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Location: Bestuursgebouw 036
Date: Thursday April 13
Time: 12:00-13:00
Title: Weak Modal Logics of Cut-Free Provability
Speaker: Saeed Salehi
Abstract
Normal propositional modal logics are usually formalized by
some set of modal axioms containing
the axiom
(K) ¤(A → B) → (¤A →
¤B)
plus the rule of necessitation
(RN) A
/ ¤A
over the classical propositional calculus.
The Gödel-Löb logic, which is known to be the
provability logic of sufficiently strong arithmetical
theories such as Peano's arithmetic or primitive recursive
arithmetic,
is then obtained by adding Löb's axiom
(L) ¤(¤A → A) →
¤A
to K.
When the modal operator ¤ is interpreted as cut-free
provability in weak arithmetics
(where the exponentiation function is not total) then the
axiom (K) does not hold.
For considering these provability logics (with weaker
provability predicates over weaker theories)
one is inclined to study non-normal modal logics.
In this talk, we review the theory of minimal modal logic E
which is axiomatized by
the single rule of inference
(RE) (A ↔ B) / (¤A ↔
¤B)
over classical propositional calculus.
Then we will see that the normal modal logic K is obtained
from E by adding the axioms
(M) ¤(A & B) → ¤A
& ¤B
and
(C) ¤A & ¤B →
¤(A & B)
and the necessitation rule (RN).
While (M) and (RN) are still valid for
cut-free provability of weak arithmetics, we observe that
(C) is not: for getting a
cut-free proof of A&B out of a cut-free proof p of A
and a cut-free proof q of B,
we should merge p and q together and perform some
arithmetical operations which
could be too costly to be handled in our weak arithmetic.
Loosely speaking,
the axiom (K) is a kind of formalized cut rule, which
should not hold is those arithmetics
that cannot prove the equivalence of cut-free provability
with the usual Hilbert-style provability.
We note that the cost of cut-elimination is of
(super-)exponential in proof theory.
We also introduce another axiom (S) valid for Herbrand
provability in IΔ0, and
derive Gödel's Second Incompleteness Theorem for
Herbrand Consistency of IΔ0;
that is the unprovability of the Herbrand Consistency of
IΔ0 in itself.
Location: Bestuursgebouw 150
Date: Tuesday April 18
Time: 12:00-13:00
Title: Computational complexity and short proofs of consistency statements
Speaker: Joost Joosten
Abstract:
In this talk I shall discuss connections between various fields of logic. First, I shall make some comments on links between computational complexity and arithmetics. Next I shall dwell on the relation between propositional logic and computational complexity.
This shall culminate in a beautiful theorem by Pudlák and Krajicek relating optimal propositional proof systems to poly-time axiomatized theories that prove in a short way all consistency statements of all poly-time axiomatized theories. I shall sketch a proof of this theorem and talk about new results that I obtained in this direction.
Although this abstract uses many difficult words, I think I can present parts of the talk on a pretty elementary level. I even wrote a popular mathematical text (in Dutch) on the above mentioned theorem of Pudlák and Krajicek which can be found in this report list or
here
Location: Bestuursgebouw 150
Date: Friday April 21
Time: 12:00-13:00
Title: First order logic of proofs
Speaker: Tatiana Yavorskaya
Moscow State University, Department of mathematical logic and algorithm theory
Abstract:
This talk will be about the ongoing research in first order logic of
proofs.
Propositional logic of proofs LP introduced by S. Artemov is
formulated in terms of the relation ``t is a proof of A'' where
proofs are represented by means of special proof terms. LP is
decidable and arithmetically complete. Also it suffices to emulate
modal logic S4 and thus provides it with the exact provability
semantics.
If we turn to first order logic of proofs, so far, most results were negative.
As in case with provability logic, first order logics of proofs are not
recursively enumerable. A recursively enumerable arithmetically complete fragment
was found by R. Yavorsky, but this fragment admits only boundeed
formulas in the scope of the proof operator, and thus it is not
sufficient for the realization of any modal logic.
In this talk we present the most recent results, namely, an arithmetically sound first order logic
of proofs which emulates first order modal logic S4, and, therefore, first order intuitionistic logic.
The most relevant papers which can be downloaded are
for negative results in first order logic of proofs see
S.Artemov and T.Sidon-Yavorskaya.
`On the first order logic of proofs,' Moscow Mathematical Journal, vol. 1, No. 4, pp. 475-490, 2001.
for brief introduction to propositional logic of proofs see
S. Artemov. ``Explicit Modal Logic,'
Workshop Proceedings Advances in Modal Logic, vol. 2, Uppsala, 1998, Technical Report CFIS 98-17, Cornell University, 1998.
Joint work with Sergei Artemov
Graduate Center, CUNY, New York
Location: Bestuursgebouw 150
Date: Tuesday April 25
Time: 12:00-13:00
Title: What makes an Ackermannian function non primitive recursive?
Speaker:
Andreas Weiermann
Abstract:
It is well known that the Ackermann function
arises naturally from a given simple start function by
iteration and diagonalization. In this talk we classify
exactly for a large class of start functions the speed
of iteration which is needed to produce a non primitive
recursive function. Among other things we prove
that if the successor function is the start
function then logarithmic iteration does not
lead beyond primitive recursion.
(This is joint work with Eran Omri.)
Location: Bestuursgebouw 036
Date: Friday April 28
Time: 12:00-13:00
Title: On provability logic with quantifiers on proofs
Speaker: Rostislav Yavorskiy
Steklov Mathematical Institute, Moscow, Russia
Abstract:
We consider first order extensions of the logic of proofs, in which
we do not change the set of atomic formulas, but allow for
quantification over proof variables.
