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A compilation of articles about Intensionality in philosophy,
logic, linguistics, and mathematics. The articles approach the
concept of Intensionality from different perspectives. Some
articles address philosophical issues raised by the possible worlds
approach to intensionality; others are devoted to technical aspects
of modal logic. The volume highlights the particular
interdisciplinary nature of intensionality with articles spanning
the areas of philosophy, linguistics, mathematics, and computer
science.
A compilation of articles about Intensionality in philosophy,
logic, linguistics, and mathematics. The articles approach the
concept of Intensionality from different perspectives. Some
articles address philosophical issues raised by the possible worlds
approach to intensionality; others are devoted to technical aspects
of modal logic. The volume highlights the particular
interdisciplinary nature of intensionality with articles spanning
the areas of philosophy, linguistics, mathematics, and computer
science.
This book on proof theory centers around the legacy of Kurt Schutte
and its current impact on the subject. Schutte was the last
doctoral student of David Hilbert who was the first to see that
proofs can be viewed as structured mathematical objects amenable to
investigation by mathematical methods (metamathematics). Schutte
inaugurated the important paradigm shift from finite proofs to
infinite proofs and developed the mathematical tools for their
analysis. Infinitary proof theory flourished in his hands in the
1960s, culminating in the famous bound 0 for the limit of
predicative mathematics (a fame shared with Feferman). Later his
interests shifted to developing infinite proof calculi for
impredicative theories. Schutte had a keen interest in advancing
ordinal analysis to ever stronger theories and was still working on
some of the strongest systems in his eighties. The articles in this
volume from leading experts close to his research, show the
enduring influence of his work in modern proof theory. They range
from eye witness accounts of his scientific life to developments at
the current research frontier, including papers by Schutte himself
that have never been published before.
This book on proof theory centers around the legacy of Kurt Schutte
and its current impact on the subject. Schutte was the last
doctoral student of David Hilbert who was the first to see that
proofs can be viewed as structured mathematical objects amenable to
investigation by mathematical methods (metamathematics). Schutte
inaugurated the important paradigm shift from finite proofs to
infinite proofs and developed the mathematical tools for their
analysis. Infinitary proof theory flourished in his hands in the
1960s, culminating in the famous bound 0 for the limit of
predicative mathematics (a fame shared with Feferman). Later his
interests shifted to developing infinite proof calculi for
impredicative theories. Schutte had a keen interest in advancing
ordinal analysis to ever stronger theories and was still working on
some of the strongest systems in his eighties. The articles in this
volume from leading experts close to his research, show the
enduring influence of his work in modern proof theory. They range
from eye witness accounts of his scientific life to developments at
the current research frontier, including papers by Schutte himself
that have never been published before.
The aim of this volume is to collect original contributions by the
best specialists from the area of proof theory, constructivity, and
computation and discuss recent trends and results in these areas.
Some emphasis will be put on ordinal analysis, reductive proof
theory, explicit mathematics and type-theoretic formalisms, and
abstract computations. The volume is dedicated to the 60th birthday
of Professor Gerhard Jager, who has been instrumental in shaping
and promoting logic in Switzerland for the last 25 years. It
comprises contributions from the symposium "Advances in Proof
Theory", which was held in Bern in December 2013. Proof theory came
into being in the twenties of the last century, when it was
inaugurated by David Hilbert in order to secure the foundations of
mathematics. It was substantially influenced by Goedel's famous
incompleteness theorems of 1930 and Gentzen's new consistency proof
for the axiom system of first order number theory in 1936. Today,
proof theory is a well-established branch of mathematical and
philosophical logic and one of the pillars of the foundations of
mathematics. Proof theory explores constructive and computational
aspects of mathematical reasoning; it is particularly suitable for
dealing with various questions in computer science.
The aim of this volume is to collect original contributions by the
best specialists from the area of proof theory, constructivity, and
computation and discuss recent trends and results in these areas.
Some emphasis will be put on ordinal analysis, reductive proof
theory, explicit mathematics and type-theoretic formalisms, and
abstract computations. The volume is dedicated to the 60th birthday
of Professor Gerhard Jager, who has been instrumental in shaping
and promoting logic in Switzerland for the last 25 years. It
comprises contributions from the symposium "Advances in Proof
Theory", which was held in Bern in December 2013. Proof theory came
into being in the twenties of the last century, when it was
inaugurated by David Hilbert in order to secure the foundations of
mathematics. It was substantially influenced by Goedel's famous
incompleteness theorems of 1930 and Gentzen's new consistency proof
for the axiom system of first order number theory in 1936. Today,
proof theory is a well-established branch of mathematical and
philosophical logic and one of the pillars of the foundations of
mathematics. Proof theory explores constructive and computational
aspects of mathematical reasoning; it is particularly suitable for
dealing with various questions in computer science.
