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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]

This paper is focused on α-generalized semantic resolution automated reasoning method in linguistic truth-valued lattice-valued propositional logic. Concretely, α-generalized semantic resolution for lattice-valued propositional logic ()P(X) is equivalently transformed into that for lattice-valued propositional logic P(X)( ∊ {1,2…,}). A similar conclusion is obtained between the α-generalized semantic resolution for linguistic truth-valued lattice-valued propositional logic P(X) and that for lattice-valued propositional logic P(X)( ∊ {1,2,…,}). Secondly, the generalized semantic resolution for lattice-valued propositional logic P(X) based on a chain-type truth-valued field is investigated and its soundness and weak completeness are given. The Presented work provides some foundations for resolution-based automated reasoning in linguistic truth-valued lattice-valued logic based on lattice implication algebra.

The counting exact satisfiablity problem (#XSAT) is a problem that computes the number of truth assignments satisfying only one literal in each clause. This paper presents an algorithm that solves the #XSAT problem in O(1.1995n), which is faster than the best algorithm running in O(1.2190n), where n denotes the number of variables. To increase the efficiency of the algorithm, a new principle, called common literals principle, is addressed to simplify formulae. This allows us to further eliminate literals. In addition, we firstly apply the resolution principles into solving #XSAT problem, and therefore it improves the efficiency of the algorithm further. [ABSTRACT FROM AUTHOR]

Various parallel logical inference algorithms based on the resolution principle are studied. Experimental study was performed on computer systems with shared memory and a cluster. The results we describe show how the architecture and features of computer systems, granularity of parallelism and heuristics influence the efficiency of parallel inference. [ABSTRACT FROM AUTHOR]

This paper focuses on resolution-based automated reasoning theory in a lattice-valued logic system with truth values that are defined in a lattice-valued logical algebraic structure—lattice implication algebras (LIAs)—which essentially aims to extend the classical logic to handle automated deduction under an uncertain environment. Concretely, we investigate a generalization of the known conjunctive normal form (CNF) in the classical logic representation that we call the generalized conjunctive normal form (GCNF), which aims to characterize the constants and implication connectives that are essentially different from the ones in classical logic. We then extend the established resolution principle at a certain truth-value level \alpha (called \alpha-resolution) in this lattice-valued logic to a more general form, i.e., from binary \alpha -resolution to multiary \alpha-resolution. The extension to multiary \alpha-resolution starts from lattice-valued propositional logic LP(X), while its theorems of both soundness and completeness are proved. Multiary \alpha-resolution principle is then further established in the corresponding lattice-valued first-order logic LF(X), along with its soundness theorem, lifting lemma, and completeness theorem. Meanwhile, an important result that multiary \alpha-resolution principle in LF(X) can be equivalently transformed into that in LP(X) to some extent is obtained. All these works will theoretically support the establishment of an automated reasoning algorithm and its implementation with further applications into automated deduction and decision-making problems under uncertainty. [ABSTRACT FROM AUTHOR]

For the medium predicate logic system MF, Pan proposed the infinite valued semantic interpretation which showed the variable procedure of two opposite concepts. However, this sort of infinite valued semantic interpretation never reflects "~A true when A fuz". On which based, this paper further investigates and gives out one improved kind of infinite valued semantic interpretation as the truth value range is [0, λ)∪(λ,1] (λ ∈ (0.5, 1)) for MF, and redefines the notion of the literal in MF. In this paper, one improved kind of λ-resolution for MF is proposed and the completeness of which is proved. From this paper, it is easy to obtain that the situation which is "~A true when A fuz" is better reflected in terms of the new infinite valued semantic interpretation of MF. [ABSTRACT FROM AUTHOR]

Most of the normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve tautologies and contradictions which is important, for example, for automated theorem provers based on refutation methods. De Morgan implicative systems are triples like the De Morgan systems, which consider fuzzy implications instead of t-conorms. These systems can be used to evaluate the formulas of a propositional language based on the logical connectives of negation, conjunction and implication. Therefore, they determine different fuzzy logics, called implicative De Morgan fuzzy logics. In this paper, we will introduce a normal form for implicative De Morgan systems and we will show that for implicative De Morgan fuzzy logics whose t-norms are strict, this normal form preserves contradictions as well as tautologies. [Copyright &y& Elsevier]

For studies toward the automated theorem proving, various methods and strategies have beam presented based on the resolution principle proposed by Robinson in 1965. Most of the theorem-proving systems at present are based on this resolution principle. In contrast to this, Jeroslow proposed the partial instantiation technique in 1988. The method proposed by Jeroslow, however, has a problem in that only the formula not containing function symbols is considered and the efficiency is low since the clause form is not assumed. The authors improved Jeroslow's method. A procedure was proposed where satisfiability is decided for the formula of the clause form not containing function symbols, and the effectiveness of the method is demonstrated. This paper extends the above procedure and proposes a theorem-proving procedure so that the formula containing function symbols can be handled. A proof is given that the proposed procedure is complete. A com- parison experiment is executed, and the effectiveness of the proposed procedure is investigated. [ABSTRACT FROM AUTHOR]

This article discusses some intelligence aspects of Chinese characters. Some basic concepts of two-dimensional pattern representation and artificial intelligence such as semantic networks, forward chaining, deduction and the resolution principle are used to analyze and interpret the syntactic structure, representation, semantics and evolution of Chinese characters. The concept of degrees of ambiguity and the principle of new characters are investigated. It is found that Chinese characters are actually not only artistically elegant and culturally rich but also semantically meaningful and intelligently sound. Finally some topics for future research such as intelligent pattern recognition for Chinese characters, automatic learning and translation, and knowledge-based Chinese language understanding are discussed. [ABSTRACT FROM AUTHOR]