In this language the modal provability
operator Box is expressed by the formula ∃ x(x : A),
so provability logic with quantifiers on proofs is also an extension
of propositional modal provability logic.
Some non-axiomatizability results for different versions of provability
logic with quantifiers on proofs are found in [1]. However,
there is a hope that the logic corresponding to the standard Gödel
proof predicate is decidable. Some partial positive results in this direction
are presented in [2, 3]. The solution of this problem is closely
related to the task of finding adequate Kripke-style semantics for this
kind of logics.
Rostislav Yavorskiy.
`On Kripke-style Semantics for the Provability
Logic of Goedel's Proof Predicate with Quantifiers on Proofs.'
Journal of Logic and Computation. Vol. 15, No. 4 (2005), pp. 539-549.
Lunch meetings 2005
We meet on a weekly basis, on thursdays, 12:00 - 13:00 in room 195
of the bestuursgebouw of Utrecht University (except when there is the F-lunch instead).
Normally we work in an informal setting (some speak while others eat).
Speaker: Thomas Dohmen
Title: Context and Error in the Epistemology of Scientific Experiment
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday January 4, 2005
Time: 12:00-13:00
Within traditional epistemology, so-called skeptical scenarios challenge
the idea of having knowledge. These scenarios demand a level of
justification which has to be delivered in order to call something
knowledge that is impossible to reach. A way to deal with these
skeptical scenarios is offered by an approach called contextualism, in
which it seems reasonable to disregard skeptical scenarios in certain
contexts, thereby justifying the attribution of knowledge in those
constrained contexts.
The project of Generating Experimental Knowledge investigates the
critical role of error in experimental science. Scientists use experiments
to generate knowledge. They rely on various standard methods to insure
that the experiment provides them with correct data. By relying on these
methods, scientists seem to be justified in attributing knowledge to the
theories that have been confirmed by experiments or to theories that
follow the outcome of experiments, although possible errors have not been
(individually) accounted for.
The claim of this part of the project is that, by referring to such
standard methods, scientists create a context of justification which
enables them to attribute knowledge in the same way that the epistemic
contextualists create a context of justification. This is done by creating
a context in which knowledge can be justifiably attributed without
regarding the factors that threaten this attribution of knowledge to the
full extent. In contextual epistemology, there is no full defense against
skeptical scenarios (these scenarios are just properly ignored in most
contexts), and in scientific experiment not every possible error is
individually accounted for (because there is a reference to a context of
similar and related experiments and standard methodologies, some
possible errors are ignored).
This PhD thesis suggests and presents an analogical relation between
skepticism in the theory of knowledge and error in the practice of
experimental science. It is an investigation into both the consequences of
the concept of knowledge and epistemic skepticism for the practice of
experimental science and the consequences of error in experimental science
for the theory of knowledge. The main focus is on the role of context in
both fields of study, since it is supposed that context determines when
knowledge can be correctly attributed in both fields.
This thesis will offer not only an evaluating overview of the debates of
the last two decades of contextual epistemology, but will also contribute
a specific perspective on the practice of experimental science from
epistemic theory, thereby offering a practical case to matters that
traditionally have always remained highly theoretical. Conversely, it
will offer a deeply philosophical background of the concept of scientific
knowledge to the practice of scientific experimentation (which is
generally thought to generate knowledge). Furthermore, the thesis will
include an extensive account of the semantic issues arising through a
contextual approach to science and its related conceptual terminology. It
is hoped that, together, these analyses will lead to a better
understanding of the relationship between the theory of knowledge
(epistemology) and the attribution of knowledge in experimental science.
Speaker: Cory Wright
Title: Minimalist explanations do not explain very much
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday January 11, 2005
Time: 12:00-13:00
Abstract:
Minimalist explanations of truth dont explain very much---and thats
fine, so long as theres little in need of explanation in the first place;
but that itself cannot be a reason for thinking that truth is not a robust
alethic phenomenon. So minimalists need a second-order explanation as to
why minimal explanations are adequate. Over the last 15 years, Paul
Horwich has provided and defended just such an explanation, and, in doing
so, has provided one of the most serious challenges to the legitimacy of
substantive theoriesone which is all the more powerful given that it does
not discriminate amongst them. Consequently, Horwichs alethic minimalism
is one of the bigger obstacles to the plausibility of substantive alethic
theories. In this talk, I consider reasons for looking askance at
Horwichs explanation as to the adequacy of minimal explanations should be
rejected, which---if gripping---would suggest that minimalism is not the
threat to substantivism that it is so often held to be.
Plaats: Ruppert Rood (let op: afwijkende plaats!)
Datum: Dinsdag 18 januari, 2005
Tijd: 12:00-13:00 (let op: afwijkende afwijkende tijd = normale tijd)
Titel: Logica 1
Spreker: Joost J. Joosten
Aflevering drie van de F-lunch.
Het is de bedoeling om zelf lunch mee te brengen.
Speaker: Tanja Yavorski
Title: Operations on proofs and labels.
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday January 25, 2005
Time: 12:00-13:00
Abstract:
This talk is about the logic of proofs (S.Artemov, 1997), the ongoing research in this field and,
in particularly, about logic of proofs as a framework for specification of operations on proofs.
Logic of proofs is formulated in the propositional language enriched by the proof predicate "t is
a proof of F". We add a new labelling predicate "x is a label for F" to the language. This enables
one to specify a wide class of operations which produce codes of proofs being given codes of some
other proofs and possibly codes of formulas. We describe logics which specify different opertions
on proofs and labels. The main result is the uniform completeness theorem for these logics.
