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Automated theorem proving: mapping logic into AI

D W Loveland
1986 Proceedings of the ACM SIGART international symposium on Methodologies for intelligent systems -  
I propose in the very limited time allotted to glimpse at the status of ATP, highlighting the different logical systems upon which A T P systems are built, look briefly at some applications already found  ...  for ATP, and add what I hope is an interesting, perhaps important, new idea in conclusion.  ...  Suppes has developed interactive theorem provers for teaching logic and set theory courses that use his version of natural deduction [24a] , [24b] .  ... 
doi:10.1145/12808.12833 fatcat:badcsorb25gufhgobxumlws7me

Logic Modelling [article]

Roger Villemaire
2015 arXiv   pre-print
This is a reflection on the author's experience in teaching logic at the graduate level in a computer science department.  ...  Finally, logic is the methodology underlying many applications, it is hence paramount to pass on its principles, methods and concepts to computer science audiences.  ...  Acknowledgments I would like to thank the anonymous reviewers for numerous comments and suggestions that have improved the final version of this paper.  ... 
arXiv:1507.03686v1 fatcat:6wzkuq4hbjautcfe3gzzderv34

A Survey on Theorem Provers in Formal Methods [article]

M. Saqib Nawaz, Moin Malik, Yi Li, Meng Sun, M. Ikram Ullah Lali
2019 arXiv   pre-print
In literature, there is a shortage of comprehensive documents that can provide proper guidance about the preferences of theorem provers with respect to their designs, performances, logical frameworks,  ...  Technically, mathematical formalisms and automated reasoning based-approaches are employed to perform inferences and to generate proofs in theorem provers.  ...  ACKNOWLEDGMENTS The work has been supported by the National Natural Science Foundation of China under grant no. 61772038, 61532019 and 61272160, and the Guandong Science and Technology Department (Grant  ... 
arXiv:1912.03028v1 fatcat:fabxqg75xjhxlh7u3uyypgyzdy

Using Automated Theorem Provers for Mistake Diagnosis in the Didactics of Mathematics [article]

Merlin Carl
2020 arXiv   pre-print
We briefly describe the concept of such an 'Anti-ATP' and explain the basic techniques used in its implementation.  ...  The Diproche system, an automated proof checker for natural language proofs specifically adapted to the context of exercises for beginner's students similar to the Naproche system by Koepke, Schr\"oder  ...  Quite frequently, these arise out of an application of a systematically false manipulation rule. In this sense, they are similar to the formal fallacies processed by the anti-ATP.  ... 
arXiv:2002.05083v1 fatcat:coqdvjqjtfe7ri4ivx6l27sk4a

Adaptative Learning Environment for Geometry [chapter]

Vanda Santos, Pedro Quaresm
2010 Advances in Learning Processes  
The different ATP methods and tools that can be used in an learning environment, have different fields of application.  ...  The algebraic proofs are, in our opinion, not very useful if we want to study/teach the deductive method in geometry, the ATPs of this type begin by reducing the geometric properties to algebraic properties  ... 
doi:10.5772/7941 fatcat:asfmjwjk2vfqzmj343arvkqnp4

Software engineering and automated deduction

Willem Visser, Nikolaj Bjørner, Natarajan Shankar
2014 Proceedings of the on Future of Software Engineering - FOSE 2014  
We focus on the underlying technology by which a number of these problems can be reduced to a logical form and answered using automated deduction.  ...  In the first part we briefly summarize the use of automated deduction within software engineering.  ...  ACL2 uses a logic based on an applicative subset of Common Lisp so that the functions defined in the ACL2 logic are directly executable as Lisp programs.  ... 
doi:10.1145/2593882.2593899 dblp:conf/icse/VisserBS14 fatcat:cdgga6syovar5hr4mfzjyyi4se

Number Theory and Axiomatic Geometry in the Diproche System [article]

Merlin Carl
2020 arXiv   pre-print
Cramer and others is a automated proof checker for proofs written in a controlled fragment of natural language specifically designed to capture the language of beginners' proving exercises in mathematics  ...  An overall presentation of the system in general was given earlier by Krapf and the author.  ...  It is of course possible to always allow the "full power" of the geometry module of the ATP, but this would make the system unsuitable for applications during the course.  ... 
arXiv:2006.01794v2 fatcat:2f3zede2unbbfnx7yu4zrkx2la

Computer-assisted human-oriented inductive theorem proving by descente infinie--a manifesto

C.-P. Wirth
2012 Logic Journal of the IGPL  
Our main motivation is to explain--on an abstract but hopefully sufficiently descriptive level--why we believe that future progress in the field is to result from human-orientedness and descente infinie  ...  In this short position paper we briefly review the development history of automated inductive theorem proving and computer-assisted mathematical induction.  ...  Acknowledgements I would like to thank Dieter Hutter and Peter Padawitz for some very helpful advice, and Tobias Schmidt-Samoa for many fruitful discussions and a long list of most profound critical suggestions  ... 
doi:10.1093/jigpal/jzr048 fatcat:qps74fzzmngmzaluxlcaqogt4y

