Disjunction Operators Research Articles

Sequential control barrier functions for mobile robots with dynamic temporal logic specifications

We address a motion planning and control problem for mobile robots to satisfy rich, time-varying tasks expressed as Signal Temporal Logic (STL) specifications. The specifications may include tasks with nested temporal operators or time-conflicting requirements (e.g., achieving periodic tasks or tasks defined within the same time interval). Moreover, the tasks can be defined in locations changing with time (i.e., dynamic targets), and their future motions are not known a priori. This unpredictability requires an online control approach which motivates us to investigate the use of control barrier functions (CBFs). The proposed CBFs take into account the actuation limits of the robots and a feasible sequence of STL tasks. They define time-varying feasible sets of states the system must always stay inside. We show the feasible sequence generation process that even includes the decomposition of periodic tasks and alternative scenarios due to disjunction operators. The sequence is used to define CBFs, ensuring STL satisfaction. We also show some theoretical results on the correctness of the proposed method. We illustrate the benefits of the proposed method and analyze its performance via simulations and experiments with aerial robots.

A Cardinality Estimator in Complex Database Systems Based on TreeLSTM.

Cardinality estimation is critical for database management systems (DBMSs) to execute query optimization tasks, which can guide the query optimizer in choosing the best execution plan. However, traditional cardinality estimation methods cannot provide accurate estimates because they cannot accurately capture the correlation between multiple tables. Several recent studies have revealed that learning-based cardinality estimation methods can address the shortcomings of traditional methods and provide more accurate estimates. However, the learning-based cardinality estimation methods still have large errors when an SQL query involves multiple tables or is very complex. To address this problem, we propose a sampling-based tree long short-term memory (TreeLSTM) neural network to model queries. The proposed model addresses the weakness of traditional methods when no sampled tuples match the predicates and considers the join relationship between multiple tables and the conjunction and disjunction operations between predicates. We construct subexpressions as trees using operator types between predicates and improve the performance and accuracy of cardinality estimation by capturing the join-crossing correlations between tables and the order dependencies between predicates. In addition, we construct a new loss function to overcome the drawback that Q-error cannot distinguish between large and small cardinalities. Extensive experimental results from real-world datasets show that our proposed model improves the estimation quality and outperforms traditional cardinality estimation methods and the other compared deep learning methods in three evaluation metrics: Q-error, MAE, and SMAPE.

Logic reasoning under data veracity concerns

Logic reasoning involving big data often requires the proper handling of data veracity. Indeed with data that cannot be trusted to the same extent, users should at least be aware on the trust they can have in the obtained reasoning. In this paper, we propose a novel logic framework that is based on so-called L-grades. L-grades are a special case of Zadeh's Z-numbers, consisting of a pair (s,c)∈[0,1]2 in which s is a suitability grade (or satisfaction grade) and c is a confidence grade denoting how confident we can be on s. Both grades are further processed using fuzzy logic. A novel negation operator and novel conjunction and disjunction operators satisfying commutativity, associativity, but not distributivity properties are proposed. Furthermore, so-called sibling aggregators for L-grades are introduced and studied. With this framework we aim to contribute to explainable computational intelligence. The practical applicability of L-grades is discussed based on the demand for more informative, explainable results in the TILES decision support system for sand extraction from the North Sea seabed.

Zero-Watermarking for Vector Maps Combining Spatial and Frequency Domain Based on Constrained Delaunay Triangulation Network and Discrete Fourier Transform.

With its lossless properties, zero-watermarking has attracted a lot of attention in the field of copyright protection for vector maps. However, the common zero-watermarking algorithm puts too much emphasis on mining for global features, making it vulnerable to cropping attacks, and the robustness is not comprehensive enough. This study provides a vector map zero-watermarking scheme that utilizes spatial statistical information and frequency domain transformation methods in an effort to solve the aforementioned issue. In order to make the scheme more resistant to cropping and compression, it is constructed on the basis of feature point extraction and point constraint blocking of the original vector map. Within each sub-block, feature points are used to build constraint Delaunay triangulation networks (CDTN), and the angular values within the triangle networks are then extracted as spatial statistics. The angle value sequence is further transformed by discrete Fourier transform (DFT), and the binarized phase sequence is used as the final feature information to build a zero watermark by executing an exclusive disjunction operation with the encrypted copyright watermark image, both of which contribute to the scheme's robustness and security. The results of the attack experiments show that the proposed vector map zero-watermarking can restore identifiable copyright images under common geometric attacks, cropping attacks, and coordinate system transformations, demonstrating a high level of robustness. The theoretical basis for the robustness of this watermarking scheme is the stability of CDTN and the geometric invariance of DFT coefficients, and both theory and experiment validate the method's validity.