Speaker: Rostik Yavorski
Title: On the first order logic of the standard proof predicate
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday February 1, 2005
Time: 12:00-13:00
Abstract:
There are two ways to consider first order extensions of the logic of
proofs LP. First, we can extend the set of atomic formulas by adding
predicate letters, individual variables etc. The second way is to
extend the language of LP with quantifiers on proofs.
In my talk I will report recent results in this field.
In particular, I will focus on the properties of the first order logics
corresponding to the standard (single conclusion) Goedel proof predicate
and its multiple conclusion modification.
Plaats: Bestuursgebouw 036
Datum: Dinsdag 8 februari 2005
Tijd: 12:00-13:00
Titel: Filosofie van de Geest
Spreker: Joel Anderson
Aflevering vier van de F-lunch.
Het is de bedoeling om zelf lunch mee te brengen.
Speaker: Siewert van Otterloo
Title: Game and Preference Logics
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday February 15, 2005
Time: 12:00-13:00
Abstract:
Several attempts have been made to develop logical languages for reasoning
about games. Many of these logics are variants of propositional modal
logic, with extra operators that address game theoretic issues, such as
time, actions, preferences and outcomes. In my talk I will compare several
of these logics, and explain what properties make these logics useful or
interesting to look at. I will do this from both a philosophical and a
computer science perspective.
Speaker: Vincent van Oostrom
Title: Delimiting Diagrams
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday February 22, 2005
Time: 12:00-13:00
Abstract:
We introduce the unifying notion of delimiting diagram. In the first part of our talk,
hitherto unrelated results such as: Minimality of the internal needed strategy for orthogonal first-order
term rewriting systems, maximality of the limit strategy for orthogonal higher-order pattern rewrite
systems (with maximality of the strategy F-infinity for the lambda-calculus as a special case), and
uniform normalisation of balanced weak Church-Rosser abstract rewriting systems, all are seen to
follow from the property that any pair of diverging steps can be completed into a delimiting diagram.
In the second part we relativise our results to deal with non-confluent systems as well.
Speaker: Vincent van Oostrom
Title: Vicious Circles in Orthogonal Rewriting
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday March 8, 2005
Time: 12:00-13:00
Abstract:
In rewriting, (head) normal forms model `results' and
objects which may be rewritten to a result are considered meaningful.
We show that for orthogonal rewrite systems, an object
which may be rewritten to itself is meaningless;
it cannot be rewritten to a result.
In other words, a circle in a reduction graph is vicious.
The proof is based on an analogy between taking residuals
of cycles and computing decimal expansions of fractions;
both are repetitive and compressible, in a technical
sense to be explained.
Speaker: Albert Visser
Title: Dynamic Semantics on Indexed Complete Boole Algebras
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday March 8, 2005
Time: 12:00-13:00
Abstract:
Groenendijk & Stokhof's Dynamic Predicate Logic or DPL was a one
dimensional system: there was no clear separation of context and content.
For various reasons it is better to set things up using a two dimensional
approach in which information growth has two components. Such an
approach involves an Indexed Complete Boole Algebra.
We will show how a seemingly negative result of van Benthem
saying that a dynamic predicate logic with certain good properties
is impossible, turns into a positive result in the two
dimensional setting. We will also discuss the notions of
satsfaction and negation in the framework of an Indexed Boole Algebra.
Speaker: Emil Jerabek
Title: Admissible rules of modal logics
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday April 12, 2005
Time: 12:00-13:00
Abstract:
Building on the work of S. Ghilardi and R. Iemhoff, we present
explicit bases of admissible rules for several normal modal systems,
including K4, GL, S4, or GL.3.
Speaker: Emil Jerabek
Title: Admissible rules of modal logics
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday April 19, 2005
Time: 12:00-13:00
Abstract:
See the announcement of April 12.
Speaker: Janneke van Lith
Title: A paradox from statistical physics
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday April 26, 2005
Time: 12:00-13:00
Abstract:
The Gibbs paradox, named after the founding father of statistical
mechanics J.W. Gibbs, is concerned with the entropy of mixing of ideal gases.
I will explain the paradox, explain it away, and discuss in passing several
more-or-less-philosophical issues: indistinguishability of particles, theory
reduction, and subjectivity in physics.
Speaker: Lev Beklemishev (Joint work with J. Joosten and M. Vervoort)
Title: Japaridze's polymodal logic: provable and unprovable facts
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday May 17, 2005
Time: 12:00-13:00
Abstract:
We examine the question whether some of the usual modal-logical
properties of Japaridze's logic GLP and its extensions by closed modal
formulas can be established by finitary methods. We give examples of
non-trivially provable (in the elementary arithmetic) as well as of
unprovable (in ACA_0) facts about this modal logic.
Speaker: Albert Visser
Title: MuGL: Lö?b's logic meets mu-calculus
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday May 17, 2005
Time: 12:00-13:00
Abstract:
There are two major modal logics of fixed points: Löb's logic and the mu-calculus.
The first corresponds to guarded fixed points and the second to minimal fixed points of
positive operators. We show that these logics are connected: Löb's logic is a
retract of the mu-calculus. A consequence is that e.g. uniform interpolation can be
transferred from the mu-calculus to Löb's logic.
Speaker: Vincent van Oostrom (Joint work with J. Ketema and J.W. Klop)
Title: Covering clusters by chains
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday June 14, 2005
Time: 12:00-13:00
Abstract:
A collection of redex-pattern occurrences in a term is said to be a cluster if their union
is a connected part of the term. We show that in weakly orthogonal TRSs, clusters may always be
covered by so-called chains, by reduction to the same property for interval algebra.
