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Self-evident Automated Geometric Theorem Proving Based on Complex Number Identity
How to automatically generate short and easy-to-understand proofs for geometric theorems has long been an issue of concern in mathematics education....
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The Nature of Theorem Proving
This chapter discusses the nature of proof and theorem proving, and we discuss automated and interactive theorem provers. We discuss the nature of...
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Theorem Proving as Constraint Solving with Coherent Logic
In contrast to common automated theorem proving approaches, in which the search space is a set of some formulae and what is sought is again a (goal)...
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What Can Large Language Models Do for Theorem Proving and Formal Methods?
With the introduction of large language models, AI for natural language have taken a leap. These systems are now also being used for tasks that has...
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Automated generation of illustrated proofs in geometry and beyond
Illustrations are only rarely formal components of mathematical proofs, however they are often very important for understanding proofs. Illustrations...
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A program to create new geometry proof problems
In a previous paper Todd (Submitted to AMAI,
2022 ), linear systems corresponding to sets of angle bisector conditions are analyzed. In a system which... -
A Matroid-Based Automatic Prover and Coq Proof Generator for Projective Incidence Geometry
We present an automatic theorem prover for projective incidence geometry. This prover does not consider coordinates. Instead, it follows a...
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Towards a geometry deductive database prover
The Geometry Automated-Theorem-Provers (GATP) based on the deductive database method use a data-based search strategy to improve the efficiency of...
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Automated Generation of Geometry Proof Problems Based on Point Geometry Identity
The automated generation of geometry proof problems represents a burgeoning research domain in the realm of artificial intelligence, with significant...
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The Nature of Theorem Proving
A mathematical proofMathematical proof includes natural language and mathematical symbols, and often many of the tedious details of the proof are...
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Automated triangle constructions in hyperbolic geometry
We describe a system for automated ruler and compass triangle constructions in hyperbolic geometry. We discuss key differences between constructions...
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A deep reinforcement learning agent for geometry online tutoring
In this paper, we apply deep reinforcement learning (DRL) for geometry reasoning and develop Dragon to facilitate online tutoring. Its success is...
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Prolog in Automated Reasoning in Geometry
In this paper a brief overview of tools for automated reasoning in geometry developed in Prolog is given. We argue that Prolog is as a good choice...
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Proving an Execution of an Algorithm Correct?
Many algorithms in computer algebra and beyond produce answers. For some of these, we have formal proofs of the correctness of the algorithm, and for...
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Method for Processing Graph Degeneracy in Dynamic Geometry Based on Domain Design
A dynamic geometry system, as an important application in the field of geometric constraint solving, is widely used in elementary mathematics...
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The Nature of Theorem Proving
This chapter discusses the nature of proof and theorem proving, and we discuss automated and interactive theorem provers. We discuss the nature of...
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Formalizing Free Groups in Isabelle/HOL: The Nielsen-Schreier Theorem and the Conjugacy Problem
Free groups are central to group theory, and are ubiquitous across many branches of mathematics, including algebra, topology and geometry. An...
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A Lower Bound for Proving Hardness of Learning with Rounding with Polynomial Modulus
Regev’s Learning with Errors (LWE) problem (STOC 2005) is a fundamental hardness assumption for modern cryptography. The Learning with Rounding (LWR)...
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