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Fast-ion loss detectors (FILDs) are crucial for analyzing fast-ion dynamics in magnetically confined fusion plasmas. A core challenge is to derive an accurate ion velocity distribution, requiring treatment of thousands of remapped camera frames for a full discharge. The ill-posed nature of this task necessitates regularization with a well-chosen regularization parameter and computationally efficient methods. In this work, we introduce the ‘resolution principle,’ a novel criterion for selecting the optimal regularization parameter, providing a distinction between genuine features and artefacts smaller than the diagnostic resolution in the reconstruction, thereby preventing misinterpretations. This principle, coupled with three iterative reconstruction techniques—Kaczmarz’s method, coordinate descent, and Cimmino’s method—demonstrates enhanced reconstruction capabilities compared to conventional methods like Tikhonov regularization. Utilizing these techniques allows rapid processing of measurements from full discharges, removing the computational bottleneck and facilitating between-discharge reconstructions. By reconstructing 6000 camera frames from an ELMy H-mode discharge at ASDEX Upgrade, we capture the temporal evolution of gyroradii and pitch angles, unveiling a direct correlation between pitch-angle behavior and changes in the toroidal magnetic field for a specific subset of lost ions accelerated by edge-localized modes (ELMs) to energies approximately twice that of the injection energy.

The purpose of this paper is to give some insights into the immense role of Frege’s first order logic (FOL) in the development of computer science. We argue that the FOL is fundamental in computer science, and that some computer science subfields could not have existed without their theoretical foundations built on this form of logic. Among these subfields, one can mention the Type Theory, Databases, Descriptive Complexity, Artificial Intelligence, Logic Programming, and Automated Theorem Proving. To illustrate our point, an in-depth attention will in particular be given to the foundational development of the most popular logic programming language, PROLOG, and the Automated Theorem Proving (ATP) systems. Importantly, when studying the interactions between logic and computer science in the literature, we can observe a significant gap in the provision of the appropriate abstraction level. Specifically, we often encounter two different levels of abstraction. The first of these is relatively high even when describing technical notions in computer science, which obviously produces a lack of precision. The second adopts a technical-oriented approach which easily makes the topic and discussion unintuitive or inaccessible to the non-specialist. The paper attempts to remedy these problems by adopting a balanced approach that provides a moderate level of abstraction that targets a deeper understanding of the topic without imposing a very technical presentation on the reader

We study techniques for solving the MaxSAT problem on instances in which the variable degree is bounded by 3. The problem is NP-hard. We show how resolution principle can be applied that converts an instance into an equivalent instance in which the CNF formula becomes a linear CNF formula. We then show how more efficient branching strategies can be applied on linear CNF formulas. As applications, we present two algorithms: one of running time O ⁎ (1.194 k) that solves the parameterized version of the problem, and the other of running time O ⁎ (1.237 n) that solves the optimization version of the problem, both significantly improving previous best upper bounds. [ABSTRACT FROM AUTHOR]

This article presents the results of research conducted on cluster systems with multicore nodes to create a method and an algorithm that implement parallel inference in the proof of formulas in first-order logic. The algorithm is based on of J. Robinson's resolution method of inference. A procedure for its parallelization, which allows one to dynamically control the uniform division of the set of resolvents distributed to the nodes of a computer system for inferring, is proposed. A number of heuristics, which make it possible to significantly reduce the time of implementing inference control decisions, are also introduced. Experiments here show that the effect on acceleration is higher than that of the previously studied parallel-inference algorithms. [ABSTRACT FROM AUTHOR]

As a generalization of probabilistic logic and uncertain logic, uncertain random logic deals with complex knowledge containing randomness and human uncertainty simultaneously. Based on uncertain random entailment model, this paper studies two uncertain random resolution principles. As byproducts, a random resolution principle and an uncertain resolution principle are also discussed. Moreover, the corresponding four formulas are proved to calculate the truth values of those resolution principles. [ABSTRACT FROM AUTHOR]

Due to the need of the logical foundation for uncertain information processing, development of efficient automated reasoning system based on non-classical logics is always an active research area. The present paper focuses on the resolution-based automated reasoning theory in a many-valued logic with truth-values defined in a lattice-ordered many-valued algebraic structure - lattice implication algebras (LIA). Specifically, as a continuation and extension of the established work on binary resolution at a certain truth-value level α (called α-resolution), a non-clausal multi-ary α-generalized resolution calculus is introduced for a lattice-valued propositional logic LP(X) based on LIA, which is essentially a non-clausal generalized resolution avoiding reduction to normal clausal form. The new resolution calculus in LP(X) is then proved to be sound and complete. The concepts and theoretical results are further extended and established in the corresponding lattice-valued first-order logic LF(X) based on LIA.

The purpose of this paper is to give some insights into the immense role of Frege's first order logic (FOL) in the development of computer science. We argue that the FOL is fundamental in computer science, and that some computer science subfields could not have existed without their theoretical foundations built on this form of logic. Among these subfields, one can mention the Type Theory, Databases, Descriptive Complexity, Artificial Intelligence, Logic Programming, and Automated Theorem Proving. To illustrate our point, an in-depth attention will in particular be given to the foundational development of the most popular logic programming language, PROLOG, and the Automated Theorem Proving (ATP) systems. Importantly, when studying the interactions between logic and computer science in the literature, we can observe a significant gap in the provision of the appropriate abstraction level. Specifically, we often encounter two different levels of abstraction. The first of these is relatively high even when describing technical notions in computer science, which obviously produces a lack of precision. The second adopts a technical-oriented approach which easily makes the topic and discussion unintuitive or inaccessible to the non-specialist. The paper attempts to remedy these problems by adopting a balanced approach that provides a moderate level of abstraction that targets a deeper understanding of the topic without imposing a very technical presentation on the reader. [ABSTRACT FROM AUTHOR]

Model counting is the problem of computing the number of models or satisfying assignments for a given propositional formula, and is # P -complete. Owing to its inherent complexity, approximate model counting is an alternative in practice. Model counting using the extension rule is an exact method, and is considered as an alternative to resolution-based methods for model counting. Based on the exact method, we propose two approximate model counting algorithms, and prove the time complexity of the algorithms. Experimental results show that they have good performance in the accuracy and efficiency. [ABSTRACT FROM AUTHOR]