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Towards the Formalization of Fractional Calculus in Higher-Order Logic
[article]

2015
*
arXiv
*
pre-print

*In*this paper, we describe an ongoing project which aims at

*formalizing*

*the*basic theories

*of*

*fractional*

*calculus*

*in*

*the*HOL Light theorem prover. ...

*Fractional*

*calculus*is a generalization

*of*classical theories

*of*integration and differentiation to arbitrary

*order*(i.e., real or complex numbers). ...

*In*this paper, we present details

*of*an ongoing project 1 to develop a

*formal*reasoning support for

*fractional*

*calculus*

*in*

*higher*-

*order*-

*logic*theorem prover. ...

##
###
Towards the Formalization of Fractional Calculus in Higher-Order Logic
[chapter]

2015
*
Lecture Notes in Computer Science
*

*In*this paper, we describe an ongoing project which aims at

*formalizing*

*the*basic theories

*of*

*fractional*

*calculus*

*in*

*the*HOL Light theorem prover. ...

*Fractional*

*calculus*is a generalization

*of*classical theories

*of*integration and differentiation to arbitrary

*order*(i.e., real or complex numbers). ...

*In*this paper, we present details

*of*an ongoing project 1 to develop a

*formal*reasoning support for

*fractional*

*calculus*

*in*

*higher*-

*order*-

*logic*theorem prover. ...

##
###
Page 467 of Mathematical Reviews Vol. , Issue 82b
[page]

1982
*
Mathematical Reviews
*

ISBN 0-19-824591-2

*The*author extends his program*of*a classical but non-Platonic foundation*of*arithmetic through a*formalization**in**higher*-*order*predicate*logic*subject to restrictions*of*simple type ... This work is a step*toward*simplifying axiomatizations*of*discussive propositional*logic*. ...##
###
Page 4128 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
*
Mathematical Reviews
*

On

*the*ground*of**the*above considerations we note that*the*classical functional*calculus*with identity can be*formalized*without axioms and without using Genzen-type rules.” ...*In**order*to claim attention*in**the*philosophical study*of*scientific heuristics, general principles used for*the*creation*of*new theories should be applicable beyond*the*context*in*which they were first ...##
###
Page 157 of Journal of Education Vol. 41, Issue 10
[page]

1895
*
Journal of Education
*

integral

*calculus*, and*the**calculus**of*variations. ... - tion, multiplication, and division, and*in**the*reduction*of**fractions*— and finds*the*road long and tedious at*In**the*case*of*decimal*fractions**the*psycho-*logical*process is more complex still; for ...##
###
The review: Approaches in teaching calculus

2022
*
figshare.com
*

Difficulty

doi:10.6084/m9.figshare.19009382.v1
fatcat:jpaym6omm5annaevm3u4n26mna
*of*learning*calculus*was faced by many students*in**higher*secondary schools because*the*teaching was teacher centered and usually focused on explaining*the*notations and symbols used*in**calculus*... With change*of*time*the*new approaches to teach*calculus*must be adopted so that what students learned*in**the*classroom ac be also apply*in*real life situations. ...*The*three events, "*Towards*a Lean and Lively*Calculus*" conference*in*1986, "*Calculus*for a New Century" symposium*in*1987, and "Priming*the**Calculus*Pump"*in*1990, signaled*the*beginning*of**calculus*reform ...##
###
Formulating tasks to develop HOTS for first-year calculus based on Brookhart abilities

2016
*
South African Journal of Science
*

We describe an approach to develop

doi:10.17159/sajs.2016/20160139
fatcat:ggo77ogqrvd5rmvzcswubtbrum
*higher*-*order*thinking skills (HOTS) among first-year*calculus*students. ... Then eight expected learning outcomes for*the*development*of*HOTS were documented,*in**the*context*of**the*study*of*first-year university*calculus*. ... Acknowledgements Professor Sanjay Wagh*of**the*Central India Research Institute*in*Nagpur (India) is acknowledged for facilitating this collaboration. ...##
###
The transition to formal thinking in mathematics

2008
*
Mathematics Education Research Journal
*

Pure mathematics

doi:10.1007/bf03217474
fatcat:5wuhevzxurbhhps3cobe2otcvu
*in*university shifts*towards*a*formal*framework*of*axiomatic systems and mathematical proof. ...*of*a complete*ordered*field. ... For instance,*in*a*formal*lecture course that took*the**logical*route*of*defining a relation as a set*of**ordered*pairs, and then specialized*the*definition to specify functions,*order*relations, and equivalence ...##
###
Toward Formalizing Common-Sense Psychology: An Analysis of the False-Belief Task
[chapter]

