Automated Practical Reasoning: Algebraic Approaches

Front Cover
Springer Science & Business Media, 1995 - Computers - 223 pages
This book is a collection of selected papers written by researchers qf our "RISC" institute (Research Institute for Symbolic Computation) along with the ESPRIT MEDLAR Project (Mechanizing Deduction in the Logics of Practical Reason ing). Naturally, the MEDLAR Project was and is the focal point for our institute whose main objective is the combination of foundational research in the area of symbolic computation and possible applications thereof for high-tech industrial projects. I am grateful to the director of the MEDLAR project, Jim Cunningham, for his enthusiasm, profound expertise, and continuous effort to manage a fruitful cooperation between various European working groups in the area of the project and for giving us the opportunity to be part of this challenging endeavor. I also acknowledge and feel indebted to Jochen Pfalzgraf for managing the RISC part of the MEDLAR project and to both him and Dongming Wang for editing this volume and organizing the refereeing process.
 

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Contents

Introduction
1
An algorithm for solving systems of algebraic equations in three variables
7
2 Definitions
8
3 Basic properties of primitive polynomial remainder sequences and elimination sequences
10
solution of systems of algebraic equations
12
5 Systems of algebraic equations in two variables
14
6 Systems of algebraic equations in three variables
23
7 Applications in neural networks theory
34
5 Reversed limits
110
6 A categorical model for CPCprocedures
115
References
123
computer algebra software for computing with algebraic sets
125
2 Intersection of algebraic sets a case study
126
3 Puiseux expansion in CASA
132
References
144
Reasoning about geometric problems using an elimination method
147

References
36
On a general notion of a hull
39
2 Basic notions
40
3 General relational structures
44
4 Some examples
46
5 Prospects
49
References
50
On robotics scenarios and modeling with fibered structures
53
2 Motivational remarks and background
54
3 Description of the first subscenario
58
4 The logical fibering model
60
5 A proposed model of the general state space of an agent
74
6 Subscenario with autonomous agents
77
7 Conclusion
79
References
80
On algorithmic parametrization methods in algebraic geometry
81
2 Rational and unirational varieties
82
3 Curves
83
4 Surfaces
86
5 Higher dimensional varieties
88
Towards a categorical calculus for criticalpaircompletion
91
2 Overview of CPCprocedures
92
3 An axiomatic framework
95
4 A little category theory
103
2 An elimination method for polynomial systems
148
3 Mechanical geometry theorem proving
152
4 Automatic derivation of unknown relations
160
5 Automatic derivation of locus equations
163
6 Implicitization of parametric objects
168
7 Existence conditions and detection of singularities
170
8 Decomposition of algebraic varieties
175
9 Inverse robot kinematics
179
10 Intersection of geometric objects
181
References
183
An implementation of the characteristic set method in Maple
187
2 Description of user functions
189
3 Modifications and strategies
191
4 Test results and remarks
196
Test problems
199
References
200
A nonmonotonic extension to Hornclause logic
203
2 Semantics of nonmonotonic Hornclause theories
204
3 Soundness and completeness of nonmonotonic Hornclause theories
208
4 Relationship to modeltheoretic semantics
210
5 Conclusion
217
References
218
Subject index
221
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