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Claudio Conforti

viernes, 18 de mayo de 2012

Around and Beyond the Square of Opposition Jean-Yves Béziau and Dale Jacquette


2012DOI: 10.1007/978-3-0348-0379-3


Series Editor
Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research Council,
Rio de Janeiro, Brazil)
Editorial Board Members
Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary)
Mark Burgin (University of California, Los Angeles, USA)
Razvan Diaconescu ˘ (Romanian Academy, Bucharest, Romania)
Josep Maria Font (University of Barcelona, Barcelona, Spain)
Andreas Herzig (Centre National de la Recherche Scientifique, Toulouse, France)
Arnold Koslow (City University of New York, New York, USA)
Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan)
Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia)
Grzegorz Malinowski (University of Łód´z, Łód´z, Poland)
Darko Sarenac (Colorado State University, Fort Collins, USA)
Peter Schröder-Heister (University Tübingen, Tübingen, Germany)
Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia)

Preface
The theory of inferences and oppositions among categorical propositions, based on Aristotelian term logic, is pictured in a striking square diagram. The graphic representation
of contradictories, contraries, subcontraries and subalterns intended as a foundation for
syllogistic logic can be understood and applied in many different ways with interesting
implications for various disciplines, notably including epistemology, linguistics, mathematics, psychology. The square can also be generalized in other two-dimensional and
multi-dimensional graphic depictions of logical and other relations, extending in breath
and depth the original Aristotelian theory. The square of opposition is accordingly a very
attractive theme which has persisted down through the centuries with no signs of disappearing or even diminishing in fascination. For the last 10 years, there has been a new
growing interest for the square due to new discoveries and challenging interpretations.
This book presents a collection of previously unpublished papers by well-regarded specialists on the theory and interpretation of the concept and application of the square of
opposition from all over the world. We thank all the authors who have contributed a paper
to this book, and the referees who have analyzed, commented on, and made invaluable
recommendations for improving the essays.
Jean-Yves Béziau
Dale Jacquette

