Multiple-valued Logic Research Articles

CNTFET‐based ternary address decoder design

SummaryWith the end of Moore's law, new paradigms are investigated for more scalable computing systems. One of the promising directions is to examine the data representation toward higher data density per hardware element. Multiple valued logic (MVL) emerged as a promising system due to its advantages over binary data representation. MVL offers higher information processing within the same number of digits when compared with binary systems. Accessing memory is considered one of the most power‐ and time‐consuming instructions within a microprocessor. In the quest for building an entire ternary computer architecture, we propose investigating the potential opportunities of ternary address decoders. This paper presents three different designs for ternary address decoder based on CNTFET. The first design is based on a cascade of Ternary to Binary blocks (T2B) and a binary decoder. The second design is built using the hierarchical structure and enables signals. The third is designed utilising a pre‐decoder and ternary logic gates. A comparison of the proposed designs and the binary address decoder in terms of power and delay under different supply voltage and temperature values is introduced. Simulation results show that the second design has the least power and delay of the proposed ternary designs.

Subjective Trusts for the Control of Mobile Robots under Uncertainty.

The paper deals with the methods of handling imperfect information and the control of mobile robots acting under uncertainty. It is assumed that the robots act in autonomous regime and are controlled internally without referring the externally defined probabilities of the states and actions. To control the activity of the robots, we suggest the novel multi-valued logic techniques based on the recently developed measures, known as the subjective trusts. In addition to specification of the robots’ movements, such a technique allows for direct definition of the robots’ swarming using the methods of artificial neural networks with mobile neurons. The suggested methods are verified by numerical simulations and running examples. The resulting framework forms a basis for processing non-probabilistic uncertainties and making individual decisions with imperfect information.

On mythical Dewaruci, Manunggaling kawula-Gusti and other non-trivial Javanese logic

Discourses on logic have been for a long time predominated by Aristotelian logic, especially that is the case in the West. Although since early 20th century there are new development towards many-valued logic, for instance by Lukasiewicz etc, and also fuzzy logic theory by Lotfi Zadeh; and also in recent years there is development by one of us (FS) on Neutrosophic Logic, Plithogenic Logic etc. But still the general public usually are only accustomed to Aristotelian way. More recently, there are growing interests to consider African, Asian and also Native American logic. Nonetheless there is very rare discussion on Javanese logic, except perhaps a report by P. Stange. This article will consider some variations of logic which may show non-triviality of Javanese logic. Hopefully more readers are interested to consider this theme further.

Efficient and Highly Reliable Spintronic Non-volatile Quaternary Memory Based on Carbon Nanotube FETs and Multi-TMR MTJs

Due to the limitations of traditional binary circuits, such as high power consumption and large area and interconnections density, multi-valued logic (MVL) was offered as a solution. Quaternary logic is a form of MVL that is highly compatible with binary systems. This paper proposes a low-cost and highly reliable non-volatile quaternary memory benefiting from the adjustable threshold voltage property of gate-all-around carbon nanotube field-effect transistors (GAA-CNTFET) and non-volatile nature of magnetic tunnel junctions (MTJ). The proposed quaternary memory occupies less area and consumes lower power. The simulation results show that the proposed design offers up to 53%, 41%, and 69% lower average power, static power, and write power. Moreover, it offers up to 47% and 34% lower read power delay product (PDP) and write PDP, respectively. The proposed latch also occupies up to 23% lower area than the state-of-the-art non-volatile quaternary memories.

Molecular Engineering of Printed Semiconducting Blends to Develop Organic Integrated Circuits: Crystallization, Charge Transport, and Device Application Analyses.

