INRIA Nancy Grand Est
We can fairly say that Logic (whichever you want to chose, be it
propositional or first order, classical or non-classical) is the
mathematical tool used, par excellence, to describe a structure.
Modal logics, for example, are particularly well suited to describe
relational structures, specially if you are interested in a
computationally well behaved formalisms (e.g., to use in formal
verification). But why can a logic only *describe* a structure? In
this talk I will introduce a family of modal logics that contain
operators that can both describe and *change* the structure. I will
present some results characterizing their complexity and expressive
power and discuss some open problems.
Logics to Describe and Change
FaMAF, Universidad Nacional de Córdoba
We define and study abstract valuation semantics for logics. In the context of the behavioral approach to the algebraization of logics (which we briefly overview), we show, by means of meaningful bridge theorems and application examples, that this algebraically well-behaved version of valuation semantics is suited to play a role similar to the one traditionally played by logical matrices. Joint work with Ricardo Gonçalves.
Our goal is to prove mathematically that Darwinian evolution works by studying what
physicists call a toy model, one that is much simpler than the real thing, but
that hopefully preserves the essential features.
DNA is digital software, so we study the evolution of randomly mutating software,
a hill-climbing random walk in software space.
This approach is starting to yield mathematical results, which we shall outline.
In particular, Gödel incompleteness is used to show that evolution is unending.
For more information, see http://www.cs.umaine.edu/~chaitin/sfi.html
Live as Evolving Software
IBM T. J. Watson Research Center, New York
The basic theories in physics, such as classical mechanics, special and general relativity, non-relativistic quantum mechanics, quantum field theory, and loop gravitation, treat space and time in different ways, and in some cases these are incompatible with one another. Therefore, among other reasons, the logic which is subjacent to physics, in the way that it is effectively developed, seems to be paraconsistent, even though it might be possible, in the future, to develop a unifying theory, as it was believed would happen in the future, with the advent of string theory. The required paraconsistent logic is the one which is called locally classical paraclassical logic. However, as non-classical logics are already being used in the field of physics, perhaps in the future the logic of physics will end up converting itself into a locally non-classical paraconsistent logic.
I will introduce various logics for change of knowledge and belief, that have become known under the name 'Dynamic Epistemic Logic'. The basic logic of public announcements, proposed by Jan Plaza in 1989, serves to formalize logic puzzles such as 'muddy children', and 'consecutive numbers'. But much more is possible in this setting, and there are generