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We describe some recent computer investigations with the 'Constraint Logic Programming over Finite Domains' library in the Prolog programming environment to search for new simple Lie algebras over the field \operatorname {GF}(2) of 2 elements. Motivated by a paper of Grishkov et al., we specifically look for those with a thin decomposition , and we settle one of their conjectures. We extrapolate from our results the existence of two new infinite families of simple Lie algebras, in addition to finding seven new sporadic examples in dimension 31. We also better contextualise some previously discovered simple algebras, putting them into families which do not seem to have ever appeared in the literature, and give an updated table of those currently known. [ABSTRACT FROM AUTHOR]

This article explores the intertwining connections among artificial intelligence, machine learning, digital transformation, and computational sustainability, detailing how these elements jointly empower citizens within a smart city framework. As technological advancement accelerates, smart cities harness these innovations to improve residents' quality of life. Artificial intelligence and machine learning act as data analysis powerhouses, making urban living more personalized, efficient, and automated, and are pivotal in managing complex urban infrastructures, anticipating societal requirements, and averting potential crises. Digital transformation transforms city operations by weaving digital technology into every facet of urban life, enhancing value delivery to citizens. Computational sustainability, a fundamental goal for smart cities, harnesses artificial intelligence, machine learning, and digital resources to forge more environmentally responsible cities, minimize ecological impact, and nurture sustainable development. The synergy of these technologies empowers residents to make well-informed choices, actively engage in their communities, and adopt sustainable lifestyles. This discussion illuminates the mechanisms and implications of these interconnections for future urban existence, ultimately focusing on empowering citizens in smart cities. [ABSTRACT FROM AUTHOR]

In this paper, we study Horn formulas from the perspective of read-once resolution refutations (RORs). A Horn formula is a Boolean formula in conjunctive normal form (CNF), in which each clause contains at most one positive literal. Horn formulas are used in a number of domains, including program verification, logic programming, and econometrics. In particular, deduction in ProLog is based on unification. Unification is based on resolution and instantiation. Resolution is a system used to prove the infeasibility of Boolean formulas. It is important to note that resolution is both sound and complete. However, resolution is inefficient in the following sense: There exist CNF formulas with resolution refutations whose lengths are bounded below by an exponential function of the input size. At the same time, these formulas admit shorter (polynomially bounded) proofs of infeasibility in other proof systems, such as Frege Systems. Despite this inefficiency, resolution is simple and easy to implement and hence used in a wide variety of theorem provers. In this paper, we study two variants of resolution. These are read-once resolution (ROR) and read-once unit resolution (UROR). Both ROR and UROR are sound. However, they are incomplete since there exist infeasible Boolean formulas which do not have either an ROR or a UROR. In this paper, we look at the problems of determining if a Horn formula has an ROR or a UROR. We also examine the problem of finding the optimal length ROR of a Horn formula from both the computational complexity and the approximation perspectives. Finally, we analyze the copy complexity of Horn formulas with respect to URORs. [ABSTRACT FROM AUTHOR]

This paper introduces and studies the sequential composition and decomposition of propositional logic programs. We show that acyclic programs can be decomposed into single-rule programs and provide a general decomposition result for arbitrary programs. We show that the immediate consequence operator of a program can be represented via composition which allows us to compute its least model without any explicit reference to operators. This bridges the conceptual gap between the syntax and semantics of a propositional logic program in a mathematically satisfactory way. [ABSTRACT FROM AUTHOR]

Inductive Logic Programming (ILP) is a research field at the intersection between machine learning and logic programming, focusing on developing a formal framework for inductively learning relational descriptions in the form of logic programs from examples and background knowledge. As an emerging method of ILP, Meta-Interpretive Learning (MIL) leverages the specialization of a set of higher-order metarules to learn logic programs. In MIL, the input includes a set of examples, background knowledge, and a set of metarules, while the output is a logic program. MIL executes a depth-first traversal search, where its program search space expands polynomially with the number of predicates in the provided background knowledge and exponentially with the number of clauses in the program, sometimes even leading to search collapse. To address this challenge, this study introduces a strategy that employs the concept of reuse, specifically through the integration of auxiliary predicates, to reduce the number of clauses in programs and improve the learning efficiency. This approach focuses on the proactive identification and reuse of common program patterns. To operationalize this strategy, we introduce MILER, a novel method integrating a predicate generator, program learner, and program evaluator. MILER leverages frequent subgraph mining techniques to detect common patterns from a limited dataset of training samples, subsequently embedding these patterns as auxiliary predicates into the background knowledge. In our experiments involving two Visual Question Answering (VQA) tasks and one program synthesis task, we assessed MILER's approach to utilizing reusable program patterns as auxiliary predicates. The results indicate that, by incorporating these patterns, MILER identifies reusable program patterns, reduces program clauses, and directly decreases the likelihood of timeouts compared to traditional MIL. This leads to improved learning success rates by optimizing computational efforts. [ABSTRACT FROM AUTHOR]

