Automated Practical Reasoning: Algebraic Approaches - Softcover

Inhaltsangabe

An algorithm for solving systems of algebraic equations in three variables.- 1 Introduction.- 2 Definitions.- 3 Basic properties of primitive polynomial remainder sequences and elimination sequences.- 4 Application of elimination sequences: solution of systems of algebraic equations.- 5 Systems of algebraic equations in two variables.- 6 Systems of algebraic equations in three variables.- 7 Applications in neural networks theory.- References.- On a general notion of a hull.- 1 Introduction.- 2 Basic notions.- 3 General relational structures.- 4 Some examples.- 5 Prospects.- 6 Concluding remarks.- References.- On robotics scenarios and modeling with fibered structures.- 1 Introduction.- 2 Motivational remarks and background.- 3 Description of the first subscenario.- 4 The logical fibering model.- 5 A proposed model of the general state space of an agent.- 6 Subscenario with autonomous agents.- 7 Conclusion.- References.- On algorithmic parametrization methods in algebraic geometry.- 1 Introduction.- 2 Rational and unirational varieties.- 3 Curves.- 4 Surfaces.- 5 Higher dimensional varieties.- References.- Towards a categorical calculus for critical-pair/completion.- 1 Introduction.- 2 Overview of CPC-procedures.- 3 An axiomatic framework.- 4 A little category theory.- 5 Reversed limits.- 6 A categorical model for CPC-procedures.- References.- CASA: computer algebra software for computing with algebraic sets.- 1 Introduction.- 2 Intersection of algebraic sets - a case study.- 3 Puiseux expansion in CASA.- References.- Reasoning about geometric problems using an elimination method.- 1 Introduction.- 2 An elimination method for polynomial systems.- 3 Mechanical geometry theorem proving.- 4 Automatic derivation of unknown relations.- 5 Automatic derivation of locus equations.- 6 Implicitization of parametric objects.- 7 Existence conditions and detection of singularities.- 8 Decomposition of algebraic varieties.- 9 Inverse robot kinematics.- 10 Intersection of geometric objects.- References.- An implementation of the characteristic set method in Maple.- 1 Introduction and notations.- 2 Description of user functions.- 3 Modifications and strategies.- 4 Test results and remarks.- Appendix: Test problems.- References.- A nonmonotonic extension to Horn-clause logic.- 1 Introduction.- 2 Semantics of nonmonotonic Horn-clause theories.- 3 Soundness and completeness of nonmonotonic Horn-clause theories.- 4 Relationship to model-theoretic semantics.- 5 Conclusion.- References.

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