Solution-based printing has contributed to the facile deposition of various types of materials, including the building blocks of printed electronics. In particular, solution-processable organic semiconductors (OSCs) are regarded as one of the most fascinating candidates for the fabrication of printed electronics. Herein, we report electrohydrodynamic (EHD) jet-printed p- and n-type OSCs, namely 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-PEN) and 6,13-bis((triisopropylsilyl)ethynyl)-5,7,12,14-tetraazapentacene (TIPS-TAP), and their use as single-OSC layers and as OSC mixed p-n layers to fabricate solution-processed p-, n-, and ambipolar-type organic field-effect transistors (OFETs). Use of the dragging mode of EHD jet printing, a process driven under a low electrostatic field with a short nozzle-to-substrate distance, was found to provide favorable conditions for growth of TIPS-PEN and TIPS-TAP crystals. In this way, the similar molecular structures of TIPS-PEN and TIPS-TAP yielded a homogeneous solid solution and showed ambipolar transport properties in OFETs. Therefore, the combination of single- and mixed-OSC layers enabled the preparation of various charge-transported devices from unit to integrated devices (NOT, NAND, NOR, and multivalued logic). Therefore, this fabrication technology can be useful for assisting in the production of OSC layers for practical applications in the near future.

Satisfiability in MultiValued Circuits

Satisfiability of Boolean circuits is among the most known and important problems in theoretical computer science. This problem is NP-complete in general but becomes polynomial time when restricted either to monotone gates or linear gates. We go outside Boolean realm and consider circuits built of any fixed set of gates on an arbitrary large finite domain. From the complexity point of view this is strictly connected with the problems of solving equations (or systems of equations) over finite algebras. The research reported in this work was motivated by a desire to know for which finite algebras $\mathbf A$ there is a polynomial time algorithm that decides if an equation over $\mathbf A$ has a solution. We are also looking for polynomial time algorithms that decide if two circuits over a finite algebra compute the same function. Although we have not managed to solve these problems in the most general setting we have obtained such a characterization for a very broad class of algebras from congruence modular varieties. This class includes most known and well-studied algebras such as groups, rings, modules (and their generalizations like quasigroups, loops, near-rings, nonassociative rings, Lie algebras), lattices (and their extensions like Boolean algebras, Heyting algebras or other algebras connected with multi-valued logics including MV-algebras). This paper seems to be the first systematic study of the computational complexity of satisfiability of non-Boolean circuits and solving equations over finite algebras. The characterization results provided by the paper is given in terms of nice structural properties of algebras for which the problems are solvable in polynomial time.

Vertically stacked, low-voltage organic ternary logic circuits including nonvolatile floating-gate memory transistors

Multi-valued logic (MVL) circuits based on heterojunction transistor (HTR) have emerged as an effective strategy for high-density information processing without increasing the circuit complexity. Herein, an organic ternary logic inverter (T-inverter) is demonstrated, where a nonvolatile floating-gate flash memory is employed to control the channel conductance systematically, thus realizing the stabilized T-inverter operation. The 3-dimensional (3D) T-inverter is fabricated in a vertically stacked form based on all-dry processes, which enables the high-density integration with high device uniformity. In the flash memory, ultrathin polymer dielectrics are utilized to reduce the programming/erasing voltage as well as operating voltage. With the optimum programming state, the 3D T-inverter fulfills all the important requirements such as full-swing operation, optimum intermediate logic value (~VDD/2), high DC gain exceeding 20 V/V as well as low-voltage operation (< 5 V). The organic flash memory exhibits long retention characteristics (current change less than 10% after 104 s), leading to the long-term stability of the 3D T-inverter. We believe the 3D T-inverter employing flash memory developed in this study can provide a useful insight to achieve high-performance MVL circuits.

Achieving Multiple Quantum-Interfered States via Through-Space and Through-Bond Synergistic Effect in Foldamer-Based Single-Molecule Junctions.