Bayesian inference provides a probabilistic reasoning process for drawing conclusions based on imprecise and uncertain data that has been successful in many applications within robotics and information processing, but is most often considered in terms of data analysis rather than synthesis of behaviours. This paper presents the use of Bayesian inference as a means by which to perform Boolean operations in a logic programme while incorporating and propagating uncertainty information through logic operations by inference. Boolean logic operations are implemented in a Bayesian network of Bernoulli random variables with tensor-based discrete distributions to enable probabilistic hybrid logic programming of a robot. This enables Bayesian inference operations to coexist with Boolean logic in a unified system while retaining the ability to capture uncertainty by means of discrete probability distributions. Using a discrete Bayesian network with both Boolean and Bayesian elements, the proposed methodology is applied to navigate a mobile robot using hybrid Bayesian and Boolean operations to illustrate how this new approach improves robotic performance by inclusion of uncertainty without increasing the number of logic elements required. As any logical system could be programmed in this manner to integrate uncertainty into decision-making, this methodology can benefit a wide range of applications that use discrete or probabilistic logic. [ABSTRACT FROM AUTHOR]

A crucial aspect of bioinformatics is sequence comparison, which entails matching recently discovered biological sequences with previously identified sequences kept in databases. To find similarities between two or more nucleotide or amino acid sequences, sequence alignment organizes the sequences. Understanding the functional, structural, and evolutionary links between the sequences is made easier by looking at these areas of commonality. This study highlighted types of alignment. Also, proposed an effective methodology for deciding which algorithm can be utilized and satisfying the objective. Hence, Multi-Criteria Decision-Making (MCDM) techniques have been harnessed with Neutrosophic theory as a supporter in uncertain situations. Herein Single Value Neutrosophic Sets (SVNSs) as a type of uncertainty theory-Neutrosophic. This process requires a set of criteria leveraged in judgment. Also, Tree Soft Sets (TrSS) are applied for the first time to model the required criteria to facilitate the decision process. The hybrid techniques are applied to support stakeholders in making optimal decisions for optimal alignment algorithms among various algorithms such as pairwise and sequence algorithms. The results of the implementation of this decision technique indicated that multiple sequence alignment is the best compared with pairwise algorithms. Thus, we implemented multiple sequences in our study and employed logic programming to perform sequence matching. To ensure optimal alignment, the approach is tested on different sets of 16S rRNA gene of Actinobacteria (Streptomyces) sequences taken from NCBI. Then, the results are compared with MEGA. [ABSTRACT FROM AUTHOR]

With its powerful expressive capability and intuitive presentation, the knowledge graph has emerged as one of the primary forms of knowledge representation and management. However, the presence of biases in our cognitive and construction processes often leads to varying degrees of incompleteness and errors within knowledge graphs. To address this, reasoning becomes essential for supplementing and rectifying these shortcomings. Logical rule-based knowledge graph reasoning methods excel at performing inference by uncovering underlying logical rules, showcasing remarkable generalization ability and interpretability. Moreover, the flexibility of logical rules allows for seamless integration with diverse neural network models, thereby offering promising prospects for research and application. Despite the growing number of logical rule-based knowledge graph reasoning methods, a systematic classification and analysis of these approaches is lacking. In this review, we delve into the relevant research on logical rule-based knowledge graph reasoning, classifying them into four categories: methods based on inductive logic programming (ILP), methods that unify probabilistic graphical models and logical rules, methods that unify embedding techniques and logical rules, and methods that jointly use neural networks (NNs) and logical rules. We introduce and analyze the core concepts and key techniques, as well as the advantages and disadvantages associated with these methods, while also providing a comparative evaluation of their performance. Furthermore, we summarize the main problems and challenges, and offer insights into potential directions for future research. [ABSTRACT FROM AUTHOR]

The biological target identification process, a pivotal phase in the drug discovery workflow, becomes particularly challenging when mutations affect proteins' mechanisms of action. COVID-19 Spike glycoprotein mutations are known to modify the affinity toward the human angiotensin-converting enzyme ACE2 and several antibodies, compromising their neutralizing effect. Predicting new possible mutations would be an efficient way to develop specific and efficacious drugs, vaccines, and antibodies. In this work, we developed and applied a computational procedure, combining constrained logic programming and careful structural analysis based on the Structural Activity Relationship (SAR) approach, to predict and determine the structure and behavior of new future mutants. "Mutations rules" that would track statistical and functional types of substitutions for each residue or combination of residues were extracted from the GISAID database and used to define constraints for our software, having control of the process step by step. A careful molecular dynamics analysis of the predicted mutated structures was carried out after an energy evaluation of the intermolecular and intramolecular interactions using the HINT (Hydrophatic INTeraction) force field. Our approach successfully predicted, among others, known Spike mutants. [ABSTRACT FROM AUTHOR]

Despite the indisputable progresses of artificial intelligence, some tasks that are rather easy for a human being are still challenging for a machine. An emblematic example is the resolution of mathematical puzzles with diagrams. Sub-symbolical approaches have proven successful in fields like image recognition and natural language processing, but the combination of these techniques into a multimodal approach towards the identification of the puzzle's answer appears to be a matter of reasoning, more suitable for the application of a symbolic technique. In this work, we employ logic programming to perform spatial reasoning on the puzzle's diagram and integrate the deriving knowledge into the solving process. Analysing the resolution strategies required by the puzzles of an international competition for humans, we draw the design principles of a Prolog reasoning library, which interacts with image processing software to formulate the puzzle's constraints. The library integrates the knowledge from different sources, and relies on the Prolog inference engine to provide the answer. This work can be considered as a first step towards the ambitious goal of a machine autonomously solving a problem in a generic context starting from its textual-graphical presentation. An ability that can help potentially every human–machine interaction. [ABSTRACT FROM AUTHOR]

