Geometric theorem proving by integrated logical and algebraic reasoning

Geometric Theorem Proving by Integrated Logical and Algebraic Reasoning

Algebraic geometric reasoning by the Griibner basis method and Wu’s method has been shown to be powerful enough to prove those complex geometric theorems that could not be proved by ordinary logical reasoning methods. These algebraic reasoning methods, however, have a crucial limitation: they cannot correctly handle any geometric concepts involving order relations such as between and congruent ...

Algebraic Representation, Elimination and Expansion in Automated Geometric Theorem Proving

Cayley algebra and bracket algebra are important approaches to invariant computing in projective and affine geometries, but there are some difficulties in doing algebraic computation. In this paper we show how the principle “breefs” – bracketoriented representation, elimination and expansion for factored and shortest results, can significantly simply algebraic computations. We present several t...

Commonsense Reasoning Meets Theorem Proving

The area of commonsense reasoning aims at the creation of systems able to simulate the human way of rational thinking. This paper describes the use of automated reasoning methods for tackling commonsense reasoning benchmarks. For this we use a benchmark suite introduced in literature. Our goal is to use general purpose background knowledge without domain specific hand coding of axioms, such tha...

Solving Geometric Construction Problems Supported by Theorem Proving

Over the last sixty years, a number of methods for automated theorem proving in geometry, especially Euclidean geometry, have been developed. Almost all of them focus on universally quantified theorems. On the other hand, there are only few studies about logical approaches of geometric constructions. Consequently, automated proving of ∀∃ theorems, that correspond to geometric construction probl...

Automatic Geometric Theorem Proving using Gröbner Bases