Contents

Part I Historical and Critical Aspects of the Square
The New Rising of the Square of Opposition . . . . . . . . . . . . . . . . . . .  3
Jean-Yves Béziau
Logical Oppositions in Arabic Logic: Avicenna and Averroes . . . . . . . . . .  21
Saloua Chatti
Boethius on the Square of Opposition . . . . . . . . . . . . . . . . . . . . . . .  41
Manuel Correia
Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as
a Procrustean Bed for His Modal Metaphysics . . . . . . . . . . . . . . . .  53
Jean-Pascal Alcantara
Thinking Outside the Square of Opposition Box . . . . . . . . . . . . . . . . .  73
Dale Jacquette
John Buridan’s Theory of Consequence and His Octagons of Opposition . . .  93
Stephen Read
Why the Fregean “Square of Opposition” Matters for Epistemology . . . . . .  111
Raffaela Giovagnoli
Part II Philosophical Discussion Around the Square of Opposition
Two Concepts of Opposition, Multiple Squares . . . . . . . . . . . . . . . . . .  119
John T. Kearns
Does a Leaking O-Corner Save the Square? . . . . . . . . . . . . . . . . . . . .  129
Pieter A.M. Seuren
The Right Square . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  139
Hartley Slater
Oppositions and Opposites . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  147
Fabien Schang
viiviii Contents
Pluralism in Logic: The Square of Opposition, Leibniz’ Principle of Sufficient
Reason and Markov’s Principle . . . . . . . . . . . . . . . . . . . . . . . .  175
Antonino Drago
Part III The Square of Opposition and Non-classical Logics
The Square of Opposition in Orthomodular Logic . . . . . . . . . . . . . . . .  193
H. Freytes, C. de Ronde, and G. Domenech
No Group of Opposition for Constructive Logics: The Intuitionistic and
Linear Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  201
Baptiste Mélès
The Square of Opposition and Generalized Quantifiers . . . . . . . . . . . . .  219
Duilio D’Alfonso
Privations, Negations and the Square: Basic Elements of a Logic of Privations 229
Stamatios Gerogiorgakis
Fuzzy Syllogisms, Numerical Square, Triangle of Contraries, Inter-bivalence . 241
Ferdinando Cavaliere
Part IV Constructions Generalizing the Square of Opposition
General Patterns of Opposition Squares and 2n-gons . . . . . . . . . . . . . . .  263
Ka-fat Chow
The Cube Generalizing Aristotle’s Square in Logic of Determination of
Objects (LDO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  277
Jean-Pierre Desclés and Anca Pascu
Hypercubes of Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  293
Thierry Libert
Part V Applications of the Square of Opposition
How to Square Knowledge and Belief . . . . . . . . . . . . . . . . . . . . . . .  305
Wolfgang Lenzen
Structures of Oppositions in Public Announcement Logic . . . . . . . . . . . .  313
Lorenz Demey
Logical Opposition and Collective Decisions . . . . . . . . . . . . . . . . . . . .  341
Srecko Kova ´ cˇ
A Metamathematical Model for A/O Opposition in Scientific Inquiry . . . . .  357
Mark WeinsteinContributors
Jean-Pascal Alcantara Centre Georges Chevrier-UMR 5605, Université de Bourgogne,
Dijon, France
Jean-Yves Béziau CNPq – Brazilian Research Council, UFRJ – University of Brazil,
Rio de Janeiro, Brazil
Ferdinando Cavaliere Cesenatico, FC, Italy
Saloua Chatti Department of Philosophy, Faculté des Sciences Humaines et Sociales,
University of Tunis, Tunis, Tunisia
Ka-fat Chow The Hong Kong Polytechnic University, Hong Kong, China
Manuel Correia Facultad de Filosofía, Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
Duilio D’Alfonso University of Calabria, Arcavacata di Rende, CS, Italy
C. de Ronde Departamento de Filosofía “Dr. A Korn”, Universidad de Buenos AiresCONICET, Buenos Aires, Argentina; Center Leo Apostel and Foundations of the Exact
Sciences, Vrije Universiteit Brussel, Brussels, Belgium
Lorenz Demey Center for Logic and Analytical Philosophy, Institute of Philosophy, KU
Leuven – University of Leuven, Leuven, Belgium
Jean-Pierre Desclés LaLIC (Langues, Logiques, Informatique et Cognition), Université
de Paris Sorbonne, Paris, France
G. Domenech Instituto de Astronomía y Física del Espacio, Buenos Aires, Argentina
Antonino Drago University of Pisa, Pisa, Italy
H. Freytes Universita degli Studi di Cagliari, Cagliari, Italy; Instituto Argentino de
Matemática, Buenos Aires, Argentina
Stamatios Gerogiorgakis University of Erfurt, Erfurt, Germany
Raffaela Giovagnoli Pontifical Lateran University, Vatican City, Italy
Dale Jacquette University of Bern, Bern, Switzerland
ixx Contributors
John T. Kearns Department of Philosophy and Center for Cognitive Science, University
at Buffalo, the State University of New York, Buffalo, NY, USA
Srecko Kova ´ cˇ Institute of Philosophy, Zagreb, Croatia
Wolfgang Lenzen Dept. of Philosophy, University of Osnabrueck, Osnabrueck, Germany
Thierry Libert Département de mathématiques, Université Libre de Bruxelles (U.L.B.),
Brussels, Belgium
Baptiste Mélès Université Blaise Pascal, Clermont-Ferrand, France
Anca Pascu LaLIC, Université de Bretagne Occidentale Brest, Brest Cedex 03, France
Stephen Read Department of Philosophy, University of St Andrews, St Andrews, Scotland, UK
Fabien Schang LHSP Henri Poincaré (UMR7117), Université de Lorraine, Nancy,
France
Pieter A.M. Seuren Max Planck Institute for Psycholinguistics, Nijmegen, The Netherlands
Hartley Slater University of Western Australia, Crawley, WA, Australia
Mark Weinstein Department of Educational Foundations, Montclair State University,
Upper Montclair, NJ, USA



Reseña:“Handbook of Practical Logic and Automated Reasoning,” by John R. Harrison, Cambridge University Press, 2009

Freek Wiedijk


F. Wiedijk (B)
Institute for Computing and Information Sciences,
Radboud University Nijmegen, Nijmegen, The Netherlands
e-mail: freek@cs.ru.nl




