A logical spreadsheet is a spreadsheet in which the formula language is composed of logical expressions. Logical spreadsheets were invented shortly after traditional electronic spreadsheets were introduced, but since then logical spreadsheet research has been somewhat sparse. Recently, however, there has been a resurgence in the interest of logical spreadsheets in the research community. In this article, we summarize logical spreadsheet research up to this point.

We present in this paper a general algorithm for solving first-order formulas in particular theories called decomposable theories. First of all, using special quantifiers, we give a formal characterization of decomposable theories and show some of their properties. Then, we present a general algorithm for solving first-order formulas in any decomposable theory T. The algorithm is given in the form of five rewriting rules. It transforms a first-order formula ϕ, which can possibly contain free variables, into a conjunction φ of solved formulas easily transformable into a Boolean combination of existentially quantified conjunctions of atomic formulas. In particular, if ϕ has no free variables then φ is either the formula true or ¬true. The correctness of our algorithm proves the completeness of the decomposable theories. Finally, we show that the theory of finite or infinite trees is a decomposable theory and give some benchmarks realized by an implementation of our algorithm, solving formulas on two-partner games in with more than 160 nested alternated quantifiers.

We study the gaps in the sequence of sums of h pairwise distinct elements of a given sequence in relation to the gaps in the sequence of sums of h not necessarily distinct elements of . We present several results on this topic. One of them gives a negative answer to a question by Burr and Erdős.

In this article, we describe PrediCalc, a logical spreadsheet that allows for many-to-many constraints and propagation in all directions. We explain PrediCalc’s update mechanism and PrediCalc’s unique approach to handling inconsistencies between the spreadsheet values and the spreadsheet formulas. We have developed a paraconsistent entailment relation for the purpose of computing the consequences of PrediCalc’s value assignments under inconsistency.

We close with thoughts on the prospects of logical spreadsheets on the World Wide Web, and describe our initial Websheet prototypes.

While a robot moves, online hand–eye calibration to determine the relative pose between the robot gripper/end-effector and the sensors mounted on it is very important in a vision-guided robot system. During online hand–eye calibration, it is impossible to perform motion planning to avoid degenerate motions and small rotations, which may lead to unreliable calibration results. This paper proposes an adaptive motion selection algorithm for online hand–eye calibration, featured by dynamic threshold determination for motion selection and getting reliable hand–eye calibration results. Simulation and real experiments demonstrate the effectiveness of our method.

Usability and usefulness have made the spreadsheet one of the most successful computing applications of all times: millions rely on it every day for anything from typing grocery lists to developing multimillion-dollar budgets. One thing spreadsheets are not very good at is manipulating the symbolic data and helping users make decisions based on them. By tapping into recent research in Logic Programming, Databases and Cognitive Psychology, we propose a deductive extension to the spreadsheet paradigm that precisely addresses this issue. The accompanying tool, which we call NEXCEL, is intended as an automated assistant for the daily reasoning and decision-making needs of computer users, in the same way as a spreadsheet application such as Microsoft Excel assists them every day with simple and complex calculations. Users without formal training in Logic or even Computer Science can interactively define logical rules in the same simple way as they define formulas in Excel. NEXCEL immediately evaluates these rules, thereby returning lists of values that satisfy them, again just like with numerical formulas. The deductive component is seamlessly integrated into the traditional spreadsheet so that a user not only still has access to the usual functionalities but is also able to use them as part of the logical inference and, dually, to embed deductive steps in a numerical calculation.

Let G be a simple graph on n vertices. A conjecture of Bollobás and Eldridge [5] asserts that if then G contains any n vertex graph H with Δ(H) = k. We prove a strengthened version of this conjecture for bipartite, bounded degree H, for sufficiently large n. This is the first result on this conjecture for expander graphs of arbitrary (but bounded) degree. An important tool for the proof is a new version of the Blow-Up Lemma.

This paper discusses about auto-laydown robot (ALR), which is applied to performing the laydown process of a solar module on earth. The robot consists of an adhesive dispensing mechanism, an auto-laydown mechanism, a pneumatic system and a control system. The method of gripping solar cells is described based on pneumatic technology. Meanwhile, a new method of controlling adhesive thickness and area during dispensing is proposed in this paper. The robot realizes the automatic laydown process of solar modules and can control the laydown pressure effectively. Compared with the manual method, the robot could control the dispensing volume and the adhesive area between solar modules and panel substrates, by means of experiments. The novel ALR greatly improves the laydown quality of solar modules and meets the lightweight trend of solar cells development.

