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Logic Programming and fuzzy logic are active areas of research, and their scopes in terms of applications are growing fast. Fuzzy logic is a branch of many-valued logic based on the paradigm of inference under vagueness. In this work we recall some of the interplay between three 3-valued logics that are relevant in these areas: The Lukasiewicz logic, the intermediate logic G3 and the paraconsistent logic G 3 ′ , and we present a contribution to the area of answer sets that consists in extending a definition of stable model based on proof theory in logic G3, to a more general definition that can be based on any of the more expressive logics G 3 ′ or Lukasiewicz. Finally we present and explore a new 4-valued logic that bears relation to G3 and to Lukasiewicz 4-valued logic.

We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property. © 2019 Elsevier B.V. We are grateful to two anonymous referees and the editor of this journal for their numerous and helpful comments. Their help greatly improved the paper. Guillermo Badia is supported by the project I 1923-N25 of the Austrian Science Fund (FWF). Grigory Olkhovikov is supported by Deutsche Forschungsgemeinschaft (DFG), project WA 936/11-1.

In 1969, Per LindstrOm proved his famous theorem and established criteria for the first-order definability of formal theories for discrete structures. The results were extrapolated for systems of modal logic and even for theories for continuous structures. This paper aims to formulate and prove LindstrOm's theorem for analytic structures based on measures. In particular, Hajek's Logic of Integral is redefined as an abstract logic with a new type of Hajek's satisfiability and considered as a minimal logic in the class of analytic structures with Lebesgue integrals.

Logic-based event recognition systems infer occurrences of events in time using a set of event definitions in the form of first-order rules. The Event Calculus is a temporal logic that has been used as a basis in event recognition applications, providing, among others, direct connections to machine learning, via Inductive Logic Programming (ILP). OLED is a recently proposed ILP system that learns event definitions in the form of Event Calculus theories, in a single pass over a data stream. We present two strategies for parallel online learning with OLED . We evaluate our proposed approaches on three datasets from the domains of activity recognition and maritime surveillance and show that they can significantly reduce training times, while they are capable of achieving super-linear speed-ups under certain circumstances.

Logic gates using magnetic tunnel junction (MTJ)-based nonvolatile logic-in-memory (NV-LIM) architecture are designed for quantized neural networks (QNNs) for Internet-of-Things applications. The NV-LIM-based implementation reduces data transfer costs between storage and logic gate components, thereby greatly enhancing the energy efficiency of inference operations in QNNs. The impact of the proposed nonvolatile logic gates for binary and ternary neural networks on energy consumption, delay, and area overhead reduction is demonstrated through circuit evaluations based on the parameters of the measured MTJ devices.

In the style of Lindstr\"om's theorem for classical first-order logic, this article characterizes propositional bi-intuitionistic logic as the maximal (with respect to expressive power) abstract logic satisfying a certain form of compactness, the Tarski union property and preservation under bi-asimulations. Since bi-intuitionistic logic introduces new complexities in the intuitionistic setting by adding the analogue of a backwards looking modality, the present paper constitutes a non-trivial modification of previous work done by the authors for intuitionistic logic in: G. Badia and G. Olkhovikov. A Lindstr\"om theorem for intuitionistic propositional logic. Notre Dame Journal of Formal Logic, 61 (1): 11-30 (2020)., Comment: 27 pages, 0 figures. arXiv admin note: text overlap with arXiv:2103.17024

Stemming from the works of Petr Hajek on mathematical fuzzy logic, graded model theory has been developed by several authors in the last two decades as an extension of classical model theory that studies the semantics of many-valued predicate logics. In this paper we take the first steps towards an abstract formulation of this model theory. We give a general notion of abstract logic based on many-valued models and prove six Lindstrom-style characterizations of maximality of first-order logics in terms of metalogical properties such as compactness, abstract completeness, the Lowenheim–Skolem property, the Tarski union property, and the Robinson property, among others. As necessary technical restrictions, we assume that the models are valued on finite MTL-chains and the language has a constant for each truth-value.

17 USC 105 interim-entered record; under temporary embargo. Logic regression (LR), not to be confused with logistic regression, is a well-known alternative tree-based method and powerful statistical learning technique that can be used to classify a binary response using Boolean combinations of binary predictors. In our case, given the binary states of the components of a network and its corresponding operating or failed status, LR can quantify the importance of the interactions of components according to their predictive capabilities (strength for classification). Meaning that, unlike traditional approaches in the reliability field, a completely different assumption is used. This paper shows the application of logic regression in six networks. Each example is characterized by a matrix representing the status of each component and a vector showing the corresponding network status. These data are analytically derived or using simulation procedures. The results show that LR could be considered as an additional assessment tool, where the most important effects (single or interactions) of components emerge naturally as a result of an optimization problem. As a byproduct, LR is also able to detect possible minimal cut/path sets. U.S. Government affiliation is unstated in article text.

Departing from basic concepts in abstract logics, this paper introduces two concepts: conjunctive and disjunctive limits. These notions are used to formalize levels of modal operators.

It is shown that propositional intuitionistic logic is the maximal (with respect to expressive power) abstract logic satisfying a certain topological property reminiscent of compactness, the Tarski union property and preservation under asimulations.

As the usage of theorem prover technology expands, so too does the reliance on correctness of the tools. Metamath Zero is a verification system that aims for simplicity of logic and implementation, without compromising on efficiency of verification. It is formally specified in its own language, and supports a number of translations to and from other proof languages. This paper describes the abstract logic of Metamath Zero, essentially a multi-sorted first order logic, as well as the binary proof format and the way in which it can ensure essentially linear time verification while still being concise and efficient at scale. Metamath Zero currently holds the record for fastest verification of the set.mm Metamath library of proofs in ZFC (including 71 of Wiedijk’s 100 formalization targets), at less than 200 ms. Ultimately, we intend to use it to verify the correctness of the implementation of the verifier down to binary executable, so it can be used as a root of trust for more complex proof systems.

