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

Umair Siddique, Osman Hasan, Sofiène Tahar
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.  ... 
arXiv:1505.02140v1 fatcat:hvyf3xhf2nbh7bj4gijiav7rai

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

Umair Siddique, Osman Hasan, Sofiène Tahar
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.  ... 
doi:10.1007/978-3-319-20615-8_21 fatcat:lgx5adcufvfenedqbkpuuo4wnu

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

Kinley .
2022 figshare.com  
Difficulty 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  ... 
doi:10.6084/m9.figshare.19009382.v1 fatcat:jpaym6omm5annaevm3u4n26mna

Formulating tasks to develop HOTS for first-year calculus based on Brookhart abilities

Aneshkumar Maharaj, Vivek Wagh
2016 South African Journal of Science  
We describe an approach to develop 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.  ... 
doi:10.17159/sajs.2016/20160139 fatcat:ggo77ogqrvd5rmvzcswubtbrum

The transition to formal thinking in mathematics

David Tall
2008 Mathematics Education Research Journal  
Pure mathematics 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  ... 
doi:10.1007/bf03217474 fatcat:5wuhevzxurbhhps3cobe2otcvu

Toward Formalizing Common-Sense Psychology: An Analysis of the False-Belief Task [chapter]

Konstantine Arkoudas, Selmer Bringsjord
2008 Lecture Notes in Computer Science  
We present an inference system for representing and reasoning about certain types 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.  ... 
doi:10.1007/978-3-540-89197-0_6 fatcat:27yz76tgk5barh4a34j4p2keoe

Towards a Substrate Framework of Computation [chapter]

Kazunori Ueda
2014 Lecture Notes in Computer Science  
Specifically, we show how fine-grained strong reduction 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  ... 
doi:10.1007/978-3-662-44471-9_15 fatcat:2dzmeq5m7nfbjb2loolqk6zxh4

Preface [chapter]

Ioannis Emmanouil, Anargyros Fellouris, Apostolos Giannopoulos, Sofia Lambropoulou
2020 First Congress of Greek Mathematicians  
vector 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  ... 
doi:10.1515/9783110663075-201 fatcat:fxrwkxhlizbwpcibpfptqmz7rm

The Teaching of Mathematics

Charles Ottermann
1908 Science  
Moreover, he is not demanding a change 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.  ... 
fatcat:6uv3gcvqmzcdhdo35ebx4xh6ie

Casl Specifications of Qualitative Calculi [chapter]

Stefan Wölfl, Till Mossakowski
2005 Lecture Notes in Computer Science  
But from a 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.  ... 
doi:10.1007/11556114_13 fatcat:7xuhplmsfbftbf7cxrcj6td6qe

Towards Distributed Ontology Reasoning for the Web

Anne Schlicht, Heiner Stuckenschmidt
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.  ... 
doi:10.1109/wiiat.2008.396 dblp:conf/webi/SchlichtS08a fatcat:dcffpwnlnrf6bfzk3e6erhc7lm

Subject-Matter Didactics [chapter]

Lisa Hefendehl-Hebeker, Rudolf vom Hofe, Andreas Büchter, Hans Humenberger, Axel Schulz, Sebastian Wartha
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.  ... 
doi:10.1007/978-3-030-11069-7_2 fatcat:uwbiuaeaujgm3ofuaaqknfpx64
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