Speaker: Joop Leo
Title: Modeling relations
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday June 21, 2005
Time: 12:00-13:00
Abstract:
We are going to consider relations "out there" in the real world.
In the way we normally look at relations the relata (objects) occupy
positions. This is no problem for the love relation, but for relations
like the adjacency relation and cyclic relations, different assignments of
objects to the positions might give exactly the same states. So, we have
to conclude that the positions are not always in the states themselves.
But, if positions are not in the states, what is the nature of the
positions? Are they metaphysically a redundant ingredient of relations? Or
are they perhaps even a consequence of a wrong conception of what a
relation is? In this presentation I will discuss different models of
relations that help to clarify the status and meaning of positions for
"real" relations.
Speaker: Fabian Battaglini and Jan van Eijck
Title: Monotonicity in Natural Reasoning
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday June 28, 2005
Time: 12:00-13:00
Abstract:
We will explain the connection between monotonicity reasoning and
polarity marking in natural language, and present a new algorithm for
polarity marking. Next, we analyse the fine structure of syllogistic
reasoning in terms of applications of the rules of symmetry,
monotonicity, and existential import. Finally, we will connect up to
concrete examples of how monotonicity can explain various aspects of
reasoning competence and performance.
Speaker: Rosja Mastop
Title: `Self-introduction of the speaker'
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Friday July 8, 2005
Time: 12:00-13:00
Summary of topics:
Mijn achtergrond, opleiding (heel in het kort)
Mijn proefschrift-onderzoek
Dit betreft taalfilosofie (illocutionaire kracht, zinstypen en de relatie tussen semantiek en pragmatiek) en meer concrete taalkunde (de relatie tussen imperatief en infinitief, verledentijdsimperatieven, en meer) en enige deontische logica (disjunctie en modaliteit, zie ook de vorige tf lunch).
Mijn (huidige en) toekomstige onderzoek
Gebiedende zinnen bevelen handelingen, niet gebeurtenissen. Handelingen zijn niet gebeurtenissen. Causaliteit is een relatie tussen gebeurtenissen, handelen is een relatie tussen personen en handelingen. Dus: handelen is niet veroorzaken.
Bij het onderzoek kijk ik naar: filosofen die zeggen dat causaliteit een projectie is van het eigen doelgericht handelen (Maine de Biran), of dat causaliteit direct wordt waargenomen (Michotte), de semantiek van de verschillende gerundium-typen (Vendler, Hyman), de manipuleerbaarheidstheorie van causaliteit (von Wright).
Speaker: Vincent van Oostrom
Title: Substitutions vs Braids
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Thursday September 29, 2005
Time: 12:00-13:00
Abstract:
The Substitution Lemma is a fundamental lemma stating that the order in
which two substitutions are applied can be interchanged. For instance,
interchanging the order in which the substitutions [x:=y+3] and [y:=7]
are applied to (x+y) yields:
(x+y)[x:=y+3][y:=7] = (x+y)[y:=7][x:=(y+3)[y:=7]]
which is correct since evaluating the substitutions yields that both
sides are equal to (7+3)+7.
In calculi which reify the notion of substitution,
so-called explicit substitution calculi,
the (general) equality is turned into a rewrite rule:
M[x:=P][y:=Q] -> M[y:=Q][x:=P[y:=Q]]
The question is whether this rule is confluent.
As an exercise one may try to join, by means of further steps,
the terms:
M[y:=Q][x:=P[y:=Q]][z:=R] and M[x:=P][z:=R][y:=Q[z:=R]]
obtained by applying the rule to M[x:=P][y:=Q][z:=R]
in either way.
We show there is a surprising analogy between the above confluence
question and that for braids, based on the idea that both the above
rule and crossing two strands in a braid correspond
to `commutativity with history'.
Speaker: Lev Beklemishev
Title: Proof, evidence, belief: Artemov's logic of proofs and the notion
of evidence in law
Place: University of Utrecht, Uithof, Bestuursgebouw 048
Date: Thursday October 13, 2005
Time: 12:00-13:00
Abstract:
We shall discuss the notion(s) of evidence in law and examine
the possibility of using the format of Artemov's Logic of Proofs LP to
model some aspects of this notion.
Speaker: Rosja Mastop
Title: De wereld omgeven met mogelijkheden
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Thursday November 10, 2005
Time: 12:00-13:00
Abstract:
Wellicht de meest fundamentele vraag in de analyse van het
causaliteitsbegrip is: met welke begrippen kan dit gedaan worden? Is
oorzakelijkheid een psychologisch fenomeen, te verklaren in termen
van associaties, perceptuele Gestalt en subjectieve projectie? Of is
het een (meta)fysische realiteit, te beschrijven in termen van
behouden grootheden? In de literatuur is ook voor een derde
mogelijkheid geopteerd: het analyseren van oorzakelijkheid aan de
hand van praktisch filosofische begrippen. Zo heeft G. H. von Wright
betoogd dat de relatie tussen oorzaak en gevolg er een is van middel
tot doel. Anders gezegd, door de oorzaak te produceren kunnen wij het
effect bewerkstelligen. Deze benadering heeft twee belangrijke
voordelen: (i) het geeft een eenvoudige verklaring voor de asymmetrie
van oorzakelijke verbanden en (ii) het verbindt het
oorzakelijkheidsbegrip met de praktijk van experimentatie.
