## Effective logic computationA powerful new approach to solving propositional logic problems in the design of expert systems Effective Logic Computation describes breakthrough mathematical methods for computation in propositional logic. Offering a highly robust and versatile alternative to the production rule- or neural net-based approaches commonly used in the design of expert systems, Dr. Truemper's combinatorial decomposition-based approach has produced a compiler that uniquely yields solution algorithms for both logic satisfiability problems and logic minimization problems. Also unique to the compiler is computation of a performance guarantee for each solution algorithm. Effective Logic Computation provides detailed algorithms for all steps carried out by the compiler. Much of the mathematics described in this book has been implemented in the Leibniz System, a commercially available software system for logic programming and a leading tool for building expert systems. This book's companion volume, Design of Intelligent Computer Systems, is in preparation and will offer detailed coverage of software implementation and use, including a complete version of the Leibniz System. Effective Logic Computation is an indispensable working resource for computer scientists and applied mathematicians involved in the design of logic programming software, researchers in artificial intelligence, and operations researchers. |

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### Contents

Introduction | 1 |

Basic Concepts | 22 |

Some Matroid Theory | 69 |

Copyright | |

13 other sections not shown

### Common terms and phrases

2-separation 2SAT Algorithm SOLVE assigned assume B1 and B2 bipartite graph Boolean closed Boolean minor bounded Chapter clause closed subregion decomposition CNF system column index set column node column resp column scaling column submatrix computational contains corresponding declare define deletion directed graph edge fc-separation first-order logic given matrix graph H graph minor Heuristic hidden nearly negative implies inequality input integer label Leibniz Lemma linear algebra logic matrix over IB matrix/vector pairs matroid minimal MINSAT instance monotone decomposition nearly negative matrices node subset nonempty nonzero entries Output partition polyhedron polynomial propositional logic range(A rational nonnegative reduced row index set row node SAT and MINSAT SAT central SAT instance SAT or MINSAT satisfiability problem satisfying solution scaling factors Section semicentral solution algorithm solution vector Step subgraph subrange subrange(A subroutine Suppose system IB Theorem totally unimodular True/False values X2 U Y2 zero zero matrix