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Automating change of representation for proofs in discrete mathematics
[article]
2015
arXiv
pre-print
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In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. ...
There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. ...
We show our work towards automating the search for representation as a tactic for use within proofs in discrete mathematics in Isabelle. ...
arXiv:1505.02449v1
fatcat:vmhhrbfaerhnlfbqembvc2hsoi
Automating Change of Representation for Proofs in Discrete Mathematics
[chapter]
2015
Lecture Notes in Computer Science
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In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. ...
There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. ...
We show our work towards automating the search for representation as a tactic for use within proofs in discrete mathematics in Isabelle. ...
doi:10.1007/978-3-319-20615-8_15
fatcat:b37uwmjze5dgdik4gdqx3zlo3q
Automating Change of Representation for Proofs in Discrete Mathematics (Extended Version)
2016
Mathematics in Computer Science
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In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used tools from Isabelle's Transfer package to automate the use of these transformations ...
There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. ...
Automated Change of Representation Up to this point we have shown how discrete mathematics involves reasoning about a few superstructures which are heavily interconnected by transformations. ...
doi:10.1007/s11786-016-0275-z
fatcat:m5cox2s75zfnrl4dmgwpojpcoi
Mathematics in Computer Science: After 10 Years
2017
Mathematics in Computer Science
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Acknowledgements I am grateful to the dedicated Staff at Birkhäuser, Basel and the Production Editor at Springer Nature for their work and effort with MCS. ...
They look at examples of representational transformations in discrete mathematics, and show how they have used tools from Isabelles Transfer package to automate the use of these transformations in proofs ...
There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. ...
doi:10.1007/s11786-017-0312-6
fatcat:4punqwiv3nabld7svrgjjxqtvu
Building theories in Nuprl
[chapter]
1989
Lecture Notes in Computer Science
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in relevance to this particular theory, and indicate the promise of our approach for other branches of constructive mathematics. ...
We accomplish this by presenting a particular theory developed in the Nuprl proof development system: nite set theory culminating in Ramsey's theorem. ...
Reasoning
Lemmas In the previous section, we described our methodology for building representations for mathematical objects. ...
doi:10.1007/3-540-51237-3_3
fatcat:lzasnrjujveevi6lbom5aqwsm4
On the Design of Mathematical Concepts
[chapter]
2002
Lecture Notes in Computer Science
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Unfortunately it has been used in the field of automated theorem proving as an argument to disregard the need for a diverse variety of representations. ...
While design issues play a major rôle in the formation of mathematical concepts, the theorem proving community has largely neglected them. ...
Acknowledgements We thank Mateja Jamnik for fruitful discussions and suggestions. Martin Pollet thanks Peter Pröhle for the insights he gave him into the process of mathematical problem solving. ...
doi:10.1007/3-540-36187-1_65
fatcat:6eayoplgzzdvbaei2yn2fye6re
Logic-based knowledge representation
1990
Discrete Applied Mathematics
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Logic-Based Knowledge Representation (MIT Press, Cambridge, MA, 1989) 255 pages PART I: AN ABSTRACT ARCHITECTURE FOR BUILDING EXPERT SYSTEMS. Chapter 1: Introduction. Outline of the book. ...
Using logic for knowledge representation. Using meta-level inference for control. Improving meta-level and object-level efficiency. Modal extensions to ...
Related work in automated
theorem proving. ...
doi:10.1016/0166-218x(90)90119-w
fatcat:2r3bb2td6raypha3jrtziyouxq
Page 3645 of Mathematical Reviews Vol. , Issue 95f
[page]
1995
Mathematical Reviews
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The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The power of the representation is illustrated by applying it to the axiomatization and solution of several standard problems from the AI literature on action and change. ...
Reason. 11 (1993), no. 3, 317-331.
95f:68214c 68T15 03B35
Zhang, Hantao (1-IA-C; Iowa City, IA)
Automated proofs of equality problems in Overbeek’s competition. (English summary)
J. Automat. ...
Wolfram Model and the Technological Architecture of the Fourth Industrial Revolution
[article]
2021
arXiv
pre-print
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In this essay, we will defend the thesis that the multi-computational paradigm is a natural way of thinking about the fourth industrial revolution. ...
