A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Rewrite Methods for Clausal and Non-Clausal Theorem Proving
Proceedings of the 10th Colloquium on Automata, Languages and Programming
Computing a Gröbner basis of a polynomial ideal over a Euclidean domain
Journal of Symbolic Computation
A Certified Polynomial-Based Decision Procedure for Propositional Logic
TPHOLs '01 Proceedings of the 14th International Conference on Theorem Proving in Higher Order Logics
Automatic generation of polynomial invariants of bounded degree using abstract interpretation
Science of Computer Programming
A Groebner Bases Based Many-Valued Modal Logic Implementation in Maple
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
A Groebner bases-based approach to backward reasoning in rule based expert systems
Annals of Mathematics and Artificial Intelligence
A taxonomy of theorem-proving strategies
Artificial intelligence today
An algebraic approach to Parkinson disease diagnosis
Expert Systems with Applications: An International Journal
A Polynomial Model for Logics with a Prime Power Number of Truth Values
Journal of Automated Reasoning
Mathematics and Computers in Simulation
Characteristic set algorithms for equation solving in finite fields
Journal of Symbolic Computation
A logic-algebraic approach to decision taking in a railway interlocking system
Annals of Mathematics and Artificial Intelligence
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A new approach for proving theorems in first-order predicate calculus is developed based on term rewriting and polynomial simplification methods. A formula is translated into an equivalent set of formulae expressed in terms of 'true', 'false', 'exclusive-or', and 'and' by analyzing the semantics of its top-level operator. In this representation, formulae are polynomials over atomic formulae with 'and' as multiplication and 'exclusive-or' as addition, and they can be manipulated just like polynomials using familiar rules of multiplication and addition. Polynomials representing a formula are converted into rewrite rules which are used to simplify polynomials. New rules are generated by overlapping polynomials using a critical-pair completion procedure closely related to the Knuth- Bendix procedure. This process is repeated until a contradiction is reached or it is no longer possible to generate new rules. It is shown that resolution is subsumed by this method.