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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 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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On vanishing sums of roots of unity in polynomial calculus and sum-of-squares
We introduce a novel take on sum-of-squares that is able to reason with complex numbers and still make use of polynomial inequalities. This proof...
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Query answering DL-lite knowledge bases from hidden datasets
Unifying access to data using structured knowledge is the main problem studied in ontology-based data access (OBDA). Data are often provided by...
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Implementing Euclid’s straightedge and compass constructions in type theory
Constructions are central to the methodology of geometry presented in the Elements . This theory therefore poses a unique challenge to those concerned...
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Rewriting input expressions in complex algebraic geometry provers
We present an algorithm to help converting expressions having non-negative quantities (like distances) in Euclidean geometry theorems to be usable in...
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Portfolio theorem proving and prover runtime prediction for geometry
In recent years, portfolio problem solving found many applications in automated reasoning, primarily in SAT solving and in automated and interactive...
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From informal to formal proofs in Euclidean geometry
In this paper, we propose a new approach for automated verification of informal proofs in Euclidean geometry using a fragment of first-order logic...
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Computing envelopes in dynamic geometry environments
We review the behavior of some popular dynamic geometry software when computing envelopes, relating the diverse methods implemented in these programs...
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Four Decades of Mizar
This special issue is dedicated to works related to Mizar , the theorem proving project started by Andrzej Trybulec in the 1970s, and other automated...
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Conformant planning as a case study of incremental QBF solving
We consider planning with uncertainty in the initial state as a case study of incremental quantified Boolean formula (QBF) solving. We report on...
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Automated generation of machine verifiable and readable proofs: A case study of Tarski’s geometry
The power of state-of-the-art automated and interactive theorem provers has reached the level at which a significant portion of non-trivial...
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Automated generation of geometric theorems from images of diagrams
We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough...
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Formalizing complex plane geometry
Deep connections between complex numbers and geometry had been well known and carefully studied centuries ago. Fundamental objects that are...
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Custom Automations in Mizar
The central aim of the Mizar project is to produce strictly formalized mathematical statements with mechanically certified proofs. When writing a...
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On Automation in the Verification of Software Barriers: Experience Report
We present an experience report on automating the verification of the software barrier synchronization primitive. The informal specification of the...
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Embedding and automating conditional logics in classical higher-order logic
A sound and complete embedding of conditional logics into classical higher-order logic is presented. This embedding enables the application of...
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The light side of interval temporal logic: the Bernays-Schönfinkel fragment of CDT
Decidability and complexity of the satisfiability problem for the logics of time intervals have been extensively studied in the recent years. Even...
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Producing and verifying extremely large propositional refutations
The importance of producing a certificate of unsatisfiability is increasingly recognized for high performance propositional satisfiability solvers....