Automated generation of machine verifiable and readable proofs: A case study of Tarski’s geometry

Đurđević, Sana Stojanović; Narboux, Julien; Janicic, Predrag

doi:10.1007/s10472-014-9443-5

Cited by 14 publications

(4 citation statements)

References 28 publications

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“…Important work to provide axioms close to human intuition has been done by [48], respective implementation is pending.…”

Section: Impsmentioning

confidence: 99%

Formal Abstraction in Engineering Education - Challenges and Technology Support

Neuper¹

2017

ADN

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Abstract. This is a position paper in the the field of Engineering Education, which is at the very beginning in Europe. It relates challenges in the new field to the emerging technology of (Computer) Theorem Proving (TP).Experience shows, that teaching abstract models, for instance the wave equation in mechanical engineering and in electrical engineering, is difficult. This paper suggests novel technology to support learning in a novel way such that abstract models are better understood eventually.Such support acknowledges learning and mastering abstraction as a long-term process, which requires revisiting physical and mathematical concepts again and again, which in turn continuously raises the level of abstraction at an individual pace and fosters students' familiarity with formal descriptions capturing essential properties of models and respective elements.The paper discusses the potential of TP to support students' process of abstraction and expected impact on teaching mathematics at engineering faculties.

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“…Important work to provide axioms close to human intuition has been done by [48], respective implementation is pending.…”

Section: Impsmentioning

confidence: 99%

Formal Abstraction in Engineering Education - Challenges and Technology Support

Neuper¹

2017

ADN

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“…In [7], Durdevic et.al. tried E, SPASS, and Vampire on the theorems from Szmielew, with a 37% success rate.…”

Section: Easy and Hard Theorems And Their Proofsmentioning

confidence: 99%

Finding Proofs in Tarskian Geometry

Beeson

Wos

2016

J Autom Reasoning

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We report on a project to use a theorem prover to find proofs of the theorems in Tarskian geometry. These theorems start with fundamental properties of betweenness, proceed through the derivations of several famous theorems due to Gupta and end with the derivation from Tarski's axioms of Hilbert's 1899 axioms for geometry. They include the four challenge problems left unsolved by Quaife, who two decades ago found some OTTER proofs in Tarskian geometry (solving challenges issued in Wos's 1998 book).There are 212 theorems in this collection. We were able to find OTTER proofs of all these theorems. We developed a methodology for the automated preparation and checking of the input files for those theorems, to ensure that no human error has corrupted the formal development of an entire theory as embodied in two hundred input files and proofs.We distinguish between proofs that were found completely mechanically (without reference to the steps of a book proof) and proofs that were constructed by some technique that involved a human knowing the steps of a book proof. Proofs of length 40-100, roughly speaking, are difficult exercises for a human, and proofs of 100-250 steps belong in a Ph.D. thesis or publication. 29 of the proofs in our collection are longer than 40 steps, and ten are longer than 90 steps. We were able to derive completely mechanically all but 26 of the 183 theorems that have "short" proofs (40 or fewer deduction steps). We found proofs of the rest, as well as the 29 "hard" theorems, using a method that requires consulting the book proof at the outset. Our "subformula strategy" enabled us to prove four of the 29 hard theorems completely mechanically. These are Ph.D. level proofs, of length up to 108.

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“…The first Mizar article formalizing Tarski's axioms [17] was inspired by another formalizations of SST: within the classical two-valued logic with Isabelle/HOL by Makarios [13,14,15], Metamath or by means of Coq [16,4]. Some of the results were obtained with the help of other automatic proof assistants, either partially [9], or completely [3]. Relatively recent achievement was the import of huge portions of code from GeoCoq into Isabelle [5].…”

Section: Introductionmentioning

confidence: 99%