlerinin Anlamları

One of the central questions in 20th-century discussions within logic and philosophy of language is where logical constants, specifically propositional connectives, get their meaning from. What kind of determination/justification bond is found between the inference rules peculiar to a given connective and the meaning of that connective? Are these rules justified by it, or rather do they contribute to its construction? An observation made by G. Gentzen, who founded in the 1930s the proof-theoretical approach at large, triggered a view (called by some logical inferentialism) that gives a remarkable answer to the above question: the meaning of a logical constant in a logical language is provided, not by some sort of representational content, but by the inferential norms that govern its overall use. In 1960 A. N. Prior fictionalized as a counter-instance the connective tonk solely using a couple of inference rules, a connective capable of overthrowing the system of deduction; N. Belnap’s 1962 reply in the form of an analysis of the tonk problem opens the way to discussions in logic-cum-philosophy of language with important outcomes. The present little study can be read as some further deflation of the tonk problem with a relatively unconstrained inferentialistic view of the matter. The two main theses of the study are (i) that the problem posed by tonk-like connectives can be captured, more simply than in Belnap’s (otherwise correct) analysis, through inferential relations of a certain type which will be dubbed alethic relations; and (ii) that Prior’s challenge, brought to completion in whichever way, cannot give any result against the inferentialist conception.

Metropolitanization through making ‘new metropolitan plans’ in China

Although mega-city regions have attracted wide attention in China, recent ‘metropolitanization’ at the multi-city scale is poorly understood. To tackle the void, this paper examines the emergent ‘metropolitan plans’ (dushiquan guihua) since 2019 and identifies a paradigm shift in metropolitanization from ‘territorial urbanization’ to ‘multi-city regionalism’ in China. We find that 1) as a fuzzy and dynamic concept, the metropolitan region has been mainly employed as a policy object for state rationalities and has been upscaled from a city region scale to a multi-city scale; 2) regarding planning practices, the new metropolitan plans function as an overall collaborative framework to support priority tasks for city regionalism in a shorter term rather than formulating long-term spatial strategies; 3) as space of governance, the recent state-orchestrated metropolitan region reflects the newest round of state rescaling process to cope with domestic uneven development and urban issues through ‘urban unification’, and its materialization heavily relies on concrete cross-boundary projects delivery and coordination through soft governance. These findings not only provide conceptual clarity and relational understandings of the metropolitanization process but also exemplify the distinctiveness of the Chinese metropolitanization approach in terms of scalar logic, planning style, and associated governance mechanisms. This paper furthers the understanding of the divergence and diversity of metropolitan planning and governance practices in different political-economic circumstances.

Thinking through Sets: Exploring How Chinese Pictographic Language Shapes Chinese Logic

The author of this paper argues that ancient Chinese thinkers practiced an alternative logic that is significantly different from Aristotelian logic. The paper has two objectives: 1) to clarify what Chinese logic looks like; 2) to re-evaluate the wisdom in classic texts with a clear understanding of Chinese logic. The author uses two major approaches in her reasoning: an etymological approach and logic of sets. An etymological study shows that Chinese pictographic characters were created according to sets - the collections of characters. The author examines how Chinese pictographic language shapes ancient Chinese thinkers’ thinking patterns and provides evidence that the habit of thinking in sets could naturally shape a practice of a primary logic of sets. Borrowing some expressions and symbols from modern Set Theory, the author demonstrates how the logic of sets was practiced by Gongsun Longzi, Confucius, Zhuangzi, as well as Chinese mathematicians in their teachings and reasoning. A theory of sets provides help with a much better understanding about reasoning methods in ancient Chinese thinkers’ minds, so that one can evaluate their wisdom fairly. Understanding Chinese logic as it is provides a fruitful opening for new research in Comparative Philosophy. Keywords: set, etymology, membership, Chinese logic, and comparative philosophy

A Deductive System for Boole’s ‘The Mathematical Analysis of Logic’ and Its Application to Aristotle’s Deductions

George Boole published the pamphlet The Mathematical Analysis of Logic in 1847. He believed that logic should belong to a universal mathematics that would cover both quantitative and nonquantitative research. With his pamphlet, Boole signalled an important change in symbolic logic: in contrast with his predecessors, his thinking was exclusively extensional. Notwithstanding the innovations introduced he accepted all traditional Aristotelean syllogisms. Nevertheless, some criticisms have been raised concerning Boole’s view of Aristotelean logic as the solution of algebraic equations. In order to circumvent such criticisms, we show here how Boole’s conclusions may be deduced from the axioms and inference rules proposed in his pamphlet, from which Aristotle’s deductions in Prior Analytics (including those that are completed through an impossibility) can be stated as theorems. We clarify his method for dealing with both universal and particular premises by means of his symbol and demystify some criticisms concerning the way he expressed particular premises. Boole’s conclusions for some of those premises for which according to Aristotle there is no deduction are also discussed. The deductive system presented here has the potential to provide a new perspective on Boole’s approach to logic in The Mathematical Analysis of Logic.

