Constraint Reasoning Based on Interval Arithmetic

Case-Based Algebraic Constraint System for Engineering Design

In this paper, we present an approach to solve design problems using different reasoning techniques. First, casebased reasoning was used in the design problem structuring phase to get the initial design of the device by retrieving similar existing designs. Then we adapting the initial design by using algebraic constraint propagation techniques, qualitative methods and interval arithmetic to sol...

Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure

In order to facilitate automated reasoning about large Boolean combinations of nonlinear arithmetic constraints involving transcendental functions, we provide a tight integration of recent SAT solving techniques with interval-based arithmetic constraint solving. Our approach deviates substantially from lazy theorem proving approaches in that it directly controls arithmetic constraint propagatio...

Spatial Inference - Learning vs. Constraint Solving

We present a comparison of two new approaches for solving constraints occurring in spatial inference. In contrast to qualitative spatial reasoning we use a metric description, where relations between pairs of objects are represented by parameterized homogenous transformation matrices with numerical (nonlinear) constraints. We employ interval arithmetics based constraint solving and methods of m...

Exact soultion of full interval linear equation AX=B based on Kaucher arithmetic

Interval Constraint Solving Using Propositional SAT Solving Techniques

In order to facilitate automated reasoning about large Boolean combinations of non-linear arithmetic constraints involving transcendental functions, we extend the paradigm of lazy theorem proving to intervalbased arithmetic constraint solving. Algorithmically, our approach deviates substantially from “classical” lazy theorem proving approaches in that it directly controls arithmetic constraint ...