Within the framework of a seminar on logic and computer science, the Centre for Logic and Philosophy of Science organizes a small workshop, under the name SLI-2003. The topic of this year's workshop will be devoted to the area of research involving logics dealing with "processes", "changes" or "interactions" in the fields of computer science and quantum physics. Indeed, changes of states and interactions between a particular system and its context or environment, is of crucial importance in both mentioned fields. As such we essentially present a program where the talks touch upon current research in : game semantics, dynamic logic, epistemic logic, game theory and quantum logic. Capturing the points of focus in several keywords, we surely have to mention "flow of information", "interaction", "(quantum) strategy", "(quantum) computation", "logic of knowledge".We are proud to announce the participation of three visitors from Oxford University. Samson Abramsky recently succeeded Tony Hoare as holder of the prestigious Christopher Strachey Chair of Computing at Oxford University. He is a world authority in theoretical computer science and logic. For example, he was the main developer of game semantics, he is the general chair of the international symposium series "Logic in Computer Science" and is the series editor of the Handbook of Logic in Computer Science. Alexandru Baltag who obtained his PhD from Indiana University under supervision of John Barwise, is a leading researcher in epistemic and game logic. Bob Coecke obtained his PhD at the VUB in theoretical physics, recently joined Comlab and is specialized in the area of quantum structures.

Due to the interdisciplinary nature, the workshop is intended to be of interest at least to philosophical and mathematical logicians, computer scientists as well as theoretical physicists.

PROGRAM - ABSTRACTS - LOCATION - ORGANIZATION

[back to top SLI-2003]

- "Games and Interaction in Logic and Computation"
- "Probabilistic Epistemic Updates"
- "Classical Arithmetic is Quite Unnatural"
- "Probability = Logic + Partiality + Entropy"
- "A brief introduction to quantum game theory"
- "Causal duality for processes as (co)tensors in a quantaloid enriched category"
- "On Quantum Modality"

Samson Abramsky (COMLAB,Oxford)

between a system and its environment* as basic. This idea of interaction

can be formalized using notions from two-person games. An area of

research on `Game Semantics' for both programming languages and logical

systems has developed significantly over the past decade. It has led to

`full completeness' theorems for a number of logical systems, which

delineate the `space of proofs' for that system; and to full abstraction

results for a range of programming languages embodying many significant

computational effects.

Current developments include an algorithmic turn, where the semantics is

captured by a machine representation as a basis for program analysis and

model-checking; and the exploration of connections with issues of

physical computation, notably reversible and quantum computation.

The talk will give an informal introduction and overview to this body of

research.

Alexandru Baltag (COMLAB,Oxford)

I give a general probabilistic modeling for "epistemic programs". These
are

programs for jointly updating every agent's state of knowledge
(or belief)

in a multi-agent system, in which the agent's uncertainty (about the
current

state of the world or about the current interaction he/she is engaged
in) is given

by a discrete probabilistic measure. Such programs are ways of computing
the

effect of (ex)changes of information ("communication", "observation")
between agents,

or between an agent and Nature. They can be intuitively understood
as programs for

"interactive learning", or more generally for inducing belief changes
in the participants.

I present my solution to the general problem of computing the
information-updating

effects of a specific communication act: an operation of
"Probabilistic-Epistemic
Product

Update", which generalizes Bayesian belief revision to the case of
many agents and of

uncertainty about announcements as well. (Both epistemic programs and
the product

update can be understood in terms of functors and natural transformations
on the category

of coalgebras for a specific functor.) I use these models to discuss
various properties of

dialogues (publicity, normalcy, responsiveness, truthfulness,
appropriateness
of questions),

but also interesting types of dialogues which break these assumptions
(rhetorical questions,

cheating and lying, impersonation, leading questions, Socratic dialogues).

I introduce a (qualitative, non-probabilistic) dynamic-epistemic logic
and a Hoare logic

(both decidable), to reason about epistemic programs, and in particular
to prove the

"partial correctness" of communication strategies with respect to given
epistemic goals

(and given epistemic presuppositions).

Jean Paul Van Bendegem (CLWF,VUB)

Based on the discussion concerning supertasks - basically, these

are tasks that consist of an infinite number of steps to be executed
in a

finite time and whereby the central question concerns the connection
between

the properties of the end-state and the properties of the preceeding
states

- I define a supertask such that (a) every step is a strictly finite

arithmetic possessing all "nice" properties one can imagine, and (b)
the

end-state is classical arithmetic where all the "nice" properties have

disappeared. In that sense classical arithmetic is not informative
about the

preceeding stages and can thus be called "unnatural". In short, this
paper

is a subtle way to defend strict finitism.

Bob Coecke (COMLAB,Oxford)

By introducing the notion of partiality in logic at an epistemic level

we can construct a space of probabilities. This gives chance a purely

qualitative status as compared to the quantative one in terms of

distributions -- which has dominated mathematics for a century.

In particular do we have:

Quantitative Probability = Qualitative probability + Shannon Entropy

where

Qualitative probability = Logic + Partiality on knowledge.