Fuzzy parallel dynamical systems on Zadeh operators

In this paper, we describe the orbital structure of homogeneous fuzzy parallel dynamical systems on Zadeh operators. In particular, we show that, when the (global) evolution operator is either the Zadeh conjunction operator AND or the Zadeh disjunction operator OR, all the points of the system are fixed points or eventually fixed points. Specifically, such systems present infinitely many fixed points. On the other hand, when the (global) evolution operator is either the Zadeh operator NOR or the Zadeh operator NAND, the orbital structure consists of an only fixed point and infinitely many 2‐periodic points.

On the orders of OWA operators

In this paper, we propose a partial ordering ⪯ on the set of ordered weighted averaging (OWA) operators. Based on this relation ⪯, we introduce the negation, conjunction and disjunction operations, and establish a bounded De Morgan lattice equipped with an involutive negation for OWA operators. Finally, we develop a similarity measure between OWA operators based on the ordering ⪯.

Relevant epistemic logic with public announcements and common knowledge

AbstractWe study a version of public announcement logic with common knowledge based on the relevant logic $\textsf {R}$. Public announcements, as represented in our framework, are not necessarily truthful and accepted by all agents, nor is it assumed that beliefs are preserved under announcements. We establish a completeness result with respect to a relational semantics, and we show that an alternative semantics based on information states is dual to the relational one. We add a question-forming inquisitive disjunction operator to the language and prove a completeness result with respect to the information semantics.

Rubric-based Learner Modelling via Noisy Gates Bayesian Networks for Computational Thinking Skills Assessment

In modern and personalised education, there is a growing interest in developing learners’ competencies and accurately assessing them. In a previous work, we proposed a procedure for deriving a learner model for automatic skill assessment from a task-specific competence rubric, thus simplifying the implementation of automated assessment tools. The previous approach, however, suffered two main limitations: (i) the ordering between competencies defined by the assessment rubric was only indirectly modelled; (ii) supplementary skills, not under assessment but necessary for accomplishing the task, were not included in the model. In this work, we address issue (i) by introducing dummy observed nodes, strictly enforcing the skills ordering without changing the network’s structure. In contrast, for point (ii), we design a network with two layers of gates, one performing disjunctive operations by noisy-OR gates and the other conjunctive operations through logical ANDs. Such changes improve the model outcomes’ coherence and the modelling tool’s flexibility without compromising the model’s compact parametrisation, interpretability and simple experts’ elicitation. We used this approach to develop a learner model for Computational Thinking (CT) skills assessment. The CT-cube skills assessment framework and the Cross Array Task (CAT) are used to exemplify it and demonstrate its feasibility.

Innovation of Visual Communication Design of Interactive Packaging for Internet-Famous Food Based on Artificial Intelligence

The combination of visual communication design of food packaging and digital media art is the new trend. In this study, the visual communication design of interactive packaging of Internet-famous food is analyzed, and an innovative identification method of the interactive packaging visual communication design based on artificial intelligence is put forward. The weighted fusion rule of conjunction disjunction double operators is used to fuse the innovative evaluation information of multiple expert groups on interactive packaging, and finally, the innovative multigroup discrimination results of interactive packaging are obtained. Considering both the consistency of evaluation information and the contradiction of evaluation information, the weight factor is introduced to achieve the balance between conjunction operator and disjunction operator. The designed conjunctive disjunctive double operator weighted fusion rule can support the contradiction handling in the innovative discrimination of interactive packaging and has the advantages of convenient application and easy programming.

Ki and naki - Alternative Question Particles in Bangla

The primary discussion of the paper is centered on two polar question particles in the Eastern Indo-Aryan language Bangla. One is ‘ki’ and the other one is ‘naki.’ These two polar question particles also appear as interrogative disjunction morphemes in alternative questions. This further leads to the argument that there exists a disjunction operator in both polar and alternative questions and the polar question particle is the lexical realization of that disjunction operator.