Deciphering gene regulatory networks' functioning is an essential step for better understanding of life, as these networks play a fundamental role in the control of cellular processes. Boolean networks have been widely used to represent gene regulatory networks. They allow to describe the dynamics of complex gene regulatory networks straightforwardly and efficiently. The attractors are essential in the analysis of the dynamics of a Boolean network. They explain that a particular cell can acquire specific phenotypes that may be transmitted over several generations. In this work, we consider a new representation of Boolean networks' dynamics based on a new semantics used in Answer Set Programming (ASP). We use logic programs and ASP to express and deal with gene regulatory networks seen as Boolean networks, and develop a method to detect all the attractors of such networks. We first show how to represent and deal with general Boolean networks for the synchronous and asynchronous updates modes, where the computation of attractors requires a simulation of these networks' dynamics. Then, we propose an approach for the particular case of circular networks where no simulation is needed. This last specific case plays an essential role in biological systems. We show several theoretical properties; in particular, simple attractors of the gene networks are represented by the stable models of the corresponding logic programs and cyclic attractors by its extra-stable models. These extra-stable models correspond to the extra-extensions of the new semantics that are not captured by the semantics of stable models. We then evaluate the proposed approach for general Boolean networks on real biological networks and the one dedicated to the case of circular networks on Boolean networks generated randomly. The obtained results for both approaches are encouraging. [ABSTRACT FROM AUTHOR]

Multi‐adjoint relation equations are defined by means of a sup‐composition operator involving different conjunctions. Former works reveal that the resolution of a multi‐adjoint relation equation is closely related to such conjunctions. This paper presents a first approach on the study of the influence of the selection of a sup‐composition operator in different aspects of multi‐adjoint relation equations, as their solvability or the extremal elements of their solution set. The obtained results are illustrated by an example concerning multi‐adjoint logic programming. Last but not least, a procedure for reducing the computation of the solution set when only the sup‐composition operator is modified is also introduced. [ABSTRACT FROM AUTHOR]

Proof-theoretic semantics (P-tS) is the paradigm of semantics in which meaning in logic is based on proof (as opposed to truth). A particular instance of P-tS for intuitionistic propositional logic (IPL) is its base-extension semantics (B-eS). This semantics is given by a relation called support, explaining the meaning of the logical constants, which is parameterized by systems of rules called bases that provide the semantics of atomic propositions. In this paper, we interpret bases as collections of definite formulae and use the operational view of them as provided by uniform proof-search|the proof-theoretic foundation of logic programming (LP)|to establish the completeness of IPL for the B-eS. This perspective allows negation, a subtle issue in P-tS, to be understood in terms of the negation-as-failure protocol in LP. Specifically, while the denial of a proposition is traditionally understood as the assertion of its negation, in B-eS we may understand the denial of a proposition as the failure to find a proof of it. In this way, assertion and denial are both prime concepts in P-tS. [ABSTRACT FROM AUTHOR]

The extensive use of Deep Neural Networks (DNNs) encourages people to design domain-specific hardware called Artificial Intelligence (AI) processors. The novel hardware makes optimizations challenging without a proper performance model that reveals working details and performance implications. This paper presents a performance model, Verrocchio, for Huawei DaVinci AI Core, which predicts the execution time of real-world DaVinci kernels. We propose specially-crafted micro-benchmarks to identify contention source, runtime behaviors, and bandwidth sharing, which significantly determine performance. Since DaVinci Core adopts a binary semaphore mechanism for synchronization, Verrocchio views each instruction as a discrete event and manages its execution time based on the programming logic. For evaluation, Verrocchio achieves average error rates of 2.62% and 2.30% in sample kernels for single-core and double-core execution. We demonstrate an optimizing process of matrix multiplications with Verrocchio, achieving speedups of 1.70× for operators and 1.53× for applications and error rates of 5.06% and 5.25%. • Detailed dissections of Huawei DaVinci AI Core, a novel AI processor. • Benchmarking the DaVinci Core bandwidth contention, the key performance factor. • Performance model for accurate execution time prediction of kernel program. • Demonstration of DaVinci kernel optimization and prediction accuracy evaluation. [ABSTRACT FROM AUTHOR]

The semantics of a multi-adjoint logic program is usually defined through the immediate consequences operator T P. However, the definition of the immediate consequences operator as the supremum of a set of values can provide some problem when imprecise datasets are considered, due to the strict feature of the supremum operator. Hence, based on the flexibility of generalized quantifiers to weaken the existential feature of the supremum operator, this paper presents a generalization of the immediate consequences operator with interesting properties for solving the aforementioned problem. [ABSTRACT FROM AUTHOR]

The relevance of polynomial classes of formulas to deductive efficiency motivated their further research, and currently, a great number of such classes is known. Nevertheless, they have been exclusively sought in the setting of propositional logic and clausal form, which is of course expressively limiting for real-world applications. Along these lines and towards making tractability applicable beyond propositional clausal logic, firstly, we define the R egular many-valued H orn Non-Clausal (NC) class, or RH , obtained by suitably amalgamating both regular classes: Horn and NC. Then we show that recognizing whether any NC formula is Horn-NC takes only linear time. Secondly, we demonstrate that the relationship between RH and: (1) its subclass of regular Horn formulas is that syntactically RH subsumes the Horn class but semantically both classes are equivalent; and (2) its superclass of regular non-clausal formulas is that RH contains all non-clausal formulas whose clausal form is Horn. Thirdly, we define Regular Non-Clausal Unit-Resolution, or RU R NC , and prove that RU R NC is complete for RH and also checks its satisfiability in polynomial time. Altogether, RH is a class recognized and solved polynomially, which shows that our intended goal is reached since RH is many-valued, non-clausal and tractable. Fourthly, based on RH , we characterize extensive classes of Horn-NC-like formulas, super-classes of RH , which are composed of formulas that are logically equivalent to some formula in RH. We furnish syntactical patterns of such Horn-NC-like formulas, being outside RH and whose satisfiability test is also decidable in polynomial time. As RH and RU R NC are, both, basic in the DPLL scheme, the most efficient in propositional logic, and can be extended to some other non-classical logics, we argue that they pave the way for efficient non-clausal DPLL-based approximate reasoning. Field: Tractable Approximate Automated Reasoning. [ABSTRACT FROM AUTHOR]