Gerhard Gentzen has been described as logic's lost genius, whom
Goedel called a better logician than himself. This work comprises
articles by leading proof theorists, attesting to Gentzen's
enduring legacy to mathematical logic and beyond. The contributions
range from philosophical reflections and re-evaluations of
Gentzen's original consistency proofs to the most recent
developments in proof theory. Gentzen founded modern proof theory.
His sequent calculus and natural deduction system beautifully
explain the deep symmetries of logic. They underlie modern
developments in computer science such as automated theorem proving
and type theory.
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Computer Science Logic - 23rd International Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra, Portugal, September 7-11, 2009, Proceedings (Paperback, 2009 ed.)
Erich Gradel, Reinhard Kahle
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R3,045
Discovery Miles 30 450
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Ships in 10 - 15 working days
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The annual conference of the European Association for Computer
Science Logic (EACSL), CSL 2009, was held in Coimbra (Portugal),
September 7-11, 2009. The conference series started as a programme
of International Workshops on Computer Science Logic, and then at
its sixth meeting became the Annual C- ference of the EACSL. This
conference was the 23rd meeting and 18th EACSL conference; it was
organized at the Department of Mathematics, Faculty of S- ence and
Technology, University of Coimbra. In response to the call for
papers, a total of 122 abstracts were submitted to CSL 2009of which
89 werefollowedby a full paper. The ProgrammeCommittee selected 34
papers for presentation at the conference and publication in these
proceedings. The Ackermann Award is the EACSL Outstanding
Dissertation Award for Logic in Computer Science. The
awardrecipient for 2009 was Jakob Nordstr om. Citation of the
award, abstract of the thesis, and a biographical sketch of the
recipient may be found at the end of the proceedings. The award was
sponsored for the years 2007-2009 by Logitech S.A.
This book constitutes the refereed proceedings of the International Seminar on Proof Theory in Computer Science, PTCS 2001, held in Dagstuhl Castle, Germany, in October 2001.The 13 thoroughly revised full papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are higher type recursion, lambda calculus, complexity theory, transfinite induction, categories, induction-recursion, post-Turing analysis, natural deduction, implicit characterization, iterate logic, and Java programming.
In this two-volume compilation of articles, leading researchers
reevaluate the success of Hilbert's axiomatic method, which not
only laid the foundations for our understanding of modern
mathematics, but also found applications in physics, computer
science and elsewhere. The title takes its name from David
Hilbert's seminal talk Axiomatisches Denken, given at a meeting of
the Swiss Mathematical Society in Zurich in 1917. This marked the
beginning of Hilbert's return to his foundational studies, which
ultimately resulted in the establishment of proof theory as a new
branch in the emerging field of mathematical logic. Hilbert also
used the opportunity to bring Paul Bernays back to Goettingen as
his main collaborator in foundational studies in the years to come.
The contributions are addressed to mathematical and philosophical
logicians, but also to philosophers of science as well as
physicists and computer scientists with an interest in foundations.
Chapter 8 is available open access under a Creative Commons
Attribution 4.0 International License via link.springer.com.
In this two-volume compilation of articles, leading researchers
reevaluate the success of Hilbert's axiomatic method, which not
only laid the foundations for our understanding of modern
mathematics, but also found applications in physics, computer
science and elsewhere. The title takes its name from David
Hilbert's seminal talk Axiomatisches Denken, given at a meeting of
the Swiss Mathematical Society in Zurich in 1917. This marked the
beginning of Hilbert's return to his foundational studies, which
ultimately resulted in the establishment of proof theory as a new
branch in the emerging field of mathematical logic. Hilbert also
used the opportunity to bring Paul Bernays back to Goettingen as
his main collaborator in foundational studies in the years to come.
The contributions are addressed to mathematical and philosophical
logicians, but also to philosophers of science as well as
physicists and computer scientists with an interest in foundations.
Kunstliche Intelligenz ist eine Schlusseltechnologie, mit der
sowohl in der Wissenschaft als auch in der Industrie grosse
Erwartungen verbunden sind. In diesem Buch werden sowohl die
Perspektiven als auch die Grenzen dieser Technologie diskutiert.
Das betrifft die praktischen, theoretischen und konzeptionellen
Herausforderungen, denen sich die KI stellen muss. In einer
Fruhphase standen in der KI Expertensysteme im Vordergrund, bei
denen mit Hilfe symbolischer Datenverarbeitung regelbasiertes
Wissen verarbeitet wurde. Heute wird die KI von statistik-basierten
Methoden im Bereich des maschinellen Lernens beherrscht. Diese
subsymbolische KI wird an den Lehren, die aus der Fruhphase der KI
gezogen werden koennen, gemessen. Als Ergebnis wird vor allem fur
eine hybride KI argumentiert, die die Potentiale beider Ansatze zur
Entfaltung bringen kann.
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