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

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]

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)

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

2017
*
Mathematics in Computer Science
*

Acknowledgements I am grateful to the dedicated Staff at Birkhäuser, Basel and the Production Editor at Springer Nature

doi:10.1007/s11786-017-0312-6
fatcat:4punqwiv3nabld7svrgjjxqtvu
*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]

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]

2002
*
Lecture Notes in Computer Science
*

Unfortunately it has been used

doi:10.1007/3-540-36187-1_65
fatcat:6eayoplgzzdvbaei2yn2fye6re
*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

doi:10.1016/0166-218x(90)90119-w
fatcat:2r3bb2td6raypha3jrtziyouxq
*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]

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

2017
*
International Journal of Advanced Research in Computer Science and Software Engineering
*

"Logic sometimes breeds monsters" -Henri Poincare This paper proposes a method

doi:10.23956/ijarcsse/v7i3/0184
fatcat:lo66767o3ne2tfbzmukyhpizj4
*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]

2018
*
arXiv
*
pre-print

Elfe is an interactive system

arXiv:1801.10513v1
fatcat:nn2rkrtahnd2dcggt4getaiu6a
*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

doi:10.1007/s11023-010-9185-z
fatcat:qunmimbouzhs5gdnr564yo65ei
*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

2010
*
2010 13th International Conference on Information Fusion
*

A fundamental

doi:10.1109/icif.2010.5711860
fatcat:6gasp47wsjaqlmkl5xmtadpave
*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

2014
*
Electronic Proceedings in Theoretical Computer Science
*

We also believe that this could considerably benefit the learning

doi:10.4204/eptcs.149.4
fatcat:skw7camyfjh3fhmpmzjqm2sbay
*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]

2011
*
arXiv
*
pre-print

We present the concept

arXiv:1108.4048v1
fatcat:hmq4d5molrhllgkuncezjibo2q
*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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