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### Automating change of representation for proofs in discrete mathematics [article]

Daniel Raggi, Alan Bundy, Gudmund Grov, Alison Pease
2015 arXiv   pre-print
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.  ...

### Automating Change of Representation for Proofs in Discrete Mathematics [chapter]

Daniel Raggi, Alan Bundy, Gudmund Grov, Alison Pease
2015 Lecture Notes in Computer Science
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.  ...

### Automating Change of Representation for Proofs in Discrete Mathematics (Extended Version)

Daniel Raggi, Alan Bundy, Gudmund Grov, Alison Pease
2016 Mathematics in Computer Science
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.  ...

### Mathematics in Computer Science: After 10 Years

Ilias S. Kotsireas
2017 Mathematics in Computer Science
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.  ...

### Building theories in Nuprl [chapter]

David A. Basin
1989 Lecture Notes in Computer Science
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.  ...

### On the Design of Mathematical Concepts [chapter]

Manfred Kerber, Martin Pollet
2002 Lecture Notes in Computer Science
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.  ...

### Logic-based knowledge representation

1990 Discrete Applied Mathematics
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.  ...

### Page 3645 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews
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]

José Manuel Rodríguez Caballero
2021 arXiv   pre-print
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.  ...

### Communicating and Negotiating Proof Events in the Cyber – Physical Systems

Gopal T V
2017 International Journal of Advanced Research in Computer Science and Software Engineering
"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.  ...

### 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.  ...  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  ...

### Indistinguishable from Magic: Computation is Cognitive Technology

2010 Minds and Machines
, 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  ...

### High-level fusion: Issues in developing a formal theory

P C G Costa, Kuo-Chu Chang, K Laskey, T Levitt, Wei Sun
2010 2010 13th International Conference on Information Fusion
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.  ...

### Teaching Formal Methods and Discrete Mathematics

Mathieu Jaume, Théo Laurent
2014 Electronic Proceedings in Theoretical Computer Science
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.  ...

### A graphical environment to express the semantics of control systems [article]

Timothy Wang, Romain Jobredeaux, E. Feron
2011 arXiv   pre-print
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.  ...
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