John Harrison’s Handbook of Practical Logic and Automated Reasoning strongly
reminds me of Donald Knuth’s The Art of Computer Programming. Both clearly are
masterpieces. And both scare me. They are so comprehensive, so erudite, and the information density is so high, that one really has to pay attention to get the most from
the exposition. Also, both are a bit idiosyncratic. On the other hand, reading those
books is an utter pleasure, because everything is so beautifully presented and there is
so much to learn.
The Handbook of Practical Logic and Automated Reasoning then, is about automation in mathematical logic. Theorem proving with a computer only becomes practical when mundane proof tasks are performed automatically (the two main types
of automation being ‘decision procedures’ and ‘proof search’). The best interactive
theorem provers are those in which this kind of automation has been developed
furthest. The Handbook is a comprehensive treatment of this kind of automation.
The book consists of three strains that have been woven together expertly. The
first strain consists of English prose, treating the topics of the book in computer
science style. The second strain is a mathematical treatment consisting of definitions
and theorems with full mathematical proofs. And the third strain is the source
code of a computer program in the programming language OCaml, that implements
everything that is being treated in detailed working code.
When reading the book one can ignore the second and third strains without losing
understanding of the subject. If one thinks ‘Yes, I believe that that theorem holds, I
am not interested in the details of the proof right now’, one can skip over the proof
without getting lost. Or if one thinks, ‘Yes, I roughly understand how that works, I
believe that it can be implemented’, one can skip over the program source without
problems too. However, if one is interested in the details of either the mathematics
or the implementation, it is all there.

If one strips the English from the book, one gets the full source of a beautiful selfcontained theorem prover. The book even includes the source for mundane things
like parsing and pretty-printing. It shows the power of functional programming that it
is possible to give full implementations of so many algorithms in a book of 681 pages,
which still also treats everything in a way that is understandable without looking
at the code. It also shows how cleverly John Harrison has built a ‘theorem proving
workbench’ in which various pieces are reused over and over again. In some sense the
book is ‘just’ an annotated listing of a program. This probably will turn some readers
off, but as already said, even when skipping over the code one still has a very readable
and detailed handbook.
The code from the book can be downloaded from
http://www.cl.cam.ac.uk/∼jrh13/atp/
and loaded into an interactive OCaml session. That way, one can easily experiment
with everything that the book discusses while reading it.
It should be noted that the theorem prover from the book is not John Harrison’s
industrial strength theorem prover HOL Light. The prover from the book implements first order logic, while HOL Light is higher order. In fact the book only briefly
mentions higher order logic on page 122. Almost all interesting proof automation
apparently can be presented in the domain of first order logic. Another difference
between these two theorem provers is that unlike HOL Light the program from the
book is purely functional. A nice challenge for the Haskell community might be to
create an attractive Haskell version.
The book seems to also be intended as a textbook of mathematical logic, as it
introduces propositional logic and first order predicate logic from scratch. Still, it
mostly treats highly technical subjects that will only be digestible to people who
already are well-versed in mathematical logic. Still, the book is self-contained and
a smart novice could in theory understand everything by paying close attention.
The table of contents of the Handbook is deceptively simple:
1. Introduction
2. Propositional logic
3. First-order logic
4. Equality
5. Decidable problems
6. Interactive theorem proving
7. Limitations
Hidden within these chapters is a wide range of subjects. For example Chapter 4
contains a comprehensive overview of term rewriting (including termination orderings and Knuth-Bendix completion). Chapter 5 treats among many other subjects
Buchberger’s algorithm for the calculation of Groebner bases (including applications
like geometric theorem proving). Chapter 7 contains a very nice presentation of
Goedel’s first incompleteness theorem (including lots of code for experimenting with
the machinery used in the proof). Note that proofs like the one of Goedel’s theorem
are not just sketched. Everything is developed and proved in full detail.
The presentation of logic in the book is sometimes a bit idiosyncratic. Occasionally
a path into a subject is taken that does not follow the most ‘standard’ treatment. The
choice of presentation then seems to have been influenced by what fits nicely in the
OCaml implementation.