The construction of multivalued logic circuits by multiple quantum-interfered states at the molecular level can make full use of molecular diversity and versatility, broadening the application of molecular electronics. Understanding charge transport through different conducting pathways and how they interact with each other in molecules with a secondary structure is an indispensable foundation to achieve this goal. Herein, we elucidate the synergistic effect from through-space and through-bond conducting pathways in foldamers derived from ortho-pentaphenylene by the separate modulation on these pathways. The shrinkage of central heterocycles' sizes allows foldamers to stack with larger overlap degrees, resulting in level-crossing and thus transformation from constructive quantum interference (CQI) to destructive quantum interference (DQI) in a through-space pathway. The alteration of central heterocycles' connection sites enhances through-bond conjugation, leading to amplified contribution from a through-bond pathway. The enhanced through-bond pathway destructively interferes with the through-space pathway, exerting a suppression effect on transmission. Therefore, four quantum-interfered states of through-space and through-bond combination are generated, including through-space CQI-dominated states, through-space DQI-dominated states, through-space CQI states with through-bond suppression, and through-space DQI states with through-bond suppression. These findings enable us to regulate charge transport within high-order structures via multiple conducting pathways and provide a proof of concept to construct multivalued logic circuits.

UNDECIDABILITY AND NON-AXIOMATIZABILITY OF MODAL MANY-VALUED LOGICS

AbstractIn this work we study the decidability of a class of global modal logics arising from Kripke frames evaluated over certain residuated lattices, known in the literature as modal many-valued logics. We exhibit a large family of these modal logics which are undecidable, in contrast with classical modal logic and propositional logics defined over the same classes of algebras. This family includes the global modal logics arising from Kripke frames evaluated over the standard Łukasiewicz and Product algebras. We later refine the previous result, and prove that global modal Łukasiewicz and Product logics are not even recursively axiomatizable. We conclude by closing negatively the open question of whether each global modal logic coincides with its local modal logic closed under the unrestricted necessitation rule.

Continuality of classes of functions in multivalued logic with minimal logarithmic growth rate

Abstract We show that in multivalued logic there exist a continual family of pairwise incomparable closed sets with minimal logarithmic growth rate and a continual chain of nested closed sets with minimal logarithmic growth rate. As a corollary we prove that any subset-preserving class in multivalued logic contains a continual chain of nested closed sets and a continual family of pairwise incomparable closed sets such that none of the sets is a subset of any other precomplete class.

Many-Valued Logics and Bivalent Modalities

In this paper, we investigate the family LS0.5 of many-valued modal logics LS0.5's. We prove that the modalities of necessity and possibility of the logics LS0.5's capture well-defined bivalent concepts of logical validity and logical consistency. We also show that these modalities can be used as recovery operators.

Unification of Imprecise Data

Inference systems are a well-defined technology derived from knowledge-based systems. Their main purpose is to model and manage knowledge as well as expert reasoning to insure a relevant decision making while getting close to human induction. Although handled knowledge are usually imperfect, they may be treated using a non classical logic as fuzzy logic or symbolic multi-valued logic. Nonetheless, it is required sometimes to consider both fuzzy and symbolic multi-valued knowledge within the same knowledge-based system. For that, we propose in this paper an approach that is able to standardize fuzzy and symbolic multi-valued knowledge. We intend to convert fuzzy knowledge into symbolic type by projecting them over the Y-axis of their membership functions. Consequently, it becomes feasible working under a symbolic multi-valued context. Our approach provides to the expert more flexibility in modeling their knowledge regardless of their type. A numerical study is provided to illustrate the potential application of the proposed methodology.

Tableau method of proof for Peirce’s three-valued propositional logic

Peirce’s triadic logic has been under discussion since its discovery in the 1960s by Fisch and Turquette. The experiments with matrices of three-valued logic are recorded in a few pages of unpublished manuscripts dated 1909, a decade before similar systems have been developed by logicians. The purposes of Peirce’s work on such logic, as well as semantical aspects of his system, are disputable. In the most extensive work about it, Turquette suggested that the matrices are related in dual pairs of axiomatic Hilbert-style systems. In this paper, we present a simple tableau proof for a fragment of Peirce three-valued logic, called P3, based on similar approaches in many-valued literature. We demonstrated that this proof is sound and complete. Besides that, taking the false as the only undesignated value and adding non-classical negations to the calculus, we can explore paraconsistent and paracompleteness theories into P3. Keywords: Charles S. Peirce, many-valued logics, theory of proof, tableau method.