A Quantum Framework for Modeling Interference Effects in Linguistic Distribution Multiple Criteria Group Decision Making

In most existing linguistic distribution multiple criteria group decision-making (MCGDM) models, the sample size of group linguistic distribution assessment (LDA) is often neglected, and the decision makers are viewed to be independent. The probabilistic distribution is closely related to the sample size, and there exist more or fewer interference effects among different individual opinions. Thus, this article develops a quantum framework for modeling interference effects in the linguistic distribution MCGDM process. First, considering the sample size information, we redefine the LDAs and provide a new computational model for them. Second, to integrate a series of LDAs, the linguistic distribution weighted averaging (LDWA) operator is presented. Mathematic proofs reveal that the new LDWA operator can not only ensure the information integrality but also can avoid the conjunctive and disjunctive operations. Third, to explore the interference effects among individual opinions, a quantum framework is constructed. In this process, individual opinions are viewed as various wave functions occurring synchronously. They interfere with each and influence the aggregation result. Finally, an illustrative example of Internet finance soft power evaluation is provided to verify the effectiveness. Sensitivity and comparative analyses are also implemented to assess the stability and validity of our method.

Improving lung region segmentation accuracy in chest X-ray images using a two-model deep learning ensemble approach

We propose a deep learning framework to improve segmentation accuracy of the lung region in Chest X-Ray (CXR) images. The proposed methodology implements a “divide and conquer” strategy where the original CXRs are subdivided into smaller image patches, segmented them individually, and then reassembled to achieve the complete segmentation. This approach ensembles two models, the first of which is a traditional Convolutional Neural Network (CNN) used to classify the image patches and subsequently merge them to obtain a pre-segmentation. The second model is a modified U-Net architecture to segment the patches and subsequently combines them to obtain another pre-segmented image. These two pre-segmented images are combined using a binary disjunction operation to get the initial segmentation, which is later post-processed to obtain the final segmentation. The post-processing steps consist of traditional image processing techniques such as erosion, dilation, connected component labeling, and region-filling algorithms. The robustness of the proposed methodology is demonstrated using two public (MC, JPCL) and one proprietary (The University of Texas Medical Branch - UTMB) datasets of CXR images. The proposed framework outperformed many state-of-the-arts competitions presented in the literature.

Context-Aware Explainable Recommendation Based on Domain Knowledge Graph

With the rapid growth of internet data, knowledge graphs (KGs) are considered as efficient form of knowledge representation that captures the semantics of web objects. In recent years, reasoning over KG for various artificial intelligence tasks have received a great deal of research interest. Providing recommendations based on users’ natural language queries is an equally difficult undertaking. In this paper, we propose a novel, context-aware recommender system, based on domain KG, to respond to user-defined natural queries. The proposed recommender system consists of three stages. First, we generate incomplete triples from user queries, which are then segmented using logical conjunction (∧) and disjunction (∨) operations. Then, we generate candidates by utilizing a KGE-based framework (Query2Box) for reasoning over segmented logical triples, with ∧, ∨, and ∃ operators; finally, the generated candidates are re-ranked using neural collaborative filtering (NCF) model by exploiting contextual (auxiliary) information from GraphSAGE embedding. Our approach demonstrates to be simple, yet efficient, at providing explainable recommendations on user’s queries, while leveraging user-item contextual information. Furthermore, our framework has shown to be capable of handling logical complex queries by transforming them into a disjunctive normal form (DNF) of simple queries. In this work, we focus on the restaurant domain as an application domain and use the Yelp dataset to evaluate the system. Experiments demonstrate that the proposed recommender system generalizes well on candidate generation from logical queries and effectively re-ranks those candidates, compared to the matrix factorization model.

The generalized sigmoid function and its connection with logical operators

In this study, we present the operator-dependent sigmoid function, which is derived from a universal unary operator called the kappa function. Here, we describe how the generalized sigmoid function is related to representable uninorms (i.e., Dombi's aggregative operator). Namely, we show that the inverse of a generalized sigmoid function is an additive generator of the aggregative operator. We provide the necessary and sufficient conditions for the form of the function that transforms the aggregative operator into a conjunctive or disjunctive logical operator. This transformation is also based on the generalized sigmoid function. Here, we show how conjunctive and disjunctive operators, which form a De Morgan system with a negation, can be derived from the aggregative operator. We point out that, under certain conditions, a set of generalized sigmoid functions is closed under the negation and modifier operators. Lastly, we demonstrate an important connection between the weighted aggregative operator and the generalized sigmoid function. Based on this connection, we provide a new interpretation of the feed-forward neural networks. We show that a perceptron-based neural network can be modeled using the aggregative operator and the generalized sigmoid function.

