Annals of Mathematics and Artificial Intelligence最新文献

In a previous paper Todd (Submitted to AMAI, 2022), linear systems corresponding to sets of angle bisector conditions are analyzed. In a system which is not full rank, one bisector condition can be derived from the others. In that paper, we describe methods for finding such rank deficient linear systems. The vector angle bisector relationship may be interpreted geometrically in a number of ways: as an angle bisector, as a reflection, as an isosceles triangle, or as a circle chord. A rank deficient linear system may be interpreted as a geometry theorem by mapping each vector angle bisector relationship onto one of these geometrical representations. In Todd (Submitted to AMAI, 2022) we illustrate the step from linear system to geometry theorem with a number of by-hand constructed examples. In this paper, we present an algorithm which automatically generates a geometry theorem from a starting point of a linear system of the type identified in Todd (Submitted to AMAI, 2022). Both statement and diagram of the new theorem are generated by the algorithm. Our implementation creates a simple text description of the new theorem and utilizes the Mathematica GeometricScene to form a diagram.

The Bipolar Argumentation Framework approach is an extension of the Abstract Argumentation Framework. A Bipolar Argumentation Framework considers a support interaction between arguments, besides the attack interaction. As in the Abstract Argumentation Framework, some researches consider that arguments have a degree of uncertainty, which impacts on the degree of uncertainty of the extensions obtained from a Bipolar Argumentation Framework under a semantics. In these approaches, both the uncertainty of the arguments and of the extensions are modeled by means of precise probability values. However, in many real application domains there is a need for aggregating probability values from different sources so it is not suitable to aggregate such probability values in a unique probability distribution. To tackle this challenge, we use credal networks theory for modelling the uncertainty of the degree of belief of arguments in a BAF. We also propose an algorithm for calculating the degree of uncertainty of the extensions inferred by a given argumentation semantics. Moreover, we introduce the idea of modelling the support relation as a causal relation. We formally show that the introduced approach is sound and complete w.r.t the credal networks theory.

We consider geometry theorems whose premises and statement comprise a set of bisector conditions. Each premise and the statement can be represented as the rows of a “bisector matrix”: one with three non zero elements per row, one element with value -2 and the others with value 1. The existence of a theorem corresponds to rank deficiency in this matrix. Our method of theorem discovery starts with identification of rank deficient bisector matrices. Some such matrices can be represented as graphs whose vertices correspond to matrix rows and whose edges correspond to matrix columns. We show that if a bisector matrix which can be represented as a graph is rank deficient, then the graph is bicubic. We give an algorithm for finding the rank deficient matrices for a Hamiltonian bicubic graph, and report on the results for graphs with 6,8,10 and 12 vertices. We discuss a method of deriving rank deficient bisector matrices with more than 2 non-zero elements. We extend the work to matrices containing rows corresponding to angle trisectors.

Tile pasting system is a parallel generating model which glues two square tiles at their edges to create intricate tiling patterns. It is extended by using three dimensional objects namely tetrahedral tiles and the patterns generated are used to decorate floors and walls. In the literature k-Tabled Tetrahedral Tile Pasting System (k-TTTPS) and Tetrahedral Tile Pasting P System (TetTPPS) were introduced to generate tetrahedral picture patterns. In this paper, Controlled Tabled Tetrahedral Tile Pasting System (CTTTPS) is proposed to generate tetrahedral picture patterns and CTTTPS is compared with k-TTTPS and TetTPPS in terms of generative powers. It is proved that CTTTPS has more generative power than the generative powers of k-TTTPS and TetTPPS. Extended Tetrahedral Tile Pasting System (ETTPS) and Extended Tetrahedral Tile Pasting P System (ETTPPS) are also proposed in this paper and are compared with CTTTPS in terms of their generative powers. This study has connections with pattern recognition and image analysis with applications in tiling of tetrahedral patterns.

Debugging agent systems can be rather difficult. It is often noted as one of the most time-consuming tasks during the development of cognitive agents. Algorithmic (or declarative) debugging is a semi-automatic technique, where the developer is asked questions by the debugger in order to locate the source of an error. We present how this can be applied in the context of a BDI agent language, demonstrate how it can speed up or simplify the debugging process and reflect on its advantages and limitations.

In this paper, we study the class of those Boolean functions that are coset leaders of first order Reed-Muller codes. We study their properties and try to better understand their structure (which seems complex), by studying operations on Boolean functions that can provide coset leaders (we show that these operations all provide coset leaders when the operands are coset leaders, and that some can even produce coset leaders without the operands being coset leaders). We characterize those coset leaders that belong to the well known classes of direct sums of monomial Boolean functions and Maiorana-McFarland functions. Since all the functions of Hamming weight at most (2^{n-2}) are automatically coset leaders, we are interested in constructing infinite classes of coset leaders having possibly Hamming weight larger than (2^{n-2}).