In deze presentatie wil ik op twee punten nader in gaan. Ten eerste
wil ik laten zien dat deze aanpak niet circulair is, zoals wordt
verondersteld door vriend en vijand van deze benadering. Ten tweede
zal ik beargumenteren dat de aanpak van von Wright op twee gedachten
hinkt: oorzakelijkheid is een op zich staand metafysisch verband (een
nomologische afhankelijkheid), maar de enige wijze waarop wij inzicht
kunnen vergaren in niet-gerealiseerde mogelijkheden is via
(intentioneel) handelen. Ik zal betogen dat dit de status van
mogelijke werelden in de theorie onduidelijk maakt. Een alternatief
kan worden ontwaard in het werk van L. Wittgenstein.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 6 januari
Tijd: 12:00-13:00
Titel: Modal matters in Interpretability logics; deel 2
Spreker: Joost J. Joosten
Het abstract is ongewijzigd. In deel twee zullen we iets meer
op technische details ingaan.
Abstract
In deze voordracht zullen we ons concentreren op de modale
semantiek van interpreteerbaarheidslogicas. We presenteren een
constructiemethode waarmee van een groot aantal logicas de
modale volledigheid kan worden bewezen. Tevens kunnen we deze
methode aanwenden om een aantal belangwekkende arithmetische resultaten
te verkrijgen.
In samenwerking met Evan Goris
Plaats: Bestuursgebouw 195
Datum: Dinsdag 13 januari
Tijd: 12:00-13:00
Titel: De rol van ergodentheorie in de filosofie van de statistische fysica
Spreker: Janneke van Lith
Tuesday January 20, Professor Tait from the University of Chicago, will
give a talk in the Tf lunch series of the philosophy department.
Speaker: William W. Tait
Title: Are there intuitionistic counterexamples to classical mathematical
logic?
Place: University of Utrecht, Uithof, Bestuursgebouw 036
Date: Tuesday January 20, 2004
Time: 11:00-13:00
Note that we start at 11:00 and not at the usual 12:00.
More information on how to get at the Uithof can be found
here.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 27 januari
Tijd: 12:00-13:00
Titel:INDUCTION IN THE CATEGORY OF INTERPRETATIONS
Spreker:Albert Visser
As is well known, the principle of induction can be viewed as a consequence of
the fact that the natural numbers form a free algebra. This insight
is reflected in the category of interpretations. An interpretation of
a weak arithmetic satisfies full induction if it is initial in
a certain sense. We explain this idea in some detail and discuss some
consequences.
Plaats: Bestuursgebouw, 048
Datum: Dinsdag 3 februari
Tijd: 12:00-13:00
Titel: Het hypothetisch oordeel bij Brouwer
Spreker:John Kuiper
De bewijsinterpretatie van de intuitionistische wiskunde en logica is
niet vanaf het begin de ons nu bekende geweest.
In zijn dissertatie stelde Brouwer zeer strenge eisen aan het
hypothetisch oordeel, veel strenger dan Kolmogorov en Heyting dat
deden (hoewel er bij de eerste ook een wijziging optrad in zijn
opvattingen).
Later accepteerde Brouwer impliciet Heytings interpretatie.
Plaats: Bestuursgebouw 038
Datum: Dinsdag 10 februari
Tijd: 12:00-13:00
Titel:INDUCTION IN THE CATEGORY OF INTERPRETATIONS, part 2
Spreker: Albert Visser
The abstract has not been changed. In the second part we will
focus more on proofs.
As is well known, the principle of induction can be viewed as a consequence of
the fact that the natural numbers form a free algebra. This insight
is reflected in the category of interpretations. An interpretation of
a weak arithmetic satisfies full induction if it is initial in
a certain sense. We explain this idea in some detail and discuss some
consequences.
Plaats: Bestuursgebouw 038
Datum: Dinsdag 17 februari
Tijd: 12:00-13:00
Titel: Procesalgebras in hybride systemen
Spreker: Jan Bergstra
Joint work with Cees Middelburg.
Plaats: Bestuursgebouw 038
Datum: Dinsdag 24 februari
Tijd: 12:00-13:00
Titel: Limit existence principles in arithmetic and related topics
Spreker: Lev D. Beklemishev
Abstract:
We study the principle asserting that a primitive recursive function
that is eventually weakly decreasing is eventually constant and some
other principles
of similar flavour in PA. We discuss some applications of such
principles
to interpretability and conservativity logic.
Plaats: Bestuursgebouw 036
Datum: Dinsdag 2 maart
Tijd: 12:00-13:00
Titel: Indirect Speech Acts, Politeness, and the Civilizing Process
Spreker: Herman Hendriks
Abstract:
I will argue that Levinson's (1983) conversation analysis
of linguistic indirectness is superior to an account in
terms of speech act theory along the lines of Searle (1979b),
especially in view of the way in which it relies on
Brown and Levinson's (1987) theory of politeness as an
explanatory mechanism. In a critical examination of their
own work, Brown and Levinson conclude that their analysis of
politeness suffers from an "overdose of cognitivism", as a
result of which it is not able to account for the fact that
social interaction has its own emergent properties which
transcend the characteristics of the individuals that jointly
produce it. Most notably, the phenomenon of politeness is
linked up with the concept of aggression, and, among other
notions that are central to the nature of the social persona,
with the concept of embarrassment. The tenet of the present
paper is that this emergent character of social interaction
can be accounted for if the study of its internal systematics
is supplemented with the theory of the development of social
structure that has been proposed within the framework of the
historical sociology of Elias (1993).
Plaats: Bestuursgebouw 048
Datum: Dinsdag 9 maart
Tijd: 12:00-13:00
Titel: Burned chips and indianenverhalen
Spreker: Joop Leo
Abstract:
Chips can become quite hot if a lot of wires switch from 0 to
1 and visa versa in a short time. For a certain class of logical
circuits I will show that they are real energy-eaters. Further, I will
discuss a relation between information complexity and energy
consumption in chips. This relation, which is of a rather general kind,
also gives some insight in the effort needed to communicate massages
with a tam-tam in a certain time.