As an example take the treatment of first order predicate logic. The semantics of
first order logic is given in Chapter 3, but a proof system only is presented in Chapter
6, and then only as a Hilbert-style calculus. Natural deduction and sequent calculus
are sketched in a few pages, but maybe too briefly for a person who does not know
these systems already. Also following Gentzen the notation → p is used for what
now is usually written as p. After defining the Hilbert-style calculus, a beautiful
LCF-style implementation of this proof system is developed, and the completeness
theorem for first order logic is proved from the fact that that implementation can
execute a complete proof search procedure. Clearly, the theory of first order logic
(semantics, proof system, completeness) is all there, but it is not put in one place.
Like many of the subjects it is woven throughout the book.
As the semantics are treated before the proof system, most of the theory is
developed in terms of the semantics. This seems one of the themes of the book.
The book refers often to the historical background of the various subjects, and
the Further Reading sections contain many pointers into the literature, referring
to an impressive list of references that goes on for 37 pages. Each chapter also is
accompanied by many interesting and sometimes very challenging Exercises.
John Harrison is one of the foremost researchers in the field of interactive theorem
proving. His HOL Light is one of the best theorem provers in existence, and his work
on formalization of mathematics is at the forefront of the technology. Now he has
written what clearly will be the book about automation in theorem proving.
People often ask me whether they should buy this book. My answer then always
is: yes, of course you should buy this book. It is a masterpiece. But beware! It might
also scare you.

Open Access This article is distributed under the terms of the Creative Commons Attribution
License which permits any use, distribution, and reproduction in any medium, provided the original
author(s) and the source are credited.


sábado, 5 de mayo de 2012

Friederike Moltmann Reference to numbers in natural language


Abstract A common view is that natural language treats numbers as abstract
objects, with expressions like the number of planets, eight, as well as the number
eight acting as referential terms referring to numbers. In this paper I will argue that
this view about reference to numbers in natural language is fundamentally mistaken.
A more thorough look at natural language reveals a very different view of the
ontological status of natural numbers. On this view, numbers are not primarily
treated abstract objects, but rather ‘aspects’ of pluralities of ordinary objects,
namely number tropes, a view that in fact appears to have been the Aristotelian view
of numbers. Natural language moreover provides support for another view of the
ontological status of numbers, on which natural numbers do not act as entities, but
rather have the status of plural properties, the meaning of numerals when acting like
adjectives. This view matches contemporary approaches in the philosophy of
mathematics of what Dummett called the Adjectival Strategy, the view on which
number terms in arithmetical sentences are not terms referring to numbers, but
rather make contributions to generalizations about ordinary (and possible) objects.
It is only with complex expressions somewhat at the periphery of language such as
the number eight that reference to pure numbers is permitted.

Albert Visser A Tractarian Universe


Abstract In this paper we develop a reconstruction of the Tractatus ontology.
The basic idea is that objects are unsaturated and that Sachlagen are like
molecules. Bisimulation is used for the proper individuation of the Sachlagen.
We show that the ordering of the Sachlagen is a complete distributive, lattice.
It is atomistic, i.e., each Sachlage is the supremum of the Sachverhalte below
it. We exhibit three normal forms for Sachlagen: the bisimulation collapse, the
canonical unraveling and the canonical bisimulation collapse. The first of these
forms is unique modulo isomorphism, the second and third are simply unique.
The subset ordering on normal forms of the second and third kind reflects the
ordering of the Sachlagen.

jueves, 3 de mayo de 2012

Giving ReasonsA Linguistic-Pragmatic Approach to Argumentation Bermejo-Luque, LilianTheory



Springer, Argumentation Library, Dordrecht, 2011,
volume 20, 209 pp
C. Andone


Bermejo-Luque’s book Giving Reasons has the ambition of developing a new
theoretical approach to argumentation that integrates logical, dialectical and
rhetorical aspects. The author uses speech act theory to realize her ideal of
‘a linguistic-pragmatic approach’ to argumentation. After a severe criticism of the
major existing approaches to the study of argumentation, the author develops what
she claims to be ‘‘a systematic and comprehensive theory of the interpretation,
analysis and evaluation of arguments.’’


Chapter 1, Argumentation and Its Study, aims at offering a critical survey of
classical backgrounds and modern studies in the field of argumentation theory. After
a swift introduction to the classical background in logic, dialectic and rhetoric,
Bermejo-Luque takes us directly to the recent developments in argumentation
studies. An enumeration of these new developments seems to suffice to draw the
conclusion that each current model has established itself within one of the classical
approaches. For instance, informal logic is a theory within the logical approach, the
new Rhetoric finds its place within the rhetorical approach, and the pragmadialectical theory within the dialectical approach.
Why Do We Need a New Theory of Argumentation? comes as a natural question
in the title of Chapter 2. Bermejo-Luque’s answer is as simple as radical. She argues
that all current theories have drawbacks and weaknesses making them unsuitable for
the analysis and evaluation of argumentation. Thus, some theories embrace a
deductivist ideal of justification which leaves aside the pragmatic conditions for

