Automated Theory Formation in Pure Mathematics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Automated Theory Formation in Pure Mathematics PDF full book. Access full book title Automated Theory Formation in Pure Mathematics by Simon Colton. Download full books in PDF and EPUB format.
Author: Simon Colton
Publisher: Springer Science & Business Media
ISBN: 1447101472
Category : Mathematics
Languages : en
Pages : 384
Get Book Here
Book Description
In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.
Author: Simon Colton
Publisher: Springer Science & Business Media
ISBN: 1447101472
Category : Mathematics
Languages : en
Pages : 384
Get Book Here
Book Description
In recent years, Artificial Intelligence researchers have largely focused their efforts on solving specific problems, with less emphasis on 'the big picture' - automating large scale tasks which require human-level intelligence to undertake. The subject of this book, automated theory formation in mathematics, is such a large scale task. Automated theory formation requires the invention of new concepts, the calculating of examples, the making of conjectures and the proving of theorems. This book, representing four years of PhD work by Dr. Simon Colton demonstrates how theory formation can be automated. Building on over 20 years of research into constructing an automated mathematician carried out in Professor Alan Bundy's mathematical reasoning group in Edinburgh, Dr. Colton has implemented the HR system as a solution to the problem of forming theories by computer. HR uses various pieces of mathematical software, including automated theorem provers, model generators and databases, to build a theory from the bare minimum of information - the axioms of a domain. The main application of this work has been mathematical discovery, and HR has had many successes. In particular, it has invented 20 new types of number of sufficient interest to be accepted into the Encyclopaedia of Integer Sequences, a repository of over 60,000 sequences contributed by many (human) mathematicians.
Author: Simon Colton
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
Get Book Here
Book Description
Automated theory formation involves, amongst other things, the production of examples, concepts and statements relating the concepts. The HR program has been developed to form theories in mathematical domains, by calculating examples, inventing concepts, making conjectures, and settling conjectures using the Otter theorem prover and MACE model generator. In addition to providing a plausible model for automated theory formation in pure mathematics, HR has been applied to other problems in Artificial Intelligence. We discuss HR's application to inducing definitions from examples, scientific discovery, problem solving and puzzle generation. For each problem, we look at how a theory formation approach can be applied and mention some initial results from the application of HR. Our aim is not to describe the applications in great detail, but rather to provide an overview of how HR is used for these problems. This will facilitate a comparison of the problems and discussion of the effectiveness of theory formation for these tasks. Our second aim is to compare HR with the Progol machine learning program. We do this first by looking at the concept formation these programs perform. Also, by suggesting how Progol could be used for the applications mentioned above, we compare the programs in terms of how they can be applied.
Author: Stéphane Demri
Publisher: Springer
ISBN: 3319085875
Category : Mathematics
Languages : en
Pages : 550
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 7th International Joint Conference on Automated Reasoning, IJCAR 2014, held as part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. IJCAR 2014 was a merger of three leading events in automated reasoning, namely CADE (International Conference on Automated Deduction), FroCoS (International Symposium on Frontiers of Combining Systems) and TABLEAUX (International Conference on Automated Reasoning with Analytic Tableaux and Related Methods). The 26 revised full research papers and 11 system descriptions presented together with 3 invited talks were carefully reviewed and selected from 83 submissions. The papers have been organized in topical sections on HOL, SAT and QBF, SMT, equational reasoning, verification, proof theory, modal and temporal reasoning, SMT and SAT, modal logic, complexity, description logics and knowledge representation and reasoning.
Author: David Basin
Publisher: Springer
ISBN: 3540259848
Category : Computers
Languages : en
Pages : 509
Get Book Here
Book Description
This volume constitutes the proceedings of the 2nd International Joint C- ference on Automated Reasoning (IJCAR 2004) held July 4–8, 2004 in Cork, Ireland. IJCAR 2004 continued the tradition established at the ?rst IJCAR in Siena,Italyin2001,whichbroughttogetherdi?erentresearchcommunitieswo- ing in automated reasoning. The current IJCAR is the fusion of the following conferences: CADE: The International Conference on Automated Deduction, CALCULEMUS: Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, FroCoS: Workshop on Frontiers of Combining Systems, FTP: The International Workshop on First-Order Theorem Proving, and TABLEAUX: The International Conference on Automated Reasoning with Analytic Tableaux and Related Methods. There were 74 research papers submitted to IJCAR as well as 12 system descriptions. After extensive reviewing, 26 research papers and 6 system - scriptions were accepted for presentation at the conference and publication in this volume. In addition, this volume also contains papers from the three invited speakers and a description of the CADE ATP system competition. We would like to acknowledge the enormous amount of work put in by the members of the program committee, the various organizing and steering c- mittees, the IJCAR o?cials, the invited speakers, and the additional referees named on the following pages. We would also like to thank Achim Brucker and Barbara Geiser for their help in producing this volume.
Author: Saso Dzeroski
Publisher: Springer Science & Business Media
ISBN: 354073919X
Category : Language Arts & Disciplines
Languages : en
Pages : 333
Get Book Here
Book Description
This survey provides an introduction to computational approaches to the discovery of communicable scientific knowledge and details recent advances. It is partly inspired by the contributions of the International Symposium on Computational Discovery of Communicable Knowledge, held in Stanford, CA, USA in March 2001, a number of additional invited contributions provide coverage of recent research in computational discovery.