In Dutch:
Titel: Aangebrande chips en indianenverhalen
Chips kunnen behoorlijk warm worden als veel draadjes in
korte tijd vaak switchen van 0 naar 1 en omgekeerd. Van een bepaalde
klasse van logische circuits zal ik laten zien dat het echte
energievreters zijn. Verder wil ik een verband tussen
informatiecomplexiteit en energieverbruik in chips bespreken. Dit
verband is van vrij algemene aard en geeft ook inzicht in de inspanning
die nodig is om berichten binnen een bepaalde tijd door te geven met de
tamtam.
Speaker: Mojtaba Aghaei
Title: Basic propositional logic, its systems and its models
Place: University of Utrecht, Uithof, Bestuursgebouw 038
Date: Tuesday March 16, 2004
Time: 12:00-13:00
Basic propositional logic was first introduced by A. Visser in 1981,
by the intention of formalizing provability. Formal provability logic
is related to the provability modal logic GL just as intuitionistic
logic is related to modal logic S4. Basic logic itself is related to
K4. It is sound and complete with respect to the class of transitive
Kripke models.
In this lecture we introduce basic propositional logic and its
motivation, and review its different axiomatic systems and its Kripke
and algebraic models.
Speaker: Mojtaba Aghaei
Title: Basic predicate logic, its proof theory and its arithmetic
Place: University of Utrecht, Uithof, Bestuursgebouw 036
Date: Tuesday March 23, 2004
Time: 12:00-13:00
Basic Predicate Calculus, BQC, was first introduced by W. Ruitenburg in
1990. He axiomatized it in sequent notation and his motivation came
from a philosophical criticism of the BHK (Brouwer-Heyting-Kolmogorov)
interpretation of the logical connectives.
In this lecture we introduce the axiomatic systems of BQC, basic
arithmetic BA, and its realizablity.
Speaker: Marta Bilkova
Title: On Computational Content of Intuitionistic Proofs
Place: University of Utrecht, Uithof, Bestuursgebouw 036
Date: Tuesday March 30, 2004
Time: 12:00-13:00
Abstract:
I follow up work of P. Pudlak and S Buss on feasibility of the disjunction
property in IPC trying to do without the cut elimination theorem.
My aim is to realize intuitionistically provable sequents by (in some
cases) poly-time computations that can be constructed from a given proof
in time polynomial in the size of this proof.
In my talk I will start with an easy fragment of IPC containing only
conjunction, disjunction, and negation and outline how this can work
admitting more complex implications.
Speaker: Albert Visser
Title: object-theory and meta-theory
or
Title: direct interpretations and discrete fibrations
Place: University of Utrecht, Uithof, Bestuursgebouw 038
Date: Tuesday April 6, 2004
Time: 12:00-13:00
At least one of the topics will be discussed.
From April 13 on, we will have our meetings, unless mentioned otherwise,
in room 195.
Speaker: No one yet
Title:
Place:
Date: Tuesday April 6, 2004
Time: 12:00-13:00
(...)
Speaker: Vincent van Oostrom
Title: reduction- vs stack-based read-back
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday April 20, 2004
Time: 12:00-13:00
Abstract:
The read-back problem is the problem to read back a term from a graph,
in a graph implementation of term rewriting.
The problem is easy to solve in the first-order case, but hard in the
higher-order case.
We present a simple reduction-based solution for the higher-order
read-back problem.
Although this yields a very simple implementation, the correctness
proof of the algorithm is not easy; it is based on a complex stack-based
solution to the read-back problem.
We present both read-back procedures and relate them.
Speaker: Herman Hendriks
Title: Indirect Speech Acts, Politeness, and the Civilizing Process, part 2
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday April 26, 2004
Time: 12:00-13:00
I will argue that Levinson's (1983) conversation analysis
of linguistic indirectness is superior to an account in
terms of speech act theory along the lines of Searle (1979b),
especially in view of the way in which it relies on
Brown and Levinson's (1987) theory of politeness as an
explanatory mechanism. In a critical examination of their
own work, Brown and Levinson conclude that their analysis of
politeness suffers from an "overdose of cognitivism", as a
result of which it is not able to account for the fact that
social interaction has its own emergent properties which
transcend the characteristics of the individuals that jointly
produce it. Most notably, the phenomenon of politeness is
linked up with the concept of aggression, and, among other
notions that are central to the nature of the social persona,
with the concept of embarrassment. The tenet of the present
paper is that this emergent character of social interaction
can be accounted for if the study of its internal systematics
is supplemented with the theory of the development of social
structure that has been proposed within the framework of the
historical sociology of Elias (1993).
Speaker: Menno Lievers
Title: Last Minute Talk
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday May 4, 2004
Time: 12:00-13:00
Speaker: Menno Lievers
Title: The justification of the generality constraint
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday May 10, 2004
Time: 12:00-13:00
Tuesday May 18
Speaker: Joost J. Joosten
Title: Models for GLP; Counting up to ε0
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday , 2004
Time: 12:00-13:00
Abstract:
In this talk I will present some "results/insights" obtained during my
stay at Steklov institute. The work is not yet finished and many statements still are
in need of rigorous proofs. The presented work is
in colaboration with Lev D. Beklemishev.