Reaction systems (RSs) are a successful natural computing framework inspired by chemical reaction networks. A RS consists of a set of entities and a set of reactions. Entities can enable or inhibit each reaction and are produced by reactions or provided by the environment. In this paper, we define two quantitative variants of RSs: the first one is along the time dimension, to specify delays for making available reactions products and durations to protract their permanency, while the second deals with the possibility to specify different concentration levels of a substance in order to enable or inhibit a reaction. Technically, both extensions are obtained by modifying in a modular way the Structural Operational Semantics (SOS) for RSs that was already defined in the literature. Our approach maintains several advantages of the original semantics definition that were: (1) providing a formal specification of the RS dynamics that enables the reuse of many formal analysis techniques and favours the implementation of tools, and (2) making the RS framework extensible, by adding or changing some of the SOS rules in a compositional way. We provide a prototype logic programming implementation and apply our tool to three different case studies: the tumour growth, the Th cell differentiation in the immune system and neural communication. [ABSTRACT FROM AUTHOR]

Intensional sets are sets given by a property rather than by enumerating their elements. In a previous work, we have proposed a decision procedure for a first-order logic language which provides restricted intensional sets (RISs), i.e. a sub-class of intensional sets that are guaranteed to denote finite—though unbounded—sets. In this paper, we show how RIS can be exploited as a convenient programming tool also in a conventional setting, namely the imperative O-O language Java. We do this by considering a Java library, called JSetL, that integrates the notions of logical variable, (set) unification and constraints that are typical of constraint logic programming languages into the Java language. We show how JSetL is naturally extended to accommodate for RIS and RIS constraints and how this extension can be exploited; on the one hand, to support a more declarative style of programming and, on the other hand, to effectively enhance the expressive power of the constraint language provided by the library. [ABSTRACT FROM AUTHOR]

A wide range of new research articles in artificial intelligence, logic programming, and other applied sciences are based on fixed-point theorems. The aim of this article is to present an approximation method for finding the fixed point of generalized Suzuki nonexpansive mappings on hyperbolic spaces. Strong and Δ -convergence theorems are proved using the Noor iterative process for generalized Suzuki nonexpansive mappings (GSNM) on uniform convex hyperbolic spaces. Due to the richness of uniform convex hyperbolic spaces, the results of this paper can be used as an extension and generalization of many famous results in Banach spaces together with C A T (0) spaces. [ABSTRACT FROM AUTHOR]

Constraint programming has roots in logic programming, where a model has both a declarative and a procedural interpretation. A model is declarative because its statements can be read as logical propositions that describe the problem, and it is procedural because the statements can be processed as instructions for how to find a solution. To make constraint programming material to practical problems one needs propagation algorithms that are both viable and proficient. The most incredible propagation algorithm for the alldifferent constraint, i.e. the one getting hyper-circular segment consistency, is to be sure extremely productive. The reason is that we can apply matching hypothesis from operations research. Likewise for the symmetric alldifferent constraint and the weighted alldifferent constraint powerful and effective propagation algorithms exist, again dependent on techniques from operations research. From this paper we show that some time alldifferent constraint is more easy way to solve the MIP. For this we will choose an auction strategy by which a company get more revenue. Despite this considerable progress, there remains great potential for further integration, with the concomitant improvement in both modeling and solution method. [ABSTRACT FROM AUTHOR]

This paper is concerned with the design and analysis of a bit-scaling based algorithm for the problem of checking integer feasibility in a system of unit two variable per inequality (UTVPI) constraints (IF). The insights developed during algorithm design result in new techniques for extracting refutations of integer feasibility in such systems. Recall that a UTVPI constraint is a linear constraint of the form: a i · x i + a j · x j ≤ b ij , where a i , a j ∈ { 0 , 1 , - 1 } and b ij ∈ Z . These constraints arise in a number of application domains including but not limited to program verification (array bounds checking and abstract interpretation), operations research (packing and covering), and logic programming. Over the years, several algorithms have been proposed for the IF problem. Most of these algorithms are based on two inference rules, viz. the transitive rule and the tightening rule. None of these algorithms are bit-scaling. In other words, the running times of these algorithms are parameterized only by the number of variables and the number of constraints in the UTVPI constraint system (UCS) and not by the sizes of input constants. We introduce a novel algorithm for the IF problem, which is based on a collection of new insights. These insights are used to design a new bit-scaling algorithm for IF that runs in O (n · m · log 2 C) time, where n denotes the number of variables, m denotes the number of constraints, and C denotes the absolute value of the most negative constant defining the UCS. An interesting consequence of our research is the development of techniques for extracting refutations of integer infeasibility in UCSs that are linearly feasible. If the UCS is linearly feasible, then our algorithm creates a 2CNF formula. The UCS has an integer refutation (i.e., does not have a lattice point) if and only if the created 2CNF formula has a resolution refutation (i.e., is unsatisfiable). [ABSTRACT FROM AUTHOR]

