Annals of Mathematics and Artificial Intelligence最新文献

Logical Analysis of Data (LAD) is a powerful technique for data classification based on partially defined Boolean functions. The decision rules for class prediction in LAD are formed out of patterns. According to different preferences in the classification problem, various pattern types have been defined. The generation of these patterns plays a key role in the LAD methodology and represents a computationally hard problem. In this article, we introduce a new approach to pattern generation in LAD based on Answer Set Programming (ASP), which can be applied to all common LAD pattern types.

We present an approach for automated theorem proving in 3D solid geometry utilizing multiple algebraic prover engines. Our solution integrates dynamic geometry systems capable of generating solid geometry constructions. We have employed two different methods to transform geometric statements into algebraic representations, while implementing and evaluating these approaches with various theorem provers. Furthermore, we have explored non-degeneracy conditions (NDG) in the context of 3D solid geometry and provided insights into their role in ensuring the validity of geometric relations.

For rational parameterization of curves, it is desirable that the angular speed is made as uniform as possible. When the rational parameterization of a curve is given, the uniformity of its angular speed may be enhanced by finding a re-parameterization that achieves better uniformity, where one natural approach is to use piecewise rational reparameterization. However, this approach does not improve the situation when the angular speed of the original rational parameterization is zero at certain points on the curve. In this paper, we demonstrate that the challenge may be tackled by utilizing piecewise radical reparameterization.

How can we efficiently determine meta-parameter values for deep learning-based time-series forecasting given a time-series dataset? This paper introduces Xtune, an efficient and novel meta-parameter tuning method for deep learning-based time-series forecasting, leveraging explainable AI techniques. In particular, this study focuses on optimizing the window size for time-series forecasting. Xtune determines the optimal meta-parameter value for these methods and can also be applied to tune the window size for anomaly detection methods that utilize deep learning-based time-series forecasting. Extensive experiments on real-world datasets and forecasting methods demonstrate that Xtune efficiently identifies the optimal meta-parameter value and consistently outperforms the existing methods in terms of execution speed.

Although there are several systems that successfully generate construction steps for ruler and compass construction problems, none of them provides readable synthetic correctness proofs for generated constructions. In this paper, we demonstrate how our triangle construction solver ArgoTriCS can cooperate with automated theorem provers for first-order logic and coherent logic so that it generates construction correctness proofs, that are both human-readable and formal (can be checked by interactive theorem provers such as Isabelle/HOL or Coq). For this purpose we identified a set of relevant lemmas and developed a coherent logic prover GCProver customized for geometry construction problems. Our experiments show that results are much better than with general purpose theorem provers.

In this paper, we consider automated solving of triangle straightedge-and-compass construction problems by reducing them to automated planning. We consider the problems from the Wernick’s list, where each problem assumes that locations of three significant points of a triangle are given, and the goal is to construct all three vertices of the triangle. We develop two different models of the corresponding planning problem. In the first model, the planning problem is described using the PDDL language, which is suitable for solving with dedicated automated planners. The second model assumes that the planning problem is first expressed as a finite-domain constraint satisfaction problem, and then encoded in the MiniZinc language. Such model is suitable for solving with constraint solvers. In both cases, we employ existing artificial intelligence tools in search for a solution of our construction problem. The main benefit of using the existing tools for such purpose, instead of developing dedicated tools, is that we can rely on the efficient search that is already implemented within the tool, enabling us to focus on geometric aspects of the problem. We evaluate our approach on 74 solvable problems from the Wernick’s list, and compare it to the dedicated triangle construction solver ArgoTriCS. The results show that our approach tends to be superior to dedicated tools in terms of efficiency, while it requires much less effort to implement. Also, we are often able to find shorter construction plans, thanks to the optimization capabilities offered by the modern planners and constraint solvers. The presented approach is only a search method and does not address proving the correctness of the obtained constructions and discussing when solutions exist, leaving these tasks to other tools. Although the paper focuses on a specific set of construction problems, the approach can be generalized to other classes of problems, which will be explored in future work.

A strongly possible constraint is an intermediate concept between possible and certain constraints, based on the strongly possible world approach (a strongly possible world is obtained by replacing NULL’s by a value from the ones appearing in the corresponding attribute of the table). In the present paper, we introduce strongly possible versions of multivalued dependencies and cross joins, and we analyse the complexity of checking the validity of a given strongly possible cross joins. We also study two approximation measures, (g_3) and (g_5), of strongly possible keys (spKeys), functional dependencies (spFDs), multivalued dependencies (spMVDs) and cross joins (spCJs). For spKeys and spFDs, we show that the (g_3) value is always an upper bound of the (g_5) value for a given constraint in a table. However, there are tables of arbitrarily large number of tuples and a constant number of attributes that satisfy (g_3-g_5=frac{p}{q}) for any rational number (0le frac{p}{q}<1). On the other hand, we show that the values of measures (g_3) and (g_5) are independent of each other in the case of spMVDs and spCJs. We prove that checking whether a given strongly possible cross join holds in an incomplete table is NP-complete, in sharp contrast to the fact that checking a given cross join in a complete table is easily seen to be polynomially solvable. We also treat complexity questions of determination of the approximation values, namely we show that both, determining (g_3) and (g_5) for spCJs are NP-complete.