argumentation as an activity of giving reasons. Pragmatic proposals, in turn, are
dubbed instrumentalist, because they offer ‘‘criteria for deciding on the value of acts
of arguing as means for achieving certain goals, such as persuading a universal
audience or resolving a difference of opinion’’ (p. 23). Therefore, the author is of the
opinion that a new normative model of argumentation is needed that overcomes the
problems of the current approaches. The model should, according to BermejoLuque, be ‘‘characterizing what justification is, […] by thinking of justification as
the value that constitutes argumentation as an activity’’ (p. 18). It remains to be seen
in the following chapters what the author exactly means with this remark.
In Chapter 3, Acts of Arguing, the author first criticizes once more the pragmatic
approaches to argumentation by focusing this time on the pragma-dialectical theory.
Although this theory provides a normative framework for the analysis and
evaluation of argumentation by understanding argumentation as a speech act
complex, it is seen as defective in three respects: (a) it advocates that the
perlocutionary goal of argumentation is to convince, (b) it contends that ‘‘the claim
for which the speaker argues is not part of the act of arguing, but is another
illocutionary act linked to the sentences uttered in argumentation’’ (p. 59), and (c) it
regards argumentation as complex because ‘‘arguing can consist of more than one
sentence’’ (p. 59). To overcome these apparent problems, Bermejo-Luque proposes
a model in which argumentation is a second-order speech act complex composed of
the speech act of adducing and the speech act of concluding. These speech acts are
characterized as second order ‘‘because they can only be performed by means of a
first order speech act—namely, constative speech acts’’ (p. 60). The author’s model
consists in formulating conditions for putting forward a reason as an illocutionary
act (also referred to as adducing), for putting forward a target-claim as an
illocutionary act (also referred to as concluding), and for the complex illocutionary
act of arguing.
Chapter 4 concerns The Logical Dimension of Argumentation. Bermejo-Luque
emphasizes that previous criticisms of formal logic as a tool for evaluating natural
language argumentation are correct. She argues that Toulmin’s conception of logic
as a non-formal normative theory of inference is instead fruitful, but normatively it
is insufficient. Therefore, the author proposes that the data, the warrant, the rebuttal,
and the backing in Toulmin’s model be ‘completed’ by adding an ontological
qualifier, which is ‘‘an explicit reference to the type of force with which we put
forward a given propositional content in claiming’’ (p. 115). Moreover, BermejoLuque suggests that the conclusion be ‘completed’ with an epistemic qualifier,
which is ‘‘an explicit reference to the type of force with which we put forward a
claim in concluding it’’ (p. 115).
Chapter 5 moves to The Dialectical Dimension of Argumentation. BermejoLuque tries to give an account of the dialectical normative conditions of
argumentation by establishing whether argumentation fulfills certain dialectical
criteria. She argues that putting forward a reason for a claim involves dialectical
conditions that are ‘‘constitutively normative for argumentation as a justificatory
device and regulatively normative for argumentative as a persuasive device’’
(p. 121). What is one to make of this idea remains unclear.

As one might expect, in Chapter 6 The Rhetorical Dimension of Argumentation is
investigated. After disagreeing with the way in which informal logic, pragmadialectics and Tindale’s rhetorical model have integrated rhetorical aspects into
argumentation theory, Bermejo-Luque emphasizes that her normative model
integrates a rhetorical perspective in order to determine ‘‘how well a piece of
argumentation does at accomplishing justification’’ (p. 140). At the end of this
chapter, the author turns to non-verbal argumentation, which she finds important
because it has ‘‘rhetorical power to induce beliefs’’ (p. 163).
The final chapter, Chapter 7, deals with Argument Appraisal, which includes a
semantic appraisal of argumentation and a pragmatic appraisal of argumentation.
With regard to the semantic appraisal—a term which remains undefined—BermejoLuque deals with enthymeme and incomplete argumentation. With regard to the
pragmatic appraisal of argumentation—again undefined—she tries to show that
there is a kind of argumentative flaw which consists in a failure to meet the
pragmatic conditions for arguing. One such example is, according to BermejoLuque, the fallacy of the ad baculum which gives the appearance of argumentation
to a threat.




The Alan Turing Centenary Conference


June 23, 2012 marks the centenary of the birth of Alan Turing. Alan Turing is arguably the most famous computer scientist of all time.