This will be done considering the geometry that emerges as the continuum limit of multiway systems. ...
This conceptual change implies a new geometric representation of time, which is no longer a straight line, but a tree. ...
arXiv:2111.03439v1
fatcat:mqvgugijzvfa5hzuma6jzb57fe
Communicating and Negotiating Proof Events in the Cyber – Physical Systems
2017
International Journal of Advanced Research in Computer Science and Software Engineering
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"Logic sometimes breeds monsters" -Henri Poincare This paper proposes a method for Communicating and Negotiating Proof Events in the Cyber -Physical Systems. ...
In the past decade linguists, neuroscientists, cognitive scientists, computer scientists, sociologists are bringing new ideas for studying mathematics with new tools. ...
In other words the mathematical notion of "Proof" is not a real thing. ...
doi:10.23956/ijarcsse/v7i3/0184
fatcat:lo66767o3ne2tfbzmukyhpizj4
The Elfe System - Verifying mathematical proofs of undergraduate students
[article]
2018
arXiv
pre-print
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Elfe is an interactive system for teaching basic proof methods in discrete mathematics. ...
Background libraries for sets, relations and functions have been developed. It has been tested by students in the beginning of their mathematical studies. ...
In the past years, several attempts have been made to create a proof verifier which accepts mathematical texts written in fair English, one of which SYS-TEM FOR AUTOMATED DEDUCTION (SAD) (Verchinine et ...
arXiv:1801.10513v1
fatcat:nn2rkrtahnd2dcggt4getaiu6a
Indistinguishable from Magic: Computation is Cognitive Technology
2010
Minds and Machines
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, and change. ...
The second is Pāṅini's invention, around the fifth century BCE, of a formal grammar for spoken Sanskrit, expressed in oral verse extending ordinary Sanskrit, and using recursive methods rediscovered in ...
The two formal theory classes, of additive and multiplicative arithmetics, are useful correlates for the changes L → L´discussed in the text (Kadvany 2007) . 18 The problem of automating number units ...
doi:10.1007/s11023-010-9185-z
fatcat:qunmimbouzhs5gdnr564yo65ei
High-level fusion: Issues in developing a formal theory
2010
2010 13th International Conference on Information Fusion
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A fundamental mathematical theory of high-level information fusion is needed to address (1) the representation of semantics and pragmatics, (2) the mathematical framework supporting its algorithmic and ...
In this paper, we propose the development of mathematical foundations that systemically address this problem from a decision theoretic perspective, and might seed the development of such fundamental theory ...
Acknowledgments Research on PROGNOS has been partially supported by the Office of Naval Research, under Contract#: N00173-09-C-4008. ...
doi:10.1109/icif.2010.5711860
fatcat:6gasp47wsjaqlmkl5xmtadpave
Teaching Formal Methods and Discrete Mathematics
2014
Electronic Proceedings in Theoretical Computer Science
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2014 pre-print arXiv:1404.6604v1 fatcat:ueqt5qatcrekpgbpjhopvrdw5m
We also believe that this could considerably benefit the learning of discrete mathematics. ...
In this paper, we claim that teaching formal methods could be done at the undergraduate level by mixing formal methods and discrete mathematics courses and we illustrate such an approach with a small develop ...
Acknowledgments The authors would like to thank Renaud Rioboo for his help and for enlightening discussions about how to program with FoCaLiZe and about teaching discrete mathematics. ...
doi:10.4204/eptcs.149.4
fatcat:skw7camyfjh3fhmpmzjqm2sbay
A graphical environment to express the semantics of control systems
[article]
2011
arXiv
pre-print
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We present the concept of a unified graphical environment for expressing the semantics of control systems. ...
We finally describe how the graphical representation of the system and its properties can be translated to annotated programs in a programming language used in verification and validation such as Lustre ...
stability proofs in discrete-time hence the problem remains that we must use the continuous-time proofs as invariants for the discretized system. ...
arXiv:1108.4048v1
fatcat:hmq4d5molrhllgkuncezjibo2q
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