Related papers: Solving Logic Grid Puzzles with an Algorithm that …
In this paper, we discuss different models for human logic systems and describe a game with nature. Godel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking.…
We consider approximations formed by the sum of a linear combination of given functions enhanced by ridge functions -- a Linear/Ridge expansion. For an explicitly or implicitly given function, we reformulate finding a best Linear/Ridge…
Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…
Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member,…
Large Language Models (LLMs) exhibit impressive reasoning abilities, yet their reliance on structured step-by-step processing reveals a critical limitation. In contrast, human cognition fluidly adapts between intuitive, heuristic (System 1)…
In this paper we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with adaptive mesh refinement. Our code uses truncation error estimates to adaptively refine the grid as part of the…
Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…
Pre-trained language models (PLMs) have shown impressive performance in various language tasks. However, they are prone to spurious correlations, and often generate illusory information. In real-world applications, PLMs should justify…
We present a logical framework to represent and reason about stochastic optimization problems based on probability answer set programming. This is established by allowing probability optimization aggregates, e.g., minimum and maximum in the…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
Human parsing is for pixel-wise human semantic understanding. As human bodies are underlying hierarchically structured, how to model human structures is the central theme in this task. Focusing on this, we seek to simultaneously exploit the…
We propose a new kind of sliding-block puzzle, called Gourds, where the objective is to rearrange 1 x 2 pieces on a hexagonal grid board of 2n + 1 cells with n pieces, using sliding, turning and pivoting moves. This puzzle has a single…
Boggle logic puzzles are based on the popular word game Boggle, where you are given list of words, and your goal is to recreate a Boggle board. In this paper we give an overview of known results and then propose a number of problems related…
Games and puzzles play important pedagogical roles in STEM learning. New AI algorithms that can solve complex problems offer opportunities for scaffolded instruction in puzzle solving. This paper presents the ALLURE system, which uses an AI…
Given a series of photographs taken during a Go game, we describe the techniques we successfully employ for pinpointing the grid lines of the Go board and for tracking their small movements between consecutive photographs; then we discuss…
Scheduling in Grid computing has been active area of research since its beginning. However, beginners find very difficult to understand related concepts due to a large learning curve of Grid computing. Thus, there is a need of concise…
In this work, an efficient blackbox-type multigrid method is proposed for solving multipoint flux approximations of the Darcy problem on logically rectangular grids. The approach is based on a cell-centered multigrid algorithm, which…
Robot-assisted navigation is a perfect example of a class of applications requiring flexible control approaches. When the human is reliable, the robot should concede space to their initiative. When the human makes inappropriate choices the…
Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…
Consider a binary classification problem solved using a feed-forward artificial neural network (ANN). Let the ANN be composed of a ReLU layer and several linear layers (convolution, sum-pooling, or fully connected). We assume the network…