Representing uncertain information is crucial for modeling real world domains. This has been fully recognized both in the field of Logic Programming and of Description Logics (DLs), with the introduction of probabilistic logic languages and various probabilistic extensions of DLs respectively. Several works have considered the distribution semantics as the underlying semantics of Probabilistic Logic Programming (PLP) languages and probabilistic DLs (PDLs), and have then targeted the problem of reasoning and learning in them. This paper is a survey of inference, parameter and structure learning algorithms for PLP languages and PDLs based on the distribution semantics. A few of these algorithms are also available as web applications. [ABSTRACT FROM AUTHOR]

ProB provides a constraint solver for the B-method written in Prolog and can make use of different backends based on SAT and SMT solving. One such backend translates B and Event-B operators to SMT-LIB using the Z3 solver. This translation uses quantifiers to axiomatize some operators, which are not well-handled by Z3. Several relational constraints such as the transitive closure are not supported by this translation. In this article, we substantially improve the translation to SMT-LIB by employing a more constructive rather than axiomatized style using Z3's lambda function. Thereby, we are able both to translate more B and Event-B operators to SMT-LIB and improve the overall performance. We further extend ProB's interface to Z3 to run different solver configurations in parallel. In addition, we present a direct implementation of SMT solving in Prolog using ProB's constraint solver as a theory solver. We hereby aim to combine the strengths of conflict-driven clause learning for identifying contradictions with ProB's constraint solver for finding solutions. We deem this implementation to be worthwhile since ProB's constraint solver is tailored toward solving B and Event-B constraints, and we herewith avoid the dependency on an external SMT solver. Empirical results show that the new integration of Z3 has improved performance of constraint solving and enables to solve several constraints which cannot be solved by ProB's constraint solver. Furthermore, the direct implementation of SMT solving in ProB shows benefits compared to ProB's constraint solver and the integration of Z3. [ABSTRACT FROM AUTHOR]

This research analyzes the inclusion of the Pseint programming language in educational institutions in South America, as a language for the beginning of programming logic through instructions in Spanish. The institutions with a registered profile that are listed in the Sourceforge platform are analyzed, from the 9 countries that speak the Spanish language, although the language is used by a large number of teachers, they are not taken into account unless they maintain this registered profile. It is shown that the countries with more institutions adopting the language are Colombia at 25.73%, Argentina at 18.93%, and Peru at 17.48%, and the proximity of each country is analyzed to know its influence. [ABSTRACT FROM AUTHOR]

The lateral prefrontal cortex (LPFC) of humans enables flexible goal-directed behavior. However, its functional organization remains actively debated after decades of research. Moreover, recent efforts aiming to map the LPFC through meta-analysis are limited, either in scope or in the inferred specificity of structure-function associations. These limitations are in part due to the limited expressiveness of commonly-used data analysis tools, which restricts the breadth and complexity of questions that can be expressed in a meta-analysis. Here, we adopt NeuroLang, a novel approach to more expressive meta-analysis based on probabilistic first-order logic programming, to infer the organizing principles of the LPFC from 14,371 neuroimaging studies. Our findings reveal a rostrocaudal and a dorsoventral gradient, respectively explaining the most and second most variance in meta-analytic connectivity across the LPFC. Moreover, we identify a unimodal-to-transmodal spectrum of coactivation patterns along with a concrete-to-abstract axis of structure-function associations extending from caudal to rostral regions of the LPFC. Finally, we infer inter-hemispheric asymmetries along the principal rostrocaudal gradient, identifying hemisphere-specific associations with topics of language, memory, response inhibition, and sensory processing. Overall, this study provides a comprehensive meta-analytic mapping of the LPFC, grounding future hypothesis generation on a quantitative overview of past findings. [ABSTRACT FROM AUTHOR]

Graph theory has been a useful tool for logic programming in many aspects. In this paper, we propose an equivalent representation of multi-adjoint logic programs using hypergraphs, which are a generalization of classical graphs that allows the use of hypergraph theory in logic programming. Specifically, this representation has been considered in this paper to increase the level and flexibility of different termination results of the computation of the least model of fuzzy logic programs via the immediate consequence operator. Consequently, the least model of more general and versatile fuzzy logic programs can be obtained after finitely many iterations, although infinite programs or programs with loops and general aggregators will be considered. [ABSTRACT FROM AUTHOR]

Fuzzy linguistic logic programming (FLLP) is a framework for representation and reasoning with linguistically expressed human knowledge. In this paper, we extend FLLP by allowing negative literals to appear in rule bodies, resulting in normal logic programs. We study the stable model semantics and well-founded semantics of such programs and their relation. The two kinds of semantics are adapted from those of classical ones based on the Gelfond–Lifschitz transformation and van Gelder's alternating fixpoint approach, respectively. To our knowledge, until now, there has been no work on the well-founded semantics of normal programs in any fuzzy logic programming (FLP) framework based on Vojtáš's FLP. Moreover, the relation between the two kinds of semantics is usually studied using a bilattice setting of the truth domain. However, our truth domains do not possess a complete knowledge-ordering lattice and, thus, do not have a bilattice structure. The two kinds of semantics possess properties similar to those of the classical case. Every stable model contains the well-founded (partial) model, and the well-founded total model coincides with the unique stable model, but not vice versa. Since the well-founded semantics is closely related to the stable model semantics, it can help compute stable models more efficiently. [ABSTRACT FROM AUTHOR]