Synthesis method for S-boxes satisfying the criterion of correlation immunity of Boolean and 4-functions

The improvement of cryptanalysis methods, in particular, using the mathematical apparatus of many-valued logic functions, determines the need to create methods for the synthesis of cryptographic primitives, first of all, S-boxes that satisfy the criteria of cryptographic quality both in the sense of component Boolean functions, and in the sense of their possible representations by functions of many-valued logic. The most important criterion characterizing the ability of the S-box, and hence, of the entire cryptographic transformation in which it is used, to resist attacks of correlation cryptoanalysis, is the criterion of the correlation immunity of component functions. At the moment, there are no methods for the synthesis of S-boxes that satisfy the criterion of correlation immunity both in the sense of component Boolean functions and in the sense of component functions of many-valued logic, which complicates the further development of symmetric cryptographic algorithms, considering their possible representation using many-valued logic functions. In this paper, we propose a method for the synthesis of a full class of S-boxes of length N=16 corresponding to both the criterion of the correlation immunity of component Boolean functions and the criterion of the correlation immunity of component 4-functions. With the help of the developed method, it was possible to construct a set of 18 304 S-boxes that satisfies the criterion of correlation immunity both in the sense of component Boolean functions and in the sense of component 4-functions. The synthesized class of S-boxes can be used to increase the diffusion and confusion of modern symmetric cryptographic algorithms, as well as to increase their protection against promising cryptanalysis attacks based on many-valued logic functions.

An approach for linguistic multi-attribute decision making based on linguistic many-valued logic

There are various types of multi-attribute decision-making (MADM) problems in our daily lives and decision-making problems under uncertain environments with vague and imprecise information involved. Therefore, linguistic multi-attribute decision-making problems are an important type studied extensively. Besides, it is easier for decision-makers to use linguistic terms to evaluate/choose among alternatives in real life. Based on the theoretical foundation of the Hedge algebra and linguistic many-valued logic, this study aims to address multi-attribute decision-making problems by linguistic valued qualitative aggregation and reasoning method. In this paper, we construct a finite monotonous Hedge algebra for modeling the linguistic information related to MADM problems and use linguistic many-valued logic for deducing the outcome of decision making. Our method computes directly on linguistic terms without numerical approximation. This method takes advantage of linguistic information processing and shows the benefit of Hedge algebra.

Mutual Interaction between Superconductors and Ferromagnetic Skyrmionic Structures in Confined Geometries

The mutual interaction between a chiral ferromagnetic disk with confined skyrmionic structures and a superconducting disk is studied. The interaction is accounted for by solving simultaneously the Brown and London equations. We find that for a superconductor under an applied uniform field, the stray field of the shielding currents can trigger switching between different skyrmionic states in the ferromagnet that is not possible without the superconductor. We discuss the effect of the different parameters on the results and some possible applications such as multivalued logic, storage, and skyrmionic metamaterials.

Multi-Valued Logics as an Advanced Basis for Artificial Intelligence (As an Example of Applied Philosophy)

It is shown that the creation of artificial intelligence systems, gradually approaching human intelligence, cannot be limited by binary logic and the classical interpretation of the category of truth. The nature of human thinking is variable, which requires the use of flexible algorithmic platforms that operate with multivalued logic. It is shown that the existing approaches to the interpretation of the essence of intelligence, going back to the Turing test, are not consistent. More adequate is a criterion built on the ability of the intellect to lie, including creative particulars. It is shown that using multi-valued logic is a promising tool for constructing the algorithmic basis of artificial intelligence. It is shown that the use of just such logic is of interest from the point of view of studying self-organization processes in a telecommunication environment, resulting in the appearance of “spontaneous intelligence”, too. An analogue of such intelligence, for example, is the phenomenon of bureaucracy. It is shown that the question of the essence of the intellect is a prerequisite for the further development of non-trivial logical systems since the functioning of the intellect cannot be reduced to the operations of classical formal logic.