Actually, the above equations are understatements. We do not only

produce a space of probabilities, but one that goes equipped with

a partial order. We obtain a domain of probability measures!

This perspective is in perfect harmony with F.P. Ramsey's conception of

probability, Dana Scott's motivation underlying domain theory,

and the operational quantum logic schools. (the above indeed

holds as well for algebraic classical, intuitionistic as for

quantum logic, in that case resulting in quantum probability).

At a more advanced level, the above analysis reveals two distinct

epistemic ingredients in quantum theory.

Everything will be illustrated with beautiful pictures.

Haroun Amira (MAPO/CLEA,VUB)

In theories such as quantum computation, quantum information and quantum cryptography

the physical representation of information as a quantum system is more successful than

the classical situation. In his 1999 seminal paper [1]Meyer proposes a 'quantization' of

game theory where the classical strategies space is replaced by a quantum version, consisting

of unitary operations on a quantum state. Implementing a quantum strategy can lead to new

and improved results. The foundations of modern game theory were largely developed by

Von Neumann [2] in order to study rational decision making in conflict situations.

Von Neumann also played a role of paramount importance for the foundations of Quantum

Theory [3]. In that regard quantum game theory can be seen as a (late) unification of the basic

ideas in both fields. In this presentation we propose an introduction to the subject and provide

an overview of the recent developments.

[1] D.A. Meyer, Quantum Strategies, Phys. Rev. Lett. 82, 1052-1055, 1999.

[2] J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior,
Princeton

University Press, Princeton,
1944.

[3] G. Birkhoff and J. Von Neumann, The Logic of Quantum Mechanics, Annals
of Mathematics 37,

823-843, 1936.

Isar Stubbe (AGEL,UCL)

The principle of "causal duality" is all about cause and consequence for
processes.

In a setting where a system is described by an ordered set of properties

(usually a complete lattice in which infimum is conjunction), the principle
of

causal duality for a given process that such a system undergoes, is mathematically

encoded as an adjunction of order preserving maps. Organizing all processes
that a

given system may undergo in a quantale (or even quantaloid) allows to express

the principle of causal duality in a very precise way: as tensors and cotensors
in a

quantaloid enriched category whose objects are the properties of the system.

Sonja Smets (CLWF,VUB)

We put forward a characterization of quantum logic that supports our
pluralistic view on logic,

favouring a perspective that allows for the comparison of different
logical systems.

First we focus on the characterization of minimal quantum logic (i.e.
orthologic) in terms

of a modal logic or algebra with a unitary modal operator. That such
an approach is possible,

is supported by the research presented in [1]. We characterize
"modal quantum logic" as MQL

and analyse its place in the landscape of other non-classical logics.
In particular, MQL is related

to the so-called "propositional flat logic" which computer scientists
introduced in the context of

hardware verification and to the structure, which has been put forward
in the research on

mathematical modalities, known as a "local Algebra".

Second, we focus on the origin of the orthomodular law and explain
how this law exposes the

inherent dynamic nature of quantum logic (see [2]). We ask which
dynamic operators are needed to

extend MQL in order to express the orthomodular law itself.

[1] B. Coecke: "Quantum Logic in Intuitionistic Perspective", Studia
Logica, 70, 411-440, 2002.

[2] B. Coecke and S. Smets: "The Sasaki Hook is not a [Static] Implicative
Connective but Induces a

Backward [in Time] Dynamic One that
Assigns Causes", International Journal of

Theoretical Physics, to appear
(quant-ph/0111076)

LOCATION:

[back to top SLI-2003]Vrije Universiteit BrusselPleinlaan 21050 Brussel

Take a look at the campus-map:

The first session takes place in building D:

Building D is located next to building C where the library is.

Take the main entrance, go upstairs, Room 2.01 (also called "promotiezaal") is on the first floor, first door at the left.

The second session takes place in building M:

Building M is the main administration building on the VUB-campus (the only one with a half-round shape), Room M429 (also called "zaal De Brock") is at the end of the hallway on the 4th floor.

Reaching the VUBby car: look at the following area-map

There is parking space under building B and C where you automatically end up by taking campus interance-number 12 from the pleinlaan.Reaching the VUB by train: "Station Etterbeek" located on the Generaal Jaqueslaan, is just a 3 min. walk away

Reaching the VUB by metro: Metro station Petillion and Metro station Delta are a 15 min. walk away from the VUB-campus, look at the subway-map.

Reaching the VUB by bus/tram:

Tram 3: (to Churchill) exit 2nd stop Lansiers

Tram 90: (to Rogier) exit 2nd stop Lansiers

Bus 34: via Waverse Steenweg

Bus 71: (to Delta) exit Fraiteur

Bus 95 and 96: exit Kroonlaan - Gen. Jacqueslaan

ORGANIZATION:

**Centre for Logic and Philosophy of Science (CLWF),
Free University of Brussels**

**Local Organization, Contact person: Sonja Smets**

**With financial support from the National
Centre for Logical Investigation (CNRL/NCNL)**