Colloque Franco-Russe « La Logique et ses applications », Institut de Mathématiques de Toulouse, 5-6 avril 2012



Lieu du colloque : Université Paul Sabatier, Institut de Mathématiques de Toulouse, salle de conférence, Bât 1R3, 1er étage.

Jeudi 5 avril, après-midi, session « Histoire de la logique »

14h15-15h45 Yury Chernoskutov (Université de Saint-Pétersbourg), Object  theory: its development in Austrian logic and philosophy of 19th century.

The attempt to trace the role of the object theory in the formation of modern logic is made in the report. The course of the object theory development in the framework of Austrian tradition of logic and philosophy is described, starting from its founder B.Bolzano. Implicit influence of Austrian objectual way of thinking via Brentano`s school on G.Frege (B.Kerry and K.Stumpf) and on B.Russell (A.Meinong) is enlighted. The connection of the object theory with the growth of non-classical applied logics is sketched.

16h-17h30 Olga Antonova (Saint-Pétersbourg, docteur en philosophie), Dedekind’s theory and development of logicism.

The fact that Dedekind’s conception of arithmetic influenced very much the development of mathematics in XX century is incontestable. Meanwhile nowadays there are many discussions about logical character of Dedekind’s conception of mathematics and in particular the relations between logicism in the sense of Frege and Dedekind’s mathematical theory. Can we say that Dedekind’s theory is a variant of traditional logicism? Is Dedekind logicist in the same sense as Frege? The aim of this talk is to examine logical aspects of Dedekind’s mathematical conception and analyze these aspects from the point of view of traditional logicism such as Frege’s theory. The study of the question about Dedekind’s logicism leads us to new comprehension of the rapport between set theory and symbolic logic in XIX- XX century. This problem is still unresolved and relevant to contemporary mathematics and logic.

Vendredi 6 avril, matin, session « Interaction de la logique avec un domaine formel »

9h30-11h Brice Halimi (Univ. Paris 10, SPHERE), Geometric Modal Logic.

Alethic modalities pertain to truths as being not only factual. The question as to whether a given proposition is possibly true is not answered by the fact that it is false (if it is false). The question as to whether a given proposition is necessarily true is not answered by the fact that it is true (if it is true). Modal questions, by their very nature, go beyond facts. Accordingly, modal logic should not be a factual science. Still, the range of what is possible (the content of the collection of all possible worlds, in modern modal semantics) is referred to as a kind of super-fact.

Modal logic should go beyond it: what the actual range of the possible turns out to be should be understood as a range among others. So apparently we are thrown back upon a new fact in the end, namely the range of all ranges for the possible. This is not so: the actual range of all possible ranges for the possible should itself be conceived of as a second-order range among others, within a third-order modal range.

In fact, it should not, but it may be conceived of in that way: everything depends on the level of modal iteration we are interested in. If we want to know whether a given proposition is possibly true (or necessarily true), we can be content with considering the actual range of all actual possible worlds. If we want to know whether the same proposition, supposed not to be possibly true, could have been possibly true, we should go beyond and consider the range of all possible first-order ranges of possible worlds. And so on and so forth.

I will argue that this intuition is at the core of modal reasoning and that the usual semantics for modal logic does not genuinely implement it. I will then suggest and set out an alternative semantical framework that interprets iterated modalities in a better way. In that framework, possible worlds of variable levels are introduced; for each modal iteration, a set of possible worlds is considered relatively to each already given possible world (the latter being thought of as the index of a modal level in discourse). The model of that picture will be the tangent space to a manifold, as devised in differential geometry.

11h15-12h45 Philippe Balbiani (CNRS, IRIT), Region-based theories of spaces

We will present formal languages interpreted over classes of structures featuring regions and relations between them. These languages stem from Whitehead’s system in which the “being in contact” relation was assumed as primitive and Grzegorczyk’s system in which the “being included” and “being separated” relations were assumed as primitives. We will provide a context for studying the confluence of four research areas: first-order mereotopologies, algebras of regions, region-based propositional modal logics of space and qualitative spatial reasoning.

Vendredi 6 avril, après-midi, session « Application de la logique à un domaine non formel »

14h15-15h45 Elena Lisanyuk (Université de Saint-Pétersbourg), How we do logic of norms in Russia: from 1958 up to now.

In my paper I am intended to suggest an overview of the development of logic of norms in Russia from three perspectives: theoretical, historical and sometimes from that of sociology of science. Projects dealing with inferential and semantic aspects of norms form the logical group which is the largest and is most respected in the Russian deontic horizon. Computation and normative reasoning make another research trend which focuses upon creating logical frameworks for legal data-bases and particular applications based on fuzzy and dynamic logic. Yet another direction is normative aspects in philosophy of law and ethics especially in what concerns the normative use of language in its analytical approach.

Deontic logic in the USSR and Russia enjoyed an exceptional fate. It started in the years of onrush of logic, flourished during the time of rapid development of its new branches (temporal, many-valued, action-oriented, non-monotonic, etc) and of yet newer semantic frameworks, survived in the considerable research decline in the years of reforms (1990-ies) and today went on creating various deontic applications in the field of philosophical logic, computer science and philosophy.

The beginning of deontic logic in Russia goes back to the year of 1958 when the first paper in Russian was published. Notwithstanding its rather young age, up to nowadays it has passed three periods:

(1) the rise and the first results (1958-1973), from the first paper to the first system;

(2) the systematic research and the foundation of a research community (1980-1990ies), from basic approaches to the development of non-standard systems (multi-modal (temporal), many-valued and dynamic);

(3) the development of non-monotonic and higher-order deontic systems and their legal applications (from 1990-ies up to the present day), from non-standard deontic systems to the their fuzzy applications in the legal data-bases.

16h-17h30 Yuri Nechitaylov (Saint-Petersburg State University), Epistemic Logic for bounded rationality.

A uniform semantic basis of the problem of logical omniscience is proposed. The basis stands on a comparison of Kripke semantics with complete and incomplete games. The ways to solve the problem by deviating the principle of compositionality of the possible worlds semantics is outlined. As a summary an Epistemic Logic for Bounded Rationality is sketched.

Organisation :

Olga Antonova (Saint-Pétersbourg, docteur en philosophie),

Brice Halimi (Univ. Paris 10, SPHERE),

Sébastien Maronne (Univ. Toulouse Paul Sabatier, IMT),

Avec le soutien de l’IMT, de la FREMIT et de l’IRIT.