Free-flying space manipulator systems, in which robotic manipulators are mounted on a free-flying spacecraft, are envisioned for assembling, maintenance, repair, and contingency operations in space. Nevertheless, even for fixed-base systems, control of mechanical manipulators is a challenging task. This is due to strong nonlinearities in the equations of motion, and consequently different algorithms have been suggested to control end-effector motion or force, since the early research in robotic systems. In this paper, first a brief review of basic concepts of various algorithms in controlling robotic manipulators is introduced. Then, specific problems related to application of such systems in space and a microgravity environment is highlighted. Basic issues of kinematics and dynamics modeling of such systems, trajectory planning and control strategies, cooperation of multiple arm space free-flying robots, and finally, experimental studies and technological aspects of such systems with their specific limitations are discussed.

An understanding of how humans and robots can successfully interact to accomplish specific tasks is crucial in creating more sophisticated robots that may eventually become an integral part of human societies. A social robot needs to be able to learn the preferences and capabilities of the people with whom it interacts so that it can adapt its behaviors for more efficient and friendly interaction. Advances in human– computer interaction technologies have been widely used in improving human–robot interaction (HRI). It is now possible to interact with robots via natural communication means such as speech. In this paper, an innovative approach for HRI via voice-controllable intelligent user interfaces is described. The design and implementation of such interfaces are described. The traditional approaches for human–robot user interface design are explained and the advantages of the proposed approach are presented. The designed intelligent user interface, which learns user preferences and capabilities in time, can be controlled with voice. The system was successfully implemented and tested on a Pioneer 3-AT mobile robot. 20 participants, who were assessed on spatial reasoning ability, directed the robot in spatial navigation tasks to evaluate the effectiveness of the voice control in HRI. Time to complete the task, number of steps, and errors were collected. Results indicated that spatial reasoning ability and voice-control were reliable predictors of efficiency of robot teleoperation. 75% of the subjects with high spatial reasoning ability preferred using voice-control over manual control. The effect of spatial reasoning ability in teleoperation with voice-control was lower compared to that of manual control.

Inspired by the agility of animal and human locomotion, the number of researchers studying and developing legged robots has been increasing at a rapid rate over the last few decades. In comparison to multilegged robots, single-legged robots have only one type of locomotion gait, i.e., hopping, which represents a highly nonlinear dynamical behavior consisting of alternating flight and stance phases. Hopping motion has to be dynamically stabilized and presents challenging control problems. A large fraction of studies on legged robots has focused on modeling and control of single-legged hopping machines. In this paper, we present a comprehensive review of developments in the field of single-legged hopping robots. We have attempted to cover development of prototype models as well as theoretical models of such hopping systems.

The promise of rule-based computing was to allow end-users to create, modify, and maintain applications without the need to engage programmers. But experience has shown that rule sets often interact in subtle ways, making them difficult to understand and reason about. This has impeded the widespread adoption of rule-based computing. This paper describes the design and implementation of XcelLog, a user-centered deductive spreadsheet system, to empower non-programmers to specify and manipulate rule-based systems. The driving idea underlying the system is to treat sets as the fundamental data type and rules as specifying relationships among sets, and use the spreadsheet metaphor to create and view the materialized sets. The fundamental feature that makes XcelLog suitable for non-programmers is that the user mainly sees the effect of the rules; when rules or basic facts change, the user sees the impact of the change immediately. This enables the user to gain confidence in the rules and their modification, and also experiment with what-if scenarios without any programming. Preliminary experience with using XcelLog indicates that it is indeed feasible to put the power of deductive spreadsheets for doing rule-based computing into the hands of end-users and do so without the requirement of programming or the constraints of canned application packages.

Let S be a finite set of integers. We consider a problem of finding D(S), the minimum size of a set A, such that S⊆ A−A. We give a characterization for ‘extremal’ sets and prove lower and upper bounds on D(S) in terms of additive properties of S.