Automated reasoning in geometry theorem proving with Prolog
Journal of Automated Reasoning
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Automated reasoning: 33 BASIC research problems
Automated reasoning: 33 BASIC research problems
Automated development of Tarski's geometry
Journal of Automated Reasoning
Automated reasoning (2nd ed.): introduction and applications
Automated reasoning (2nd ed.): introduction and applications
Geometric reasoning
Journal of the ACM (JACM)
A generic graphic framework for combining inference tools and editing proofs and formulae
Journal of Symbolic Computation - Special issue on design and implementation of symbolic computation systems
The resolution calculus
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
Automatic Theorem Proving With Renamable and Semantic Resolution
Journal of the ACM (JACM)
Formalizing mathematics in higher-order logic: a case study in geometric modelling
Theoretical Computer Science
Semantic Generalizations for Proving and Disproving Conjectures by Analogy
Journal of Automated Reasoning
Automatic Discovery of Theorems in Elementary Geometry
Journal of Automated Reasoning
A Deductive Database Approach to Automated Geometry Theorem Proving and Discovering
Journal of Automated Reasoning
Ordered Semantic Hyper-Linking
Journal of Automated Reasoning
User-oriented theorem proving with the ATINF graphic proof editor
FAIR '91 Proceedings of the International Workshop on Fundamentals of Artificial Intelligence Research
Building Proofs or Counterexamples by Analogy in a Resoluton Framework
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
Formal Specification and Theorem Proving Breakthroughs in Geometric Modeling
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Partial Matching for Analogy Discovery in Proofs and Counter-Examples
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
A Semantically Guided Deductive System for Automatic Theorem Proving
IEEE Transactions on Computers
SCOTT: a model-guided theorem prover
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Analogy and abduction in automated deduction
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Extending semantic resolution via automated model building: applications
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
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The underlying principles and main original techniques used in a running generic logic-based theorem prover are presented. The system (a prototype) is called HOARDATINF (Human Oriented Automated Reasoning on your Desk) and has been specialized in this work to proof learning through geometry. It is based on a new calculus, particularly suited to the class of problems we deal with. The calculus allows treatment of equality and automatic model building. HOARDATINF has some other original characteristics such as proving by analogy (using matching techniques), some possibilities of discovering lemmata (using diagrams), handling standard theories in geometry such as commutativity and symmetry (by encoding them in the unification algorithm used by the calculus), and proof verification in a rather large sense (by using capabilities of the calculus). As this work is intended to set theoretical bases of a new logic-based approach to geometry theorem proving, a comparison of features of our system with respect to those of other important, representative logic-based systems is given. Some running examples give a good taste of the HOARDATINF capabilities. One of these examples allows us to compare qualitatively our approach with that of a powerful prover described in a recent paper [8]. Some directions of future research are mentioned.