Refutational theorem proving using term-rewriting systems
Artificial Intelligence
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Applications of Gro¨bner bases in non-linear computational geometry
Mathematical aspects of scientific software
Wu's method and its application to perspective viewing
Geometric reasoning
Multi-valued logic and Gröner bases with applications to modal logic
Journal of Symbolic Computation
A polynomial model for multi-valued logics with a touch of algebraic geometry and computer algebra
Selected papers from the 1996 or 1997 IMACS-ACA conference on Non-standard applications of computer algebra
Railway interlocking systems and Gröbner bases
Mathematics and Computers in Simulation - Selected papers from the IMACS-ACA sponsored conferences: “Non-standard applications of computer algegra II&rdqu; (held in Waileau Maui, Hawaii and Prague, Czech Republic)
A machine program for theorem-proving
Communications of the ACM
A logic and computer algebra-based expert system for diagnosis of anorexia
Mathematics and Computers in Simulation
Automatic Discovery of Theorems in Elementary Geometry
Journal of Automated Reasoning
An Interpretation of the Propositional Boolean Algebra as k-algebra. Effective Calculus
AISMC-2 Selected Papers from the Second International Conference on Integrating Symbolic Mathematical Computation and Artificial Intelligence
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Expert Systems with Applications: An International Journal
A pommaret division algorithm for computing Grobner bases in boolean rings
Proceedings of the twenty-first international symposium on Symbolic and algebraic computation
An equational approach to theorem proving in first-order predicate calculus
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
A Polynomial Model for Logics with a Prime Power Number of Truth Values
Journal of Automated Reasoning
| Hi-index | 0.00 |
The aim of this paper is to present theoretically a new algebraic method for detecting potentially dangerous states in a Rule Based Expert System whose knowledge is represented by propositional Boolean logic. Given a dangerous state which does not happen at present, our method is able to detect a possible input fact such that, if it also occurred, the dangerous situation really would happen. This method, inspired by automatic discovery of geometric theorems, is based on calculating just one reduced Groebner basis of a polynomial ideal representing the system's knowledge. An implementation in the computer algebra system Maple is included.