Recent advances in computational models of natural argument

Chris Reed, Floriana Grasso
2006 International Journal of Intelligent Systems  
used and extended to model and handle real world argument in a wide variety of domains including law, education, medicine, and e-commerce.  ...  The article has two distinct foci: first, examining the ways in which argumentation has inspired new models of logical and computational intelligence, and second, exploring how AI techniques have been  ...  s 11 logic of argumentation, LA, that uses a labeled deductive system to support the construction of an argumentation theorem prover, ATP.  ... 
doi:10.1002/int.20187 fatcat:2ybgxpg44jhyxpg2pyohnc7m2m

The logicist manifesto: At long last let logic-based artificial intelligence become a field unto itself

Selmer Bringsjord
2008 Journal of Applied Logic  
The paper includes a self-contained summary of logic-based AI, as well as rebuttals to a number of objections that will inevitably be brought against the declaration of independence herein expressed.  ...  This paper is a sustained argument for the view that logic-based AI should become a self-contained field, entirely divorced from paradigms that are currently still included under the AI "umbrella"-paradigms  ...  E.g., resolution-based Vampire [89] can find this proof in an instant, and so can natural deduction-based Oscar [75] .  ... 
doi:10.1016/j.jal.2008.09.001 fatcat:ifonuea7zfgube4nmlrenbbugi

Let's plan it deductively!

W. Bibel
1998 Artificial Intelligence  
The attraction of a logical and deductive approach to planning is emphasized and the state of automated deduction briefly described. 0 1998 Elsevier Science B.V. All rights reserved.  ...  ) can be modelled in TL in a rather natural way.  ...  Acknowledgments An earlier version of this paper appeared in the Proceedings of the 15th International Joint Conference on Artificial Intelligence, published by IJCAII.  ... 
doi:10.1016/s0004-3702(98)00064-2 fatcat:d23xyfi57ve2lk4aw2hgkiulhm

Evaluating general purpose automated theorem proving systems

Geoff Sutcliffe, Christian Suttner
2001 Artificial Intelligence  
to problems based on their difficulty  ...  In order to build more powerful systems, it is important to understand which systems, and hence which techniques, work well for what types of problems.  ...  Interactive systems find application in hardware and software verification, formalization of informal mathematical proofs, teaching logic, and as tools of mathematical and meta-mathematical research.  ... 
doi:10.1016/s0004-3702(01)00113-8 fatcat:2meauulrlve73nve5xdsupb7k4

Towards an Intelligent Tutor for Mathematical Proofs

Serge Autexier, Dominik Dietrich, Marvin Schiller
2012 Electronic Proceedings in Theoretical Computer Science  
In this paper, we discuss a novel approach to developing an intelligent tutoring system for teaching textbook-style mathematical proofs.  ...  Our approach is motivated by phenomena found in a corpus of tutorial dialogs that were collected in a Wizard-of-Oz experiment.  ...  The AProS project (see [60] for an overview) provides an integrated environment for strategic proof search and tutoring in natural deduction calculi for predicate logic.  ... 
doi:10.4204/eptcs.79.1 fatcat:xyvxfeicwbaxfb3wfd2oaagnbq

Automated Theorem Proving in GeoGebra: Current Achievements

Francisco Botana, Markus Hohenwarter, Predrag Janičić, Zoltán Kovács, Ivan Petrović, Tomás Recio, Simon Weitzhofer
2015 Journal of automated reasoning  
Since including automated deduction tools in GeoGebra could bring a whole new range of teaching and learning scenarios, and since automated theorem proving and discovery in geometry has reached a rather  ...  GeoGebra is an open-source educational mathematics software tool, with millions of users worldwide.  ...  GeoGebra is an open-source mathematics software application for learning and teaching, with millions of users worldwide, and hence an excellent choice for showing and promoting the benets of ATP educational  ... 
doi:10.1007/s10817-015-9326-4 fatcat:rh7lvmmy75eipaqmkvf3dqxs3a

The Elfe System - Verifying mathematical proofs of undergraduate students [article]

Maximilian Doré, Krysia Broda
2018 arXiv   pre-print
Elfe is an interactive system for teaching basic proof methods in discrete mathematics.  ...  The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas.  ...  To convince us that this construction is sound, we have to use two additional natural deduction rules: (∧I) : P Q P ∧ Q (→ E) : P → Q P Q These rules will be used in the proof of Lemma 3 which is an abstract  ... 
arXiv:1801.10513v1 fatcat:nn2rkrtahnd2dcggt4getaiu6a
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