Algorithmic basis for the functioning of private autonomous combat neural networks: algebraization of language forms

It is shown that the modern development of weapons and military equipment will trigger the issue of improving artificial intelligence systems, in particular, their gradual convergence with human intelligence. It is shown that this requires the discovery of the algorithmic basis of artificial intelligence systems, including on the basis of the transition to multivalued logics. A close relationship has been established between the algebraization of natural language and the creation of the language of combat neural networks distributed systems in which processing is carried out based on the same operations that are involved in the human brain. The basis for this is the natural definition of language as a transpersonal structure, which largely determines the nature of human intelligence. A universal means of aggregating police multi-valued logics is provided, many elements can be placed at the disposal of General Galois. Thus, an analogue of the Zhegalkin polynomial is used, which is valid for achieving multi-valued logic with the use of properties (the Zhegalkin polynomial itself applies only to the case of binary logic). A selective case study that proves the constructiveness of the proposed application, a discoverable solution that tests the operation of a ternary adder using a Galois field containing three elements.

FEBSRA: Fuzzy Trust Based Energy Aware Balanced Secure Routing Algorithm for Secured Communications in WSNs

Energy efficiency playsa major role in designing a sensor network to improve network lifetime. Trust is also important for providing security to the data communication process. Delay is also a major challenge today due to the enormous volume of network users. To overcome all these issues, many researchers have developed energy-efficient security mechanisms for fulfilling the requirements. Even though they are not able to satisfy the current requirements and users in terms of energy consumption, delay, and security. For this purpose, this paper proposes a new algorithm called Fuzzy Trust-Based Energy-Aware Balanced Secure Routing Algorithm, which can provide the effective delay constrained secure routing. It uses fuzzy logic as a form of many-valued logic. In this method, the truth values of variables may be any real number between 0 and 1, both inclusive for making a final decision over sensor nodes. Considering the number of hops between the source and destination nodes, the energy level of the nodes, the trust scores. Moreover, a new trust model has introduced a new formula for calculating trust scores with the energy level of the communication delay, which is calculated by using the number of hops used for the specific communication, taking into account the number of hops between the source and destination nodes. The experimental results of the proposed secured routing algorithm demonstrated that the performance in terms of energy consumption, less delay, and high throughput with security is better when compared to the existing systems.

A method for synthesis of S-boxes with good avalanche characteristics of component Boolean and quaternary functions

The widespread use of block symmetric ciphers in modern information security systems makes the task of increasing their efficiency urgent, as well as the task of synthesizing high-quality cryptographic primitives used in modern block symmetric ciphers, primarily S-boxes. In particular, the S-boxes must have good avalanche characteristics not only of their component Boolean functions, but also of the component functions of many-valued logic. In this paper, we propose a recursive method for the synthesis of large lengths S-boxes that satisfy the strict avalanche criterion of component 4-functions. As a raw material for the construction of such an S-boxes, small-length S-boxes are used that satisfy the strict avalanche criterion of component 4-functions. In the constructed set of S-boxes that satisfy the strict avalanche criterion of component 4-functions, we found those that simultaneously satisfy the criterion of the maximum avalanche effect of component Boolean functions. The avalanche characteristics of these S-boxes are of high quality both from the point of view of their representation with help of Boolean functions, and from the point of view of their representation using 4-functions. These S-boxes can be recommended for practical use to modernize existing symmetric cryptographic algorithms, as well as to build new perspective ciphers.