It is difficult to provide GLP with a natural Kripke semantics, yet GlP is a very
natural and useful logic. It contains a hierarchy of strength-increasing
proof predicates. The logic has proven a fruitful tool in the study of
natural ordinal notation systems and in providing independent combinatorial
principles. Some tricks have been developed to surmount the impossibility of
a natural Kripke semantics for GLP. We shall present a semantics invented by
Ignatiev for the closed fragment and pronounce a hope that, by restricting the
possible valuations, this universal model can also be used to give GLP semantics.
The model turns out to be deep, rather deep. Actually very deep,
namely ε0-deep. However, we would like to have properties of the model
provable inside theories that can not see the well foundedness of orderings
ε0.
This calls for finite approximations using a Norm-function on ordinals.
Speaker: Joost J. Joosten
Title: Models for GLP; Counting up to є0, part 2: almost there
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday , 2004
Time: 12:30-13:30
Abstract: unchanged.
Speaker: Marta Bilkova
Title: A proof-theoretic proof of uniform interpolation of the modal
logic K
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday , 2004
Time: 12:00-13:00
Abstract:
I'm going to present a proof theoretic proof of uniform interpolation for the modal
propositional logic K based on Pitts' proof for intuitionistic
propositional logic. The proof uses a simulation of
quantifiers over propositional variables and a terminating sequent
calculus for which structural rules are admissible.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 8 juni
Tijd: 12:00-13:00
Titel: FD a la Mellies
Spreker: Vincent van Oostrom
For a given term t, a development of a set of redexes T in t
is a sequence of reduction steps from t in which only residuals
of redexes in T may be contracted (so no created redexes).
The Finite Developments Theorem (FD) expresses that all
developments are finite. Intuitively this holds because
only existing redexes may be contracted and since
we only start with a finite supply (T) of them, we will
eventually run out of redexes to contract.
A complication is that (residuals of) redexes may replicate one another.
Mellies has introduced some abstract conditions guaranteeing
that replication does not get out of hand, of which we present
a version in the concrete setting of second-order rewriting.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 15 juni
Tijd: 12:00-13:00
Titel: Towards a Game-theoretical Notion of Consequence
Spreker: Paul Harrenstein
Von Neumann and Morgenstern presented game-theory as a branch of
mathematics that deals with problems that had nowhere been dealt with
before. From a mathematical point of view, the participants in a
situation of conflict can be seen as each trying to maximize the same
function (the outcome of the game) according to an idiosyncratic
principle (their preferences).
Moreover, none of the players have control over all variables of the
function. The also argued that the usual notion of optimality is no
longer available and new solution concepts had to be developed to
take its place. Most notably among these game-theoretical solution
concepts is still that of a Nash-equilibirum.
Logical notions of consequence have frequently been related to
game-theoretical solution concepts. The correspondence between a
formula being classically valid and the existence of a winning
strategy for a player in a related two-person game, has been most
prominent in this context. We propose a conservative extension of the
classical notion of consequence for propositional logic based on a
generalization of
Nash-equilibrium.
We construe propositional variables as decision variables that are
possibly in the control of various agents and pursue the logical
consequences of this idea. The game-theoretical concept of
consequence that results opens up a line of theoretical research
in which logic, game theory and social choice theory interact at
the same level.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 22 juni
Tijd: 12:00-13:00
Titel: Measuring Theories
Spreker: Albert Visser
One way of comparing objects is by assigning simpler objects to the
given objects. The simple objects will be comparable in some familiar way.
The simpler objects may be real numbers, groups, ...
We compare theories by assigning certain extensions of a
weak theory to the given theories. The assigned theories are compared
via the subset ordering. Our way of proceeding is a modification of
the familiar notion of consistency strength. We will explain why
our notion is *extensional*, where consistency strength is
*intensional*.
It turns out that for a wide class of theories our notion coincides with
local interpretability.
Dinsdag
Plaats: Bestuursgebouw 195
Datum: Dinsdag 29 juni
Tijd: 12:00-13:00
Titel: Recursive sets and N-labelled graphs
Spreker: Jaap van Oosten
Abstract:
We shall present a combinatorial
problem concerning these things, and explain the
relevance of it.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 14 September
Tijd: 13:00-14:00
Titel: Two topics from my thesis
Spreker: Joost J. Joosten
Abstract:
This talk consists of two parts. In the first part we will study
Beklemishevs approach to natural ordinal notation systems. His approach is
based on graded provability algebras and makes extensively use of closed
modal formulae. We shall focus on the universal model of the closed
fragment of GLP; a modal semantics of depth $\epsilon_0$.
The second part of the talk is devoted to relativized interpretability as a
tool for proof-strength comparison. Our main interest will be in the
calculation of interpretability logics.
In rough lines, I will present this talk on Saturday September 18
in Heidelberg:
http://math.uni-heidelberg.de/logic/CL_2004/
Plaats: Bestuursgebouw 195
Datum: Dinsdag 19 october
Tijd: 12:00-13:00
Titel: Realizability and Propositional Logic
Spreker: Albert Visser
This talk is a report on the project "Realizability and Propositional Logic" of
Jaap van Oosten, Rosalie Iemhoff & Albert Visser. Kleene Realizability is one of the
possible `metamathematifications' of the Brouwer-Heyting-Kolmogorov Explanation
of the logical connectives. In spirit it is closely connected to the tenets of the Markov
school: ( All Mathematical Objects are Finite ) & ( Effective = Turing
Computable ).
The question adressed in the project, is the simpe question:
What is the propositional logic of realizability?
Most of the talk will be devoted to getting the various possible
explications of the question on the board.
