Ebook: Automated Practical Reasoning: Algebraic Approaches

This book presents a collection of articles on the general framework of mechanizing deduction in the logics of practical reasoning. Topics treated are novel approaches in the field of constructive algebraic methods (theory and algorithms) to handle geometric reasoning problems, especially in robotics and automated geometry theorem proving; constructive algebraic geometry of curves and surfaces showing some new interesting aspects; implementational issues concerning the use of computer algebra systems to deal with such algebraic methods. Besides work on nonmonotonic logic and a proposed approach for a unified treatment of critical pair completion procedures, a new semantical modeling approach based on the concept of fibered structures is discussed; an application to cooperating robots is demonstrated.

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This book presents a collection of articles on the general framework of mechanizing deduction in the logics of practical reasoning. Topics treated are novel approaches in the field of constructive algebraic methods (theory and algorithms) to handle geometric reasoning problems, especially in robotics and automated geometry theorem proving; constructive algebraic geometry of curves and surfaces showing some new interesting aspects; implementational issues concerning the use of computer algebra systems to deal with such algebraic methods. Besides work on nonmonotonic logic and a proposed approach for a unified treatment of critical pair completion procedures, a new semantical modeling approach based on the concept of fibered structures is discussed; an application to cooperating robots is demonstrated.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
An Algorithm for Solving Systems of Algebraic Equations in Three Variables....Pages 7-37
On a General Notion of a Hull....Pages 39-51
On Robotics Scenarios and Modeling with Fibered Structures....Pages 53-80
On Algorithmic Parametrization Methods in Algebraic Geometry....Pages 81-89
Towards a Categorical Calculus for Critical-Pair/Completion....Pages 91-124
CASA: Computer Algebra Software for Computing with Algebraic Sets....Pages 125-146
Reasoning about Geometric Problems using an Elimination Method....Pages 147-185
An Implementation of the Characteristic Set Method in Maple....Pages 187-201
A Nonmonotonic Extension to Horn-Clause Logic....Pages 203-220
Back Matter....Pages 221-227

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This book presents a collection of articles on the general framework of mechanizing deduction in the logics of practical reasoning. Topics treated are novel approaches in the field of constructive algebraic methods (theory and algorithms) to handle geometric reasoning problems, especially in robotics and automated geometry theorem proving; constructive algebraic geometry of curves and surfaces showing some new interesting aspects; implementational issues concerning the use of computer algebra systems to deal with such algebraic methods. Besides work on nonmonotonic logic and a proposed approach for a unified treatment of critical pair completion procedures, a new semantical modeling approach based on the concept of fibered structures is discussed; an application to cooperating robots is demonstrated.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-5
An Algorithm for Solving Systems of Algebraic Equations in Three Variables....Pages 7-37
On a General Notion of a Hull....Pages 39-51
On Robotics Scenarios and Modeling with Fibered Structures....Pages 53-80
On Algorithmic Parametrization Methods in Algebraic Geometry....Pages 81-89
Towards a Categorical Calculus for Critical-Pair/Completion....Pages 91-124
CASA: Computer Algebra Software for Computing with Algebraic Sets....Pages 125-146
Reasoning about Geometric Problems using an Elimination Method....Pages 147-185
An Implementation of the Characteristic Set Method in Maple....Pages 187-201
A Nonmonotonic Extension to Horn-Clause Logic....Pages 203-220
Back Matter....Pages 221-227
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