2008
*
Lecture Notes in Computer Science
*

We present an inference system for representing and reasoning about certain types

doi:10.1007/978-3-540-89197-0_6
fatcat:27yz76tgk5barh4a34j4p2keoe
*of*mental states, and use it to provide a*formal*analysis*of**the*false-belief task. ...*The*system allows for*the*representation*of*information about events, causation, and perceptual, doxastic, and epistemic states (vision, belief, and knowledge), incorporating ideas from*the*event*calculus*... They are,*in*fact, explicitly defined*in**the**higher*-*order**logic*PVS by quantifying over states. ...##
###
Towards a Substrate Framework of Computation
[chapter]

2014
*
Lecture Notes in Computer Science
*

Specifically, we show how fine-grained strong reduction

doi:10.1007/978-3-662-44471-9_15
fatcat:2dzmeq5m7nfbjb2loolqk6zxh4
*of**the*λ-*calculus*can be concisely encoded into hypergraph rewriting with a small set*of*primitive operations. ... A grand challenge*in*computing is to establish a substrate computational model that encompasses diverse forms*of*non-sequential computation. ... Acknowledgments*The*author is indebted to*the*present and past members*of**the*LMNtal group for fruitful discussions and building*the*(Hyper)LMNtal system on which*the*present work was successfully based ...##
###
Preface
[chapter]

2020
*
First Congress of Greek Mathematicians
*

vector

doi:10.1515/9783110663075-201
fatcat:fxrwkxhlizbwpcibpfptqmz7rm
*calculus*for*the*case*of**higher*-dimensional problems*in*a physical domain. ...*In*this paper,*the*impact*of**the*mentioned*formalisms**in*three separate areas is reviewed. ... We hope*the*reader finds*in*this small collection*of*excellent papers a sense*of**the*spirit*of**the*First Congress*of*Greek Mathematicians and that this Congress will be*the*beginning*of*a sequence*of*similar ...##
###
The Teaching of Mathematics

1908
*
Science
*

Moreover, he is not demanding a change

fatcat:6uv3gcvqmzcdhdo35ebx4xh6ie
*in**the*course*of*study, but rather is urging that advantage be taken*of**the*present leaning*toward**calculus*, and carried out to its*logical*sequence. ... Continued*fractions*and applications; arithmetical series*of*second*order*; cubic equations; problems*in*maxima and minima. OBERPRIMA (age, 17-18 years) I. Geometry, 3 hours. ...##
###
Casl Specifications of Qualitative Calculi
[chapter]

2005
*
Lecture Notes in Computer Science
*

But from a

doi:10.1007/11556114_13
fatcat:7xuhplmsfbftbf7cxrcj6td6qe
*formal*point*of*view these calculi are often closely related to each other. ...*The*most prominent temporal calculi are*the*point algebra*of*linear time and Allen's interval*calculus*. ... Acknowledgments This work was partially supported by*the*Deutsche Forschungsgemeinschaft (DFG) as part*of**the*Transregional Collaborative Research Center SFB/TR 8 Spatial Cognition. ...##
###
Towards Distributed Ontology Reasoning for the Web

2008
*
2008 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology
*

*The*use

*of*description

*logics*as one

*of*

*the*primary

*logical*languages for knowledge representation on

*the*Web has created new challenges with respect to reasoning

*in*these

*logics*. ...

*The*method is complete for first

*order*

*logic*, terminates for ALC ontologies and avoids duplication

*of*axioms and inferences. ... As Description

*logics*are a strict subset

*of*first

*order*

*logic*, resolution can be applied to ontologies as well by transforming

*the*DL ontology into a set

*of*first

*order*clauses. ...

##
###
Subject-Matter Didactics
[chapter]

2019
*
Combating Wildlife Crime in South Africa
*

*In*

*the*1980s, views upon

*the*nature

*of*learning as well as objects and methods

*of*research

*in*mathematics education changed and

*the*perspective was widened and opened

*towards*new directions. ...

*In*

*the*development

*of*didactics

*of*mathematics as a professional field

*in*Germany, subject-related approaches play an important role. ... not only

*formal*

*logic*but also

*the*inner

*logic*

*of*

*the*subject plays an important part. ...

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