The purpose of the current study was to form theoretical issues and practical recommendations on development of methodology evaluation for companies implementing modern financial technologies. The research was conducted based on methodology of systematic research, synthesis, abstract logic and scientific forecast, statistical methods and factor analysis methods, expert evaluation, real option method, explored fuzzy logic. Research resulted in discovery of such companies’ features that implement modern financial technology as evaluation objects, as well as exogenous and endogenous factors that impact the evaluation of the researched companies, and these factors’ classification offered; there were methodological recommendations developed on qualitative and quantitative ranking of specific indeterminacy; there were adaptations performed to discounted cash flows, real options, and ratio methods. The methodology developed was approbated based on domestic and foreign companies that provide consulting and evaluations services. As a result of its usage, a more precise evaluation was provided for the companies implementing modern financial technologies. A separate practical usage regarded the adopted method of discounting rate calculation based on the correction for specific fintech implementation risks and the developed mechanism of real options usage for additional company’s value that allows receiving a more accurate evaluation numbers. The classification manual of specific risks developed by the author is used by evaluation practitioners. The scientific issues and practical recommendations on improvement of the companies’ evaluation that were developed within the study are being used for teaching of “Evaluation and business value management” course in Financial University.

When children learn to count, do they understand its logic independent of the number list that they learned to count with? Here we tested CP-knowers' (ages three to five) understanding of how counting reveals a set's cardinality, even when non-numerical lists are used to count. Participants watched an agent count unobservable objects in two boxes and were asked to identify the larger set. Participants successfully identified the box with more objects when the agent counted using their familiar number list (Experiment 1) and when the agent counted using a non-numeric ordered list, as long as the items in the list were not linguistically used as number words (Experiments 2–3). Additionally, children's performance was strongly influenced by visual cues that helped them link the list's order to representations of magnitude (Experiment 4). Our findings suggest that three- to six-year-olds who can count also understand how counting reveals a set's cardinality, but they require additional time to understand how symbols on any arbitrary ordered list can be used as numerals.

Logic reasoning, a fundamental ability of human intelligence, is an important topic in artificial intelligence. Often, these reasoning patterns need to beforehand be provided by some domain experts, which has resulted in an interesting research topic: can reasoning patterns be directly learned from given data in which meaning of any symbols is not known in advance? In order to study this issue, in this study, we design four visual logic data set (named Fashion-Logic) using the Fashion-MNIST data, in which first each image is embedded with n special figure symbols each of which is a picture from the Fashion-MNIST data set, then a relation (the relations: Bitwise And, Bitwise Or, Addition and Subtraction are used in this paper) is added to any two images to generate one output image. And these resulting images are called the logical images. Our aim is to obtain a learning model that can directly mine and reason the logic relation between two input images and one output image, without presetting any reasoning patterns (i.e. a learning model does not know the meaning of the figure symbols embedded in the images and the relation between the input images and the output image in advance). This novel task, mining the logic patterns from the Fashion-Logic data set, is called a fashion logic task in this paper. In this work, we test the performances of many typical neural network models on Fashion-Logic data set, and produce fruitful results which indicates that it is feasible to directly mine the logic reasoning patterns using a learning strategy from given data. Last, we test and find that the ability of models is very poor to mine the abstract logic patterns on the more complex data sets called Fashion-LogicV2.

Logic locking/obfuscation has emerged as an auspicious solution for protecting the semiconductor intellectual property (IP) from the untrusted entities in the design and fabrication process. Logic locking disguises the implementation and functionality of the IP by implanting additional key-gates in the circuit. The right output of the locked chip is produced, once the correct key value is available at the input of the key-gates. The confidentiality of the key is imperative for the security of the locked IP as it stands as the lone barrier against IP infringement. Therefore, the logic locking is considered as a broken scheme once the key value is exposed. The logic locking techniques have shown vulnerability to different classes of attacks, such as Oracle-guided and physical attacks. Although the research community has proposed a number of countermeasures against such attacks, none of them is simultaneously unbreakable against Oracle-guided, Oracle-less, and physical attacks. Under such circumstances, a defense-in-depth mechanism can be considered as a feasible approach in addressing the vulnerabilities of logic locking. Defense-in-depth is a multilayer defense strategy where several independent countermeasures are implemented in the device to provide aggregated protection against different attack vectors. Introducing such a multilayer shielding model in logic locking is the major contribution of this paper. With regard to this, we first identify the core components of logic locking schemes, which need to be protected. Afterwards, we categorize the vulnerabilities of core components according to potential threats for the locking key in logic locking schemes. Furthermore, we propose several defense layers and countermeasures to protect the device from those vulnerabilities. In conclusion, we believe that a logic locking technique with a layered defense mechanism can be a possible solution against IP piracy.

This Innovative Practice Full Paper presents our study of promoting critical thinking and achievement in mathematics with the use of technology via easily accessible resources. We believe that creating easy-to-use learning modules that are accessible for students everywhere is a great way to help students comprehend abstract logic process in problem solving. More specifically, we developed a series of learning modules that interactively visualize and illustrate the steps of Geometry proofs by using GeoGebra, a dynamic learning platform for mathematics [5, 10]. Survey study shows that our interactive learning modules are beneficial in promoting students’ learning interests and ability of critical thinking.