On union and intersection of type-2 fuzzy sets not expressible by the sup-t-norm extension principle

This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hernández et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.

On the distributivity of fuzzy implications and the weighted S-implications

The distributivity properties of fuzzy implication functions play an important role in fuzzy research. Making use of the solution of the autodistributivity functional equations, we give the necessary and sufficient conditions of two types of the distributivity property of fuzzy implications. It is essentially based on the weighted disjunctive operator, and new weighted and mean (S,N)-implication functions are introduced. Then using the pliant operators – where all the operators have a common generator function – we give a parametric form of the implication, namely the neutral value-dependent implication, and we show that some weakened properties of the fuzzy weighted implications are valid such as the identity principle, the ordering principle, the T-conditionality, the strong negation principle, etc. With this new concept, we use the fixed point of the negation as a threshold. We give a specific form of the new implication.

Faster and Better Simple Temporal Problems

In this paper we give a structural characterization and extend the tractability frontier of the Simple Temporal Problem (STP) by defining the class of the Extended Simple Temporal Problem (ESTP), which augments STP with strict inequalities and monotone Boolean formulae on inequations (i.e., formulae involving the operations of conjunction, disjunction and parenthesization). A polynomial-time algorithm is provided to solve ESTP, faster than previous state-of-the-art algorithms for other extensions of STP that had been considered in the literature, all encompassed by ESTP. We show the practical competitiveness of our approach through a proof-of-concept implementation and an experimental evaluation involving also state-of-the-art SMT solvers.

A unified approach to four important classes of unary operators

In this paper, we study operator dependent modifiers and we interpret the dual pair of modal operators based on an algebraic definition. It is a known fact that the substantiating and weakening modifier operators can be induced by repeating the arguments of conjunctive and disjunctive operators. We provide the conditions for which these modifier operators satisfy the requirements for a dual pair of necessity and possibility operators. Next, the necessary and sufficient condition for the distributivity of unary operators over conjunctive and disjunctive operators is presented. This also means that setting the distributivity as a requirement results in a unary operator that is identical to the modal operators mentioned above. Using this property, we establish an important connection between modal operators and linguistic hedges. Previously, we demonstrated that the unary operators induced by compositions of two strong negations satisfy the requirements for a dual pair of modal operators. Here, we view the negation operator as a modifier operator. Then, it is shown that (1) the strong negations, (2) the substantiating and weakening modifier operators, modal operators and linguistic hedges mentioned above, and (3) the unary operators, which are distributive over conjunctive and disjunctive operators, may be viewed as special cases of a unified unary operator class.

Atmospheric reentry hemisphere prediction for prograde orbits using logical disjunction

A unique logic-based algorithm for atmospheric reentry hemisphere prediction is presented for spacecraft in low-eccentricity, prograde low Earth orbits at altitudes of 300 km and lower. Using two-line element (TLE) data for initial orbit conditions, coupled with coarse estimates for spacecraft aerodynamic characteristics, the algorithm relies on logical disjunction operations based on a dual analysis of histogram and two-weighted Gaussian probability density function (PDF) fits of predicted reentry latitude data. The algorithm requires the execution of a series of parametric simulations to determine the reentry hemisphere for variations in spacecraft aerodynamic coefficients and drag reference area. When implemented, the algorithm yields accurate hemisphere predictions on average 15 days from reentry as demonstrated by historical reentry cases from 1979 to 2018. All reentry cases were selected to demonstrate the algorithm’s ability to deliver accurate reentry hemisphere predictions for spacecraft with varying physical size and mass, and reentering during different periods of solar cycle activity.

Cardinality Estimation of an SQL Query Using Recursive Neural Networks

To learn complex interactions between predicates and accurately estimate the cardinality of an SQL query, we develop a novel framework based on recursive tree-structured neural networks, which take into account the natural properties of logical expressions: compositionality and n-ary associativity. The proposed architecture is an extension of MSCN (multi-set convolutional network) for queries containing both conjunction and disjunction operators. The goal is to represent an arbitrary logical expression in a continuous vector space by combining sub-expression vectors according to the operator type. We compared the proposed approach with the histogram-based approach on the real-world dataset and showed that our approach significantly outperforms histograms with a large margin.