Learning first-order logic programs from relational facts yields intuitive insights into the data. Inductive logic programming (ILP) models are effective in learning first-order logic programs from observed relational data. Symbolic ILP models support rule learning in a data-efficient manner. However, symbolic ILP models are not robust to learn from noisy data. Neuro-symbolic ILP models utilize neural networks to learn logic programs in a differentiable manner which improves the robustness of ILP models. However, most neuro-symbolic methods need a strong language bias to learn logic programs, which reduces the usability and flexibility of ILP models and limits the logic program formats. In addition, most neuro-symbolic ILP methods cannot learn logic programs effectively from both small-size datasets and large-size datasets such as knowledge graphs. In the paper, we introduce a novel differentiable ILP model called differentiable first-order rule learner (DFORL), which is scalable to learn rules from both smaller and larger datasets. Besides, DFORL only needs the number of variables in the learned logic programs as input. Hence, DFORL is easy to use and does not need a strong language bias. We demonstrate that DFORL can perform well on several standard ILP datasets, knowledge graphs, and probabilistic relation facts and outperform several well-known differentiable ILP models. Experimental results indicate that DFORL is a precise, robust, scalable, and computationally cheap differentiable ILP model. [ABSTRACT FROM AUTHOR]

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming. [ABSTRACT FROM AUTHOR]

In the last decade, there has been increasing interest in extensions of answer set programming (ASP) that cater for quantitative information such as weights or probabilities. A wide range of quantitative reasoning tasks for ASP and logic programming, among them probabilistic inference and parameter learning in the neuro-symbolic setting, can be expressed as algebraic answer set counting (AASC) tasks, i.e., weighted model counting for ASP with weights calculated over some semiring, which makes efficient solvers for AASC desirable. In this article, we present ▪, a new solver for AASC that pushes the limits of efficient solvability. Notably, ▪ provides improved performance compared to the state of the art in probabilistic inference by exploiting three insights gained from thorough theoretical investigations in our work. Namely, we consider the knowledge compilation step in the AASC pipeline, where the underlying logical theory specified by the answer set program is converted into a tractable circuit representation, on which AASC is feasible in polynomial time. First, we provide a detailed comparison of different approaches to knowledge compilation for programs, revealing that translation to propositional formulas followed by compilation to sd-DNNF seems favorable. Second, we study how the translation to propositional formulas should proceed to result in efficient compilation. This leads to the second and third insight, namely a novel way of breaking the positive cyclic dependencies in a program, called T P -Unfolding, and an improvement to the Clark Completion, the procedure used to transform programs without positive cyclic dependencies into propositional formulas. Both improvements are tailored towards efficient knowledge compilation. Our empirical evaluation reveals that while all three advancements contribute to the success of ▪, T P -Unfolding improves performance significantly by allowing us to handle cyclic instances better. • In depth theoretical comparison of strategies. • Improvements over existing strategies. • Efficient implementation. • In depth empirical evaluation of our and SoTA solvers. [ABSTRACT FROM AUTHOR]

Motivation Network-based driver identification methods that can exploit mutual exclusivity typically fail to detect rare drivers because of their statistical rigor. Propagation-based methods in contrast allow recovering rare driver genes, but the interplay between network topology and high-scoring nodes often results in spurious predictions. The specificity of driver gene detection can be improved by taking into account both gene-specific and gene-set properties. Combining these requires a formalism that can adjust gene-set properties depending on the exact network context within which a gene is analyzed. Results We developed OMEN: a logic programming framework based on random walk semantics. OMEN presents a number of novel concepts. In particular, its design is unique in that it presents an effective approach to combine both gene-specific driver properties and gene-set properties, and includes a novel method to avoid restrictive, a priori filtering of genes by exploiting the gene-set property of mutual exclusivity, expressed in terms of the functional impact scores of mutations, rather than in terms of simple binary mutation calls. Applying OMEN to a benchmark dataset derived from TCGA illustrates how OMEN is able to robustly identify driver genes and modules of driver genes as proxies of driver pathways. Availability and implementation The source code is freely available for download at www.github.com/DriesVanDaele/OMEN. The dataset is archived at https://doi.org/10.5281/zenodo.6419097 and the code at https://doi.org/10.5281/zenodo.6419764. Supplementary information Supplementary data are available at Bioinformatics online. [ABSTRACT FROM AUTHOR]

The Lightning Network (LN) has emerged as one of the prominent solutions to overcome the biggest limit of blockchain based on PoW: scalability. LN allows for creating a layer on top of an existing blockchain where users can send payments and micro-payments without waiting long confirmation times. One of the key features of LN is that payments can also be sent towards nodes that are not directly connected. From the routing perspective, the balance of an edge that connects two nodes is known, but the distribution between the two involved ends is unknown. Thus, the process of sending payments is based on a trial and error approach, and the routing can be considered probabilistic. Probabilistic Logic Programming (PLP) is a powerful formalism that allows the representation of complex relational domains characterized by uncertainty. In this paper, we study the problem of reasoning about the existence of a path between two nodes that can route a payment of a given size leveraging multiple models based on PLP. We adopt some recently proposed extensions of PLP and develop several models that can be adapted to represent multiple scenarios. [ABSTRACT FROM AUTHOR]