Efficient co-planar adder designs in quantum dot cellular automata: Energy and cost optimization with crossover elimination

Quantum dot cellular automata (QCA) stands as a highly promising nanotechnology, capable of outperforming conventional CMOS technology. Leveraging its advantages, this paper addresses the challenges in adder circuits related to size, delay, and cost by integrating QCA technology. A novel layout for a co-planar full adder in QCA is introduced, featuring a half-adder design with 23 cells in a single layer without any crossover, achieving a delay of 0.25 clock cycles. By utilizing inter-cellular effects inherent in QCA technology, the presented designs offer significant improvements in a variety of design metrics, and a cost efficiency of 64.3%, distinguishing them from traditional logic design approaches. Additionally, in order to ensure an efficient routing channel and a consistent structure of the adder design, a Universal, Scalable, and Efficient (USE) clocking scheme has also been employed. The adder design is further used to build 4-bit and 8-bit Ripple Carry Adders. An extensive study on energy dissipation using QCADesigner-E and QCAPro tools is conducted for three tunneling energies (0.5 Ek, 1 Ek, and 1.5 Ek). The full adder design showcases substantial improvement in energy to delay cost when compared to the closest reported design, achieving improvements of 91.66%, 89.03%, and 88% at 0.5 Ek, 1 Ek, and 1.5 Ek, respectively. The results highlight enhanced circuit efficiency and streamlined layouts, outperforming existing models and offering substantial benefits to high-performance and energy-efficient computing systems.

On the impact of fuzzy-logic based BDI agent model for cyber–physical systems

Cyber–Physical Systems (CPS) interconnect embedded computing technologies into the physical world, forming a complex, multi-disciplinary, physically-effective system. However, interacting with the physical world brings unpredictability, as real-world events are uncertain and dynamic by its nature. Consequently, CPS must be capable of reasoning about these unpredictable situations and adapt their behaviour accordingly. Therefore, it is essential to enhance the intelligence of CPS to overcome this challenge effectively, leading to the development of smart CPS. As an approach, a reasoning mechanism can support the system to reason about its state and actions to handle unpredictable changes. In this study, we employ intelligent Belief-Desire-Intention (BDI) agents to achieve this objective. Nevertheless, traditional logic approaches based on crisp numbers, which are used in typical BDI agents, may not effectively handle uncertainty. Hence, the reasoning mechanism can be extended with fuzzy logic to deal with run-time uncertainties. Thus, the target system’s suitable inputs, outputs and reasoning phases are fuzzified to indicate the impact of the fuzzy logic on the CPS. To this end, an architecture is provided to deploy BDI agents integrated with a fuzzy reasoning model for handling imprecise information and improving process control. The approach is validated and evaluated on a complex case study with a heterogeneous structure controlled by multiple agents, namely the “smart production system”. The multiple modular and end-to-end experiments conducted reveal that, on the whole, the fuzzy BDI agent outperforms the classical one by up to three times, with only requiring approximately 10% more computation time.

مراتب التأويل في إرث الفكر البلاغي

This study aims to show the interpretive thought of the masters of rhetoric, especially when explaining the summary, based on their interpretive pauses for time in Qur’anic texts in particular and linguistic contexts in general regarding the adverbial situation such as expressing the future in the past and vice versa. The study also embodies a condensed rhetorical interpretive document par excellence, taken from The Bride of Weddings and Al-Mutawil and Al-Awal to explain Al-Khatib Al-Qazwini’s summary as a model in the chapter on attribution and restriction by condition, to embody a model of rhetorical thought towards linguistic structures, their timing, and the elaboration of their meanings. It also attempts to highlight the method used in interpretation based on an assumption and its rebuttal or starting from the conclusion to the premise or vice versa, due to what distinguished the masters of the commentators of summary in terms of organized logic and philosophical thought, for which their counterparts - the owners of the literary rhetorical school - have always held them accountable for the stagnation and backwardness of rhetoric. In this study, there is proof and response to what is common among specialists in the study of linguistics in the West, that the Semitic languages, including Arabic, lack the indication of time with their verbs. Arabic has only two verbs, either completed or unfinished - from their point of view - as it does not care about the forms of the three verbs and their branches. This study, even if it is not specialized in temporal actions, nevertheless talks about time in multiple forms to prove and support that the language was able to embody time with words such as forenoon, sunrise, dawn, early morning, and morning, despite the difficulty in distinguishing between these times in many cases. In other languages, except with sentences and structures, it is not natural for a people to reach a sense of time and then have their words devoid of indication of the feeling in various places.