Ternary Logic Research Articles

The Roles of Rule Type and Word Term in the Deductive Reasoning of Adults with and without Dyslexia.

Despite its importance to everyday functioning, reasoning is underexplored in developmental dyslexia. The current study investigated verbal deductive reasoning on the Wason selection task, not previously used in dyslexia research despite its well-established pedigree. Reasoning rule was manipulated, with the conditional rules varying in the logical values presented. The word frequency and imageability of the word terms was also manipulated. Twenty-six adults with dyslexia and 31 adults without dyslexia completed Wason selection task problems. No group difference in reasoning accuracy or completion time was found. However, the participants were most accurate when reasoning with the rule type "If p, then not q" and least accurate with the rule type "If p then q". More trials were also answered correctly when the word terms were highly imageable but of average word frequency. These findings are in line with the general reasoning literature. Dyslexia status did not interact with either rule type or word term type. The study expands upon previous research by testing verbal deductive reasoning in dyslexia, highlighting the role of imageability in facilitating reasoning performance for all, regardless of the presence or absence of dyslexia. Implications for the design of educational materials are considered.

Design and Simulation of Balanced Ternary Priority Encoder

The priority encoder is a frequently used circuit in binary logic and is mostly used for interrupt handling and other priority resolving tasks. On the other hand, Ternary computing has tremendous potential for handling a wide variety of functions involving large range of numbers, whereas, the literature is confined to very basic functions. The proposed balanced priority encoder circuit that uses three logic symbols i.e.−1,0 and 1. In this study, we develop the design and architecture of a Ternary Priority Encoder circuit with an estimation of its time complexity. The intricacy of the circuit under consideration is supposed to highlight the capabilities of the ternary logic system. The flexibility of the circuit lies in its implementation using simple binary counterparts. As there is no simulator available for Ternary Logic, we have developed a Balanced Ternary Logic Simulator which is freely available from https://github.com/Aggtur11/Ternary-Logic-Simulator. The logic behaviour of the proposed priority encoder circuits is verified using the developed simulator.

The Value Logic of Digital Technology Empowering the Deep Integration of Culture-tourism in Huaian Section of Grand Canal

In response to the problems of weak identification of cultural and tourism products, insufficient driving force of the cultural and tourism industry to economic development, and low level of dissemination and innovation of culture in Huaian section of Grand Canal, it is proposed that value innovation is the internal logical path to promote cultural and tourism integration and achieve sustainable development of products, industries, and culture of cultural and tourism; The empower- ment of digital technology is an external logical path to promote the deep integration of cultural and tourism and achieve iteration and spiral development of products, industries, and cultural of cultural and tourism. It is revealed that the value logic of the deep integration of cultural and tourism and is used to guide the development of products and industries , the culture utilization of cultural and tourism in the Huaian section of Grand Canal. The aim is to make the cultural-tourism products fresh, the cultural-tourism industry revitalized, and the cultural-tourism spirit survival long-term.

Aristotle’s Sea Battle, Excluded Middle and Bivalence

In this paper, I present a formal reconstruction of the classical argument for fatalism set forth by Aristotle in On Interpretation 9. From there, I expose two different formal solutions for avoiding the unwanted conclusion based on the traditional interpretation of Aristotle’s rejection of the Principle of Bivalence: On the one hand, Łukasiewicz's three-valued logic and, on the other hand, supervaluation semantics. I also address some criticisms made against these two proposals. To finish, I remark on some alternative interpretations of Aristotle’s intentions maintaining that the Stagirite philosopher rejected fatalism without abandoning the Principle of Bivalence.

Designing Unconventional Molecular Ternary INHIBIT Logic Gate and Crafting Multifunctional Molecular Logic Systems.

The paper describes an improved method for building flexible interswitchable logic gates such as rare-type molecular ternary INHIBIT and combinational logic circuits using a specially designed pyridine-end oligo-p-phenylenevinylene compound featuring alkyl substituents (-C16H33) in a THF medium. The probe molecule showed distinct opto-chemical signals upon interaction with Cu(II) and Hg(II) in THF medium. It is interesting to note that the presence of certain anions (S2-, I-, and CN-) could specifically mask the interaction of either of these metal ions or both. The most exciting thing is that we used a completely new gate design technique to construct a rare-type ternary INHIBIT logic gate using Cu(II), Hg(II), and CN- ions as three chemical inputs. With the identical set of chemical inputs, two more ternary combinational logic circuits were created out of these case-specific, independent reversible and irreversible spectroscopic studies. Finally, we were able to design adaptive molecular logic systems composed of several logic gates, including NOR, AND, IMPLICATION, INHIBIT, TRANSFER, and COMPLEMENT, that in this specific situation change the sort of logic sense by effortless optical toggling.