The hedge-algebras (HA) theory has been effectively applied in different fields such as fuzzy database, logic programming, classification and regression, data mining, linguistic database summarization, and process control. This work presents a simple approach to design an HA-based controller in stabilizing a nonlinear and underactuated system, an inverted pendulum-cart model, including four input state variables and one output control variable. The HA-based controller is divided into four intermediate controllers with one input state and one output control variable. The combination method of the above intermediate controllers to achieve values of the global control variable in control loops is proposed following the influence level of state variables on the stable state of the system and the principle of HA-Inference step. The proposed approach is appropriate for controlling underactuated systems. Simulation results have indicated that the HA-based controller has high performance, adaptation, stability, and robustness. Moreover, the proposed method significantly reduces the computational time of the controller when compared to a classical Sugeno-type fuzzy controller. [ABSTRACT FROM AUTHOR]

This survey provides an overview of rule learning systems that can learn the structure of probabilistic rules for uncertain domains. These systems are very useful in such domains because they can be trained with a small amount of positive and negative examples, use declarative representations of background knowledge, and combine efficient high-level reasoning with the probability theory. The output of these systems are probabilistic rules that are easy to understand by humans, since the conditions for consequences lead to predictions that become transparent and interpretable. This survey focuses on representational approaches and system architectures, and suggests future research directions. [ABSTRACT FROM AUTHOR]

One of the elements of the modern trade and services market is a business chain solution (chain store/retail chain). An example of a business chain is, e.g., a restaurant chain, where each restaurant in the chain has the same decor, organization, menu, and delivery method. Although such solutions have been known for decades, the rapid development of IT technology, the widespread access to the Internet as well as the development of mobile technologies have changed and modernized their formula. Many customers place orders remotely with the option of delivery to their door. This method of ordering and fulfilling orders is becoming more and more popular and ever more common in the recent period due to the pandemic and the resulting restrictions and limitations on the functioning of trade and services. The following key questions arise in relation to customer order processing for chain business managers: How to allocate individual customer orders to selected branches so that the cost of their processing (production and delivery) is the lowest?, How to deliver on time ?, etc. To answer these questions, a decision support model has been developed, which combines routing, allocation and planning problems for restaurant/store chains. Two ways to implement the model have been proposed. The first one uses the methods of mathematical modeling and programming, and the other, which is a proprietary approach that integrates the mechanisms of evolution (specialized representations, repair mechanisms, genetic operators, etc.), uses constraint logic programming and dedicated heuristics. In addition, procedures for constraint handling and presolving have been developed. [ABSTRACT FROM AUTHOR]

One of the key challenges in computer networks is network security. For securing the network, various solutions have been proposed, including network security protocols and firewalls. In the case of so-called packet-filtering firewalls, policy rules are implemented to monitor changes to the network and preserve the required security level. Due to the dramatic increase of devices, however, and herewith the rapid increase of the size of the policy rules, firewall policy anomalies occur more frequently. This requires careful implementation of the policy rules to ensure cost-efficient solutions for anomaly detection to support network security. In this study, we present an anomaly detection framework for detecting intrafirewall policy anomaly rules. The framework supports the simulation of packets through the firewall ruleset for validating and enhancing the security level of the network. The framework is validated using four different types of firewall policy anomalies. Experimental results demonstrate that the framework is effective and efficient in detecting firewall policy anomalies. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the challenges of the education that high school students are facing while developing specific competencies related to the functional programming style (FPS). The presented educational approach consists of two components: first, learning FPS by comparing it with the imperative, procedural, object-oriented and logic programming paradigms and second, using competencies based approach for solving practical problems with functional programming. The paper presents a problem set and the phases of its application in the learning process. The results and the analysis of the approach are presented in two groups of high school students which develop successfully their specific competencies for using FPS for practical problem solving. The presented results show that the students are understanding easier FPS and its differences from their known paradigms (imperative, procedural, object-oriented and logical) by using a problem set with properly prepared practical problems which they can solve in multiple ways which lead them to the FPS solution. [ABSTRACT FROM AUTHOR]

This work presents the mapping of the traveling salesperson problem (TSP) based in pseudo-Boolean constraints to a graph of the D-Wave Systems Inc. We first formulate the problem as a set of constraints represented in propositional logic and then resort to the SATyrus approach to convert the set of constraints to an energy minimization problem. Next, we transform the formulation to a quadratic unconstrained binary optimization problem (QUBO) and solve the problem using different approaches: (a) classical QUBO using simulated annealing in a von Neumann machine, (b) QUBO in a simulated quantum environment, (c) QUBO using the D-Wave quantum machine. Moreover, we study the amount of time and execution time reduction we can achieve by exploring approximate solutions using the three approaches. Results show that for every graph size tested with the number of nodes less than or equal to 7, we can always obtain at least one optimal solution. In addition, the D-Wave machine can find optimal solutions more often than its classical counterpart for the same number of iterations and number of repetitions. Execution times, however, can be some orders of magnitude higher than the classical or simulated approaches for small graphs. For a higher number of nodes, the average execution time to find the first optimal solution in the quantum machine is 26% ( n = 6 ) and 47% ( n = 7 ) better than the classical. [ABSTRACT FROM AUTHOR]