We will present some of the more startling results of the field concerning the
explosive marriage of Church's Thesis (CT) and Markov's Principle (MP), to wit:
1) the predicate logic of suitable theories containing (CT+MP) is complete \Pi^0_2;
2) the propositional logic of suitable theories containing (CT+MP) is more than
Intuitionisitic Propositional Logic (IPC)
Plaats: Bestuursgebouw 195
Datum: Dinsdag 26 october
Tijd: 12:00-13:00
Titel: Menno over Lyn Rudder Baker
Spreker: Menno Lievers
Abstract:
Lynne Rudder Baker betoogt in haar artikel "Persons and Other Things" dat er
geen essentieel onderscheid is tussen artefacten, zoals koffiekopjes en
stoelen, en substanties, zoals koeien en bloemen. In beide soorten van
objecten speelt volgens haar constitutie eenzelfde rol. Dit geldt ook voor
mensen, maar in dat geval dient de notie van constitutie ook om een cruciaal
onderscheid te maken tussen personen en hun lichaam. Mijn kritiek is
tweeledig: ten eerste dat er wel degelijk een essentieel onderscheid bestaat
tussen artefacten en substanties; ten tweede dat er geen essentieel
onderscheid bestaat tussen personen en hun lichaam.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 2 november
Tijd: 12:00-13:00
Titel: An informal introduction to Logic in Law
Spreker:Lev Beklemishev
An informal introduction to Logic in Law
Speaker: Henry Prakken
Title: Logic and dialogue in legal reasoning: an inevitable intertwining
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday , 2004
Time: 12:00-13:00
Legal Reasoning is inherently defeasible, and it often takes place in an adversarial setting. I will argue
that these two aspects of legal reasoning are inevitably intertwined, so that logical accounts of legal
reasoning cannot separate inferential from dialogical aspects.
Speaker: Andrey Bovykin
Title: Independent arithmetical statements: present and future
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday November 16, 2004
Time: 12:00-12:30
Speaker: Lorenzo Carlucci
Title: U-shaped learning may be necessary
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday November 16, 2004
Time: 12:30-13:00
Abstract
Lorenzo Carlucci (University of Siena, University of Delaware)
Abstract Andrey Bovykin (St.Petersburg Department of Steklov Mathematical Institute, and The University of Liverpool):
This is a "popular mathematics" talk that will
introduce independence results to a general audience
(and remind logicians of what they may already know).
I shall sketch a very simple proof of unprovability of
an adapted version of the Paris-Harrington Principle,
quote some new developments and give a glimpse of the near future of
the subject as I see it: what we are now able to do
and what we should try to accomplish.
Plaats: Bestuursgebouw 048
Datum: Dinsdag 23 november
Tijd: 13:00-14:00
Titel: Wijsgerige Ethiek
Spreker: Marcus Duewell
Dit is de eerste aflevering in de serie F-lunches.
Doel: kennis nemen van de inhoud van vakken uit het eerste jaar van de studie
wijsbegeerte en suggesties bespreken over meer onderlinge verwijzingen en
coherentie in het onderwijsaanbod.
Vorm: +-45 minuten, een spreker, de toehoorders gebruiken de lunch, dit eens
per maand.
Plaats: Bestuursgebouw 195
Datum: Dinsdag 7 December
Tijd: 12:00-13:00
Titel: Qualia overboord? Een analyse van het qualiabegrip in Dennett's "Quining
Qualia.".
Spreker: Janne Willems
In zijn artikel "Quining Qualia" uit 1990 betoogt Dennett dat 'qualia' een
ondefinieerbaar begrip is en dat het niets toevoegt aan bewuste ervaring.
Dit begrip kan daarom het beste verdwijnen. In mijn lezing zal ik ingaan
op manier waarop Dennett het begrip 'Qualia' in dit artikel hanteert. Ik
beargumenteer dat Dennett verstrikt lijkt te raken in zijn eigen gebruik
van het begrip 'qualia'. Zo schrijft hij eigenschappen aan het begrip
'qualia' toe die hij volgens zijn definitie niet aan dit concept mag
toekennen en gebruikt hij in zijn argumentatie twee definities van het
begrip 'qualia', waar hij zegt dat hij er een gebruikt.
Speaker: Michael Moortgat
Title: Arrow reversal in categorial grammar
Place: University of Utrecht, Uithof, Bestuursgebouw 195
Date: Tuesday December 14, 2004
Time: 12:00-13:00
Abstract:
The aim of categorial grammar is to identify the invariant
principles that govern the correspondence between form and
meaning, and to obtain language diversity throught the
interaction of these invariants with a restricted set of
non-logical axioms, or structural postulates.
Since the introduction of the framework in 1958, invariants
have been discussed in terms of residuated families of
logical constants/type-forming operations. This restriction
of the logical vocabulary makes that core phenomena of
natural language syntax and semantics require the introduction
of non-logical axioms--clearly an undesirable situation.
We show that by broadening the vocabulary, we can bring
such phenomena within the reach of the invariant core logic.
We illustrate with scope construal of generalized quantifiers
and related phenomena, which we analyse in terms of
*dual* residuated families (cotensor, co-implications).
Plaats: Bestuursgebouw 195
Datum: Dinsdag 21 december
Tijd: 12:00-13:00
Titel: Geschiedenis I
Spreker: Teun Tieleman
Aflevering twee van de F-lunch.
Het is de bedoeling om zelf lunch mee te brengen.
Indien mogelijk zullen we de bijeenkomst in BG 048 houden. In dit geval
zal ik dinsdag ochtend nog een mailtje sturen.
There exists a mailing list for the lunch meetings. If you are interested in signing up,
or if you have any suggestions or comments, please contact me.
Vincent van Oostrom
Last modified: Wed Apr 26 15:18:06 MET DST 2006