Author: Jacques Calmet
Publisher: Springer
ISBN: 3540454705
Category : Computers
Languages : en
Pages : 355
Get Book Here
Book Description
AISC 2002, the 6th international conference on Arti?cial Intelligence and S- bolic Computation, and Calculemus 2002, the 10th symposium on the Integ- tion of Symbolic Computation and Mechanized Reasoning, were held jointly in Marseille, France on July 1-5, 2002. This event was organized by the three universities in Marseille together with the LSIS (Laboratoire des Sciences de l'Information et des Syst` emes). AISC 2002 was the latest in a series of specialized conferences founded by John Campbell and Jacques Calmet with the initial title "Arti?cial Intelligence and Symbolic Mathematical Computation" (AISMC) and later denoted "Art- cial Intelligence and Symbolic Computation" (AISC). The scope is well de?ned by its successive titles. AISMC-1 (1992), AISMC-2 (1994), AISMC-3 (1996), AISC'98, and AISC 2000 took place in Karlsruhe, Cambridge, Steyr, Plattsburgh (NY), and Madrid respectively. The proceedings were published by Springer-Verlag as LNCS 737, LNCS 958, LNCS 1138, LNAI 1476, and LNAI 1930 respectively. Calculemus 2002 was the 10th symposium in a series which started with three meetings in 1996, two meetings in 1997, and then turned into a yearly event in 1998. Since then, it has become a tradition to hold the meeting jointly with an event in either symbolic computation or automated deduction. Both events share common interests in looking at Symbolic Computation, each from a di?erent point of view: Arti?cial Intelligence in the more general case of AISC and Automated Deduction in the more speci?c case of Calculemus.
Author: Danny A. J. Gómez Ramírez
Publisher: Springer Nature
ISBN: 3030502732
Category : Mathematics
Languages : en
Pages : 268
Get Book Here
Book Description
This volume discusses the theoretical foundations of a new inter- and intra-disciplinary meta-research discipline, which can be succinctly called cognitive metamathematics, with the ultimate goal of achieving a global instance of concrete Artificial Mathematical Intelligence (AMI). In other words, AMI looks for the construction of an (ideal) global artificial agent being able to (co-)solve interactively formal problems with a conceptual mathematical description in a human-style way. It first gives formal guidelines from the philosophical, logical, meta-mathematical, cognitive, and computational points of view supporting the formal existence of such a global AMI framework, examining how much of current mathematics can be completely generated by an interactive computer program and how close we are to constructing a machine that would be able to simulate the way a modern working mathematician handles solvable mathematical conjectures from a conceptual point of view. The thesis that it is possible to meta-model the intellectual job of a working mathematician is heuristically supported by the computational theory of mind, which posits that the mind is in fact a computational system, and by the meta-fact that genuine mathematical proofs are, in principle, algorithmically verifiable, at least theoretically. The introduction to this volume provides then the grounding multifaceted principles of cognitive metamathematics, and, at the same time gives an overview of some of the most outstanding results in this direction, keeping in mind that the main focus is human-style proofs, and not simply formal verification. The first part of the book presents the new cognitive foundations of mathematics’ program dealing with the construction of formal refinements of seminal (meta-)mathematical notions and facts. The second develops positions and formalizations of a global taxonomy of classic and new cognitive abilities, and computational tools allowing for calculation of formal conceptual blends are described. In particular, a new cognitive characterization of the Church-Turing Thesis is presented. In the last part, classic and new results concerning the co-generation of a vast amount of old and new mathematical concepts and the key parts of several standard proofs in Hilbert-style deductive systems are shown as well, filling explicitly a well-known gap in the mechanization of mathematics concerning artificial conceptual generation.
Author: Jonathan M. Borwein
Publisher: Springer Science & Business Media
ISBN: 3540371044
Category : Computers
Languages : en
Pages : 303
Get Book Here
Book Description
Constitutes the proceedings of the 5th International Conference on Mathematical Knowledge Management, MKM 2006, held in Wokingham. This book includes 22 full papers which cover the whole area of mathematical knowledge management in the intersection of mathematics, computer science, library science, and scientific publishing.
Author: Tamas Horváth
Publisher: Springer
ISBN: 3540399178
Category : Computers
Languages : en
Pages : 411
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 13th International Conference on Inductive Logic Programming, ILP 2003, held in Szeged, Hungary in September/October 2003. The 23 revised full papers presented were carefully reviewed and selected from 53 submissions. Among the topics addressed are multirelational data mining, complexity issues, theory revision, clustering, mathematical discovery, relational reinforcement learning, multirelational learning, inductive inference, description logics, grammar systems, and inductive learning.
Author: Toby Walsh
Publisher: Springer
ISBN: 3540455787
Category : Computers
Languages : en
Pages : 794
Get Book Here
Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Principles and Practice of Constraint Programming, CP 2001, held in Paphos, Cyprus, in November/December 2001. The 37 revised full papers, 9 innovative applications presentations, and 14 short papers presented were carefully reviewed and selected from a total of 135 submissions. All current issues in constraint processing are addressed, ranging from theoretical and foundational issues to advanced and innovative applications in a variety of fields.