Usability of visualizing position and orientation deviations for manual precise manipulation of objects in augmented reality

Manual precise manipulation of objects is an essential skill in everyday life, and Augmented Reality (AR) is increasingly being used to support such operations. In this study, we investigate whether detailed visualizations of position and orientation deviations are helpful for AR-assisted manual precise manipulation of objects. We developed three AR instructions with different visualizations of deviations: the logical deviation baseline instruction, the precise numerical deviations-based instruction, and the intuitive color-mapped deviations-based instruction. All three instructions visualized the required directions for manipulation and the logical values of whether the object met the accuracy requirements. Additionally, the latter two instructions provided detailed visualizations of deviations through numerical text and color-mapping respectively. A user study was conducted with 18 participants to compare the three AR instructions. The results showed that there were no significant differences found in speed, accuracy, perceived ease-of-use, and perceived workload between the three AR instructions. We found that the visualizations of the required directions for manipulation and the logical values of whether the object met the accuracy requirements were sufficient to guide manual precise manipulation. The detailed visualizations of the real-time deviations could not improve the speed and accuracy of manual precise manipulation, and although they could improve the perceived ease-of-use and user experience, the effects were not significant. Based on the results, several recommendations were provided for designing AR instructions to support precise manual manipulation.

19F NMR Probes: Molecular Logic Material Implications for the Anion Discrimination and Chemodosimetric Approach for Selective Detection of H2O2.

Detection and discrimination of similar solvation energies of bioanalytes are vital in medical and practical applications. Currently, various advanced techniques are equipped to recognize these crucial bioanalytes. Each strategy has its own benefits and limitations. One-dimensional response, lack of discrimination power for anions, and reactive oxygen species (ROS) generally limit the utilized fluorescent probe. Therefore, a cutting-edge, refined method is expected to conquer these limitations. The use of 19F NMR spectroscopy for detecting and discriminating essential analytes in practical applications is an emerging technique. As an alternative strategy, we report two fluorinated boronic acid-appended pyridinium salts 5-F-o-BBBpy (1) and 5-CF3-o-BBBpy (2). Probe (1) acts as a chemosensor for identifying and discriminating inorganic anions with similar solvation energies with strong bidirectional 19F shifts in the lower ppm range. Probe (2) turns as a chemo dosimeter for the selective detection and precise quantification of hydrogen peroxide (H2O2) among other competing ROS. To demonstrate real-life applicability, we successfully quantified H2O2 via probe (2) in different pharmaceutical, dental, and cosmetic samples. We found that tuning the -F/-CF3 moiety to the arene boronic acid enables the π-conjugation, a crucial prerequisite for the discrimination of anions and H2O2. Characteristic 19F NMR fingerprints in the presence of anions revealed a complementary implication (IMP)/not implication (NIMP) logic function. Finally, the 16 distinct binary Boolean operations on two logic values are defined for "functional completeness" using the special property of the IMP gate. Boolean logic's ability to handle information by utilizing characteristic 19F NMR fingerprints has not been seen previously in a single chemical platform for detecting and differentiating such anions.

The Generative Logic, Main Content and Contemporary Value of the Ecological Thought of Marx and Engels

The ecological thought of Marx and Engels is an important part of Marxist theory, and is the theoretical guidance and guide to action for the harmonious development of human and nature in contemporary human society. The ecological thought of Marx and Engels is formed on the basis of in-depth criticism and reasonable absorption of the natural thought of Hegel and Feuerbach in the context of the age of the advancing industrial revolution. Marx and Engels have important theoretical and practical value in contemporary thinking and solving ecological problems, as they demonstrate the priority of nature, the dialectical relationship between humans and nature, the capitalist system as the root of ecological crisis, and communism as the main content of achieving an ideal society of harmonious coexistence between humans and nature.

Truth diagrams for some non-classical and modal logics

This paper examines truth diagrams for some non-classical, modal and dynamic logics. Truth diagrams are diagrammatic and visual ways to represent logical truth akin to truth tables, developed by Peter C.-H. Cheng. Currently, it is only given for classical propositional logic. In this paper, we establish truth diagrams for Priest's Logic of Paradox, Belnap–Dunn's Four-Valued Logic, MacColl's Connexive Logic, Bochvar–Halldén's Logic of Non-Sense, Carnielli–Coniglio's logic of formal inconsistency as well as classical modal logic and its dynamic extension to shed light on the semantic behaviour of some non-classical and modal logics.