The Turing Centenary Conference will be held in Manchester on June 22-25, 2012, hosted by The University in Manchester, where Turing worked in 1948-1954. The main theme of the conference is Alan Turing’s Centenary. It has the following aims:
  • to celebrate the life and research of Alan Turing;
  • to bring together the most distinguished scientists, to understand and analyse the history and development of Computer Science and Artificial Intelligence

Invited Speakers

Rodney Brooks (MIT)Frederick P. Brooks, Jr. (University of North Carolina, Turing Award winner)
Vint Cerf (Google, Turing Award winner)Edmund M. Clarke (Carnegie Mellon University, Turing Award winner)
Jack Copeland (University of Canterbury)George Ellis (University of Cape Town, Templeton Award winner)
David Ferrucci (IBM)Sir Tony Hoare (Microsoft, Turing Award winner)
Garry Kasparov (Kasparov Chess Foundation)Samuel Klein (Wikipedia)
Don Knuth (Stanford University, Turing Award winner)Yuri Matiyasevich (Institute of Mathematics, St. Petersburgh)
Hans Meinhardt (Max Planck Institute for Developmental Biology)Sir Roger Penrose (Oxford, Wolf Prize)
Michael O. Rabin (Harvard University, Turing Award winner)Adi Shamir (Weizmann Institute of Science, Turing Award winner)
Leslie Valiant (Harvard University, Turing Award winner)Manuela M. Veloso (Carnegie Mellon University)
Andrew Chi-Chih Yao (Tsinghua University, Turing Award winner)


TimeEventSpeaker

Friday June 22, 2012 (University Place)
18:30 – 20:00Evening invited talk for the General Public: Alan Turing, Pioneer of the Information AgeJack Copeland

Saturday June 23, 2012 (Turing Centenary Day) Manchester Town Hall (Manchester Town Hall)
09:00 – 10:00Opening invited talk: Turing's Legacy in the Networked WorldVint Cerf
10:00 – 11:00Invited talk: Turing, Church, Gödel, Computability, Complexity and Randomization - a Personal PerspectiveMichael Rabin
Coffee break
11:30 – 12:30Invited talk: Alan Turing and Number TheoryYuri Matiyasevich
Lunch
13:30 – 14:30Invited talk: Beyond Jeopardy! The Future of WatsonDavid Ferrucci
14:30 – 15:30Invited talk: Turing's Cryptography from a Modern PerspectiveAdi Shamir
Coffee break
15:45 – 16:45Invited talk: Pilot ACE Architecture in ContextFrederick P. Brooks
16:45 – 18:15Young Scholars Competition Award Ceremony
Laudation (awards to be handed over) – 2 invited talks by selected winners (30 minutes each)
18:15Reception

Sunday, June 24, 2012 (Manchester Town Hall)
09:00 – 10:00Invited talk: Quantum Computing: A Great Science in the MakingAndrew Chi-Chih Yao
10:00 – 11:00Invited talk: Temporal Logic Model CheckingEdmund Clarke
Coffee break
11:30 – 12:30Invited talk: Can Computers Understand Their Own Programs?Tony Hoare
Lunch
14:00 – 15:00Invited talk: Symbiotic Autonomy: Robots, Humans and the WebManuela Veloso
15:00 – 16:00Invited talk: Computer Science as a Natural ScienceLeslie Valiant
Coffee break
16:30 – 18:00Panel Discussion: The Big Questions in Computation, Intelligence and Life
Break
19:00Dinner, starting with the Dinner SpeechDonald E. Knuth

Monday, June 25, 2012 (Manchester Town Hall)
09:00 – 10:00Invited talk: The Reconstruction of Turing's "Paper Machine"Garry Kasparov
10:00 – 11:00Invited talk: Turing's Humanoid Thinking MachinesRodney Brooks
Coffee break
11:30 – 12:30Panel Discussion: Turing Test
Lunch
14:00 – 15:00Invited talk: On the Nature of Causation in Digital Computer SystemsGeorge Ellis
15:00 – 16:00Invited talk: Turing’s pioneering paper “The Chemical Basis of Morphogenesis” and the subsequent development of theories of biological pattern formationHans Meinhardt
Coffee break
16:30 – 17:30Invited talk: TBC.
17:30 – 18:30Closing invited talk: TBC.Samuel Klein
Break
20:00 – 21:30Evening invited talk for the General Public: The Problem of Modelling the Mathematical MindRoger Penrose