In the present study, we proposed a greedy randomized adaptive search procedure (GRASP) for integrated scheduling of dynamic flexible job shops with a novel preventive maintenance policy. In most of the real-life scheduling practices, unexpected and unknown events occur frequently, which necessitates solving operations and maintenance scheduling problems dynamically. Dynamic events like new order arrival, machine breakdown, changes in due date, order cancellation, and urgent order are considered in this study. Moreover, order acceptance/rejection decisions and an order review release mechanism are also taken into account in order to enhance the overall performance by adjusting capacity regarding to customer due date requirements. Four objectives namely mean tardiness, schedule instability, makespan, and mean flow time are considered within a lexicographic programming logic. Random test instances are generated for the stated dynamic scheduling problem. In order to confirm the applicability of the proposed GRASP-based algorithm, extensive experiments were also conducted on well-known job shop scheduling benchmark instances and flexible job shop scheduling benchmark instances with preventive maintenance activities. Computational experiments conducted under various experimental settings such as flexibility level and due date tightness in addition to different preventive maintenance policies. To the best of our knowledge, the present study presents the first attempt through GRASP for simultaneous dynamic scheduling of operations and preventive maintenance activities in flexible job shops. Results of the extensive computational experiments demonstrate that simultaneous scheduling of manufacturing operations and preventive maintenance activities is a viable and effective approach for performance improvement in dynamic flexible job shop scheduling environments. [ABSTRACT FROM AUTHOR]

• The copy complexity of a Horn formula equals the copy complexity of the corresponding system of constraints. • The copy complexity of Horn formulas with respect to unit resolution is (m − 1) when copies of derived clauses are allowed. • A polynomial time algorithm that can determine if a 2-CNF formula has a unit read-once resolution refutation. In this paper, we discuss the copy complexity of Horn formulas with respect to unit resolution. A Horn formula is a boolean formula in conjunctive normal form (CNF) with at most one positive literal per clause. Horn formulas find applications in a number of domains, such as program verification (abstract interpretation) and logic programming (answer set programming). Quantified Horn clauses are used extensively in temporal verification of universal properties. Resolution is one of the oldest proof systems (refutation systems) for the boolean satisfiability problem (SAT), when the input is presented in conjunctive normal form (CNF). It is both sound and complete, although inefficient, when compared to other stronger proof systems for boolean formulas. Despite its inefficiency, the simple nature of resolution makes it an integral part of several theorem provers. Unit resolution is a restricted form of resolution in which each resolution step needs to use a clause with only one literal (unit literal clause). While not complete for general CNF formulas, unit resolution is complete for Horn formulas. Read-once resolution is a form of resolution in which each clause (input or derived) may be used in at most one resolution step. As with unit resolution, read-once resolution is incomplete in general and complete for Horn clauses. This paper focuses on a combination of unit resolution and read-once resolution called unit read-once resolution. Unit read-once resolution is incomplete for Horn clauses. In this paper, we study the copy complexity problem in Horn formulas with respect to unit read-once resolution. Briefly, the copy complexity of a formula with respect to unit read-once resolution, is the smallest number k , such that replicating each clause k times guarantees the existence of a unit read-once resolution refutation (UROR). This paper focuses on two problems related to the copy complexity of Horn formulas with respect to unit read-once resolution. We first relate the copy complexity of Horn formulas with respect to unit read-once resolution to the copy complexity of the corresponding Horn constraint system with respect to the addition rule. We also examine a form of copy complexity in which we permit replication of derived clauses, in addition to the input clauses. Finally, we provide a polynomial time algorithm for the problem of checking if a 2-CNF formula has a UROR. [ABSTRACT FROM AUTHOR]

This study proposed a hybridization of higher-order Random Boolean kSatisfiability (RANkSAT) with the Hopfield neural network (HNN) as a neuro-dynamical model designed to reflect knowledge efficiently. The learning process of the Hopfield neural network (HNN) has undergone significant changes and improvements according to various types of optimization problems. However, the HNN model is associated with some limitations which include storage capacity and being easily trapped to the local minimum solution. The Election algorithm (EA) is proposed to improve the learning phase of HNN for optimal Random Boolean kSatisfiability (RANkSAT) representation in higher order. The main source of inspiration for the Election Algorithm (EA) is its ability to extend the power and rule of political parties beyond their borders when seeking endorsement. The main purpose is to utilize the optimization capacity of EA to accelerate the learning phase of HNN for optimal random k Satisfiability representation. The global minima ratio (mR) and statistical error accumulations (SEA) during the training process were used to evaluate the proposed model performance. The result of this study revealed that our proposed EA-HNN-RANkSAT outperformed ABC-HNNRANkSAT and ES-HNN-RANkSAT models in terms of mR and SEA. This study will further be extended to accommodate a novel field of Reverse analysis (RA) which involves data mining techniques to analyse real-life problems. [ABSTRACT FROM AUTHOR]

Reaction Systems (RSs) are a successful computational framework inspired by biological systems. A RS pairs a set of entities with a set of reactions over them. Entities can be used to enable or inhibit each reaction, and are produced by reactions. Entities can also be provided by an external context sequence to simulate in silico biological experiments. In this paper we define an extension of RSs considering nondeterministic and recursive context operators, and give an original labelled transition system (LTS) for extended RSs in the structural operational semantics (SOS) style. Thanks to extended contexts, a single LTS can now account for several biological experiments. The rich information recorded in transition labels is useful to guarantee the compositionality of SOS inference rules as well as to define an assertion language to tailor behavioural and logical equivalences on some specific properties or entities. The SOS rules have been also exploited to design a flexible prototype implementation in logic programming that allows to inspect the LTS and to extract useful information when performing experiments on a RS. Our implementation provides a rapid prototyping tool for (extensions of) RSs, with a user friendly online interface to our interpreter. A parser allows to introduce the logical formulas and the contexts using the usual comfortable concrete syntax. The user can visualise and inspect the LTS for a RS and make some analysis of its underlying computation patterns, can check if the main RS satisfies a given property and if it is equivalent to a second adversarial RS. Finally, the SOS approach is suited to drive additional enhancements of RSs. [ABSTRACT FROM AUTHOR]