Efficient Ternary Logic Circuits Optimized by Ternary Arithmetic Algorithms

Efficient Ternary Logic Circuits Optimized by Ternary Arithmetic Algorithms

Disruptive market-shaping processes: Exploring market formation for autonomous vehicle solutions

In the race toward autonomous vehicle solutions, providers engage in disruptive market-shaping processes to overcome barriers to commercialization and trigger market formation. This study investigates how disruptive market-shaping processes unfold by employing a multiple case study of 10 AVS providers. Our findings reveal a disruptive market-shaping process comprising four dimensions: shaping the value logic, nurturing the demand side, forging ecosystem alliances, and catalyzing institutional changes. Furthermore, we analyze the temporal unfolding of these activities to illustrate a comprehensive market-shaping process comprising three phases: market exploration, market preparation, and market experimentation. We make significant contributions to the market-shaping and AVS literature. By showing empirically how disruptive market-shaping processes unfold, we refine existing knowledge on the broader market formation stage, anchoring it to the emergence of new markets. Our framework offers micro-level insights into the sequencing of activities and phases embedded in shaping new markets. We argue that successful disruptive market shaping is contingent on creating an attractive market value proposition. Finally, we identify the foundational activities required to overcome market barriers and advance the commercialization of autonomous solutions. We find that granular systems logic reveals AVS's true value, questioning traditional market logic and paving the way for a sustainable, autonomous future.

Design of a Ternary Logic Processor Using CNTFET Technology

Design of a Ternary Logic Processor Using CNTFET Technology

Where George Spencer-Brown went wrong – re-entry recalculated

PurposeThe paper uncovers a mathematical error in George Spencer-Brown's genesis of re-entry. It distinguishes between the two interpretations of re-entry presented in “Laws of Form”: recursive versus sequential. The Indeterminacy inferred by George Spencer-Brown from his recursive genesis of re-entry is refuted in three different ways. The calculation of the Modulator from “Laws of Form” demonstrates that only the sequential interpretation of re-entry is reasonable. This contributes to the demystification of re-entry and enables a deeper understanding. Finally, six differences between the concept of form from “Laws of Form” and Niklas Luhmann's sociological systems theory are presented.Design/methodology/approachMethodologically, the paper uses the ternary logic of discrete mathematics, which extends {0, 1} by “don't care” to {0, 1, -}. George Spencer-Brown's Indeterminicy is refuted by using three different methods: complete induction, Theorems 14 and 15 and the software XBOOLE. For the calculation of the Modulator, the only practical application of re-entry in “Laws of Form”, techniques from automata theory are used.FindingsThe paper reveals a mathematical error in George Spencer-Brown's genesis of the re-entry of “Laws of Form” and refutes the assumption of Indeterminicy. The analysis of the only practical application of re-entry presented by George Spencer-Brown shows that the functioning of this Modulator can only be described correctly with the sequential interpretation of re-entry.Originality/valueThe paper emphasizes the interdisciplinary potential of sociology and information technology and provides methods and tools of discrete mathematics for use in the analysis of the works of George Spencer-Brown and Niklas Luhmann.

Investigation of an LED Strip Controller Based on a PWM Driver and a PIC Series Microcontroller

Investigation of an LED Strip Controller Based on a PWM Driver and a PIC Series Microcontroller

Paraconsistency in Non-Fregean Framework

AbstractA non-Fregean framework aims to provide a formal tool for reasoning about semantic denotations of sentences and their interactions. Extending a logic to its non-Fregean version involves introducing a new connective $$\equiv $$ ≡ that allows to separate denotations of sentences from their logical values. Intuitively, $$\equiv $$ ≡ combines two sentences $$\varphi $$ φ and $$\psi $$ ψ into a true one whenever $$\varphi $$ φ and $$\psi $$ ψ have the same semantic correlates, describe the same situations, or have the same content or meaning. The paper aims to compare non-Fregean paraconsistent Grzegorczyk’s logics (Logic of Descriptions $$\textsf{LD}$$ LD , Logic of Descriptions with Suszko’s Axioms $$\textsf{LDS}$$ LDS , Logic of Equimeaning $$\textsf{LDE}$$ LDE ) with non-Fregean versions of certain well-known paraconsistent logics (Jaśkowski’s Discussive Logic $$\textsf{D}_2$$ D 2 , Logic of Paradox $$\textsf{LP}$$ LP , Logics of Formal Inconsistency $$\textsf{LFI}{1}$$ LFI 1 and $$\textsf{LFI}{2}$$ LFI 2 ). We prove that Grzegorczyk’s logics are either weaker than or incomparable to non-Fregean extensions of $$\textsf{LP}$$ LP , $$\textsf{LFI}{1}$$ LFI 1 , $$\textsf{LFI}{2}$$ LFI 2 . Furthermore, we show that non-Fregean extensions of $$\textsf{LP}$$ LP , $$\textsf{LFI}{1}$$ LFI 1 , $$\textsf{LFI}{2}$$ LFI 2 , and $$\textsf{D}_2$$ D 2 are more expressive than their original counterparts. Our results highlight that the non-Fregean connective $$\equiv $$ ≡ can serve as a tool for expressing various properties of the ontology underlying the logics under consideration.

On a Four-Valued Logic of Formal Inconsistency and Formal Undeterminedness

On a Four-Valued Logic of Formal Inconsistency and Formal Undeterminedness

Categoricity Problem for LP and K3

AbstractEven though the strong relationship between proof-theoretic and model-theoretic notions in one’s logical theory can be shown by soundness and completeness proofs, whether we can define the model-theoretic notions by means of the inferences in a proof system is not at all trivial. For instance, provable inferences in a proof system of classical logic in the logical framework do not determine its intended models as shown by Carnap (Formalization of logic, Harvard University Press, Cambridge, 1943), i.e., there are non-Boolean models that satisfy its provable inferences. In the literature, this is known as the Categoricity problem or Carnap’s problem. In this paper, we will discuss the Categoricity problem (or Carnap’s problem) for three-valued logics K3 and LP. We will provide three different restrictions on admissible models that will deliver us categoricity results, some of which draw from the solutions provided for the Categoricity problem for classical logic in Belnap and Massey (Stud Log 49(1):67–82, 1990) and Bonnay and Westerståhl (Erkenntis 81(4):721–739, 2016). We will then argue that two of those solutions are philosophically well-motivated: (1) restricting the admissible models where negation is interpreted as a Strong Kleene truth-function, and (2) restricting the admissible models where a complex formula is assigned the third value when its immediate subformulas are assigned the third value.

Bahasa Bali Dalam Tradisi Tamblang Waluh Desa Adat Bungaya, Kecamatan Bebandem, Kabupaten Karangasem: Kajian Fungsi dan Nilai

The Tamblang Waluh tradition is a rare form of culture and is rarely found in other areas. Therefore, it is necessary to carry out an in-depth study so that the sustainability of the traditions, functions, and values ​​contained therein are known. The research method used is qualitative research method so the type of research used in this research is a type of qualitative research using a naturalistic inquiry approach, field study or phenomenology. researchers used observation, interviews, documents, and literature to collect data, analyzed with triangulation techniques and presented with qualitative descriptive. Based on the research that has been done by researchers, it is concluded that the aspects contained in the Tamblang Waluh tradition, including settings, participants, end, act of sequence, keys, instrumentalities, norms, and genres are still maintained today. The sustainability of these aspects directly affects the sustainability of the function of the Balinese language within it, which functions as a sign, as a form of communication of intimacy and as a cultural identity. The Tamblang Waluh tradition is a cultural asset for the people of the Bungaya Traditional Village, as well as a medium for inheriting life values, including religious values, logical values, ethical values, and aesthetic values.

A Monte Carlo simulation-based decision support system for radiation oncologists in the treatment of glioblastoma multiforme.

In the present research, we have developed a model-based crisp logic function statistical classifier decision support system supplemented with treatment planning systems for radiation oncologists in the treatment of glioblastoma multiforme (GBM). This system is based on Monte Carlo radiation transport simulation and it recreates visualization of treatment environments on mathematical anthropomorphic brain (MAB) phantoms. Energy deposition within tumour tissue and normal tissues are graded by quality audit factors which ensure planned dose delivery to tumour site thereby minimising damages to healthy tissues. The proposed novel methodology predicts tumour growth response to radiation therapy from a patient-specific medicine quality audit perspective. Validation of the study was achieved by recreating thirty-eight patient-specific mathematical anthropomorphic brain phantoms of treatment environments by taking into consideration density variation and composition of brain tissues. Dose computations accomplished through water phantom, tissue-equivalent head phantoms are neither cost-effective, nor patient-specific customized and is often less accurate. The above-highlighted drawbacks can be overcome by using open-source Electron Gamma Shower (EGSnrc) software and clinical case reports for MAB phantom synthesis which would result in accurate dosimetry with due consideration to the time factors. Considerable dose deviations occur at the tumour site for environments with intraventricular glioblastoma, haematoma, abscess, trapped air and cranial flaps leading to quality factors with a lower logic value of 0. Logic value of 1 depicts higher dose deposition within healthy tissues and also leptomeninges for majority of the environments which results in radiation-induced laceration.

About Logically Probable Sentences

The starting point of this paper is the empirically determined ability to reason in natural language by employing probable sentences. A sentence is understood to be logically probable if its schema, expressed as a formula in the language of classical propositional calculus, takes the logical value of truth for the majority of Boolean valuations, i.e., as a logically probable formula. Then, the formal system P is developed to encode the set of these logically probable formulas. Based on natural semantics, a strong completeness theorem for P is proved. Alternative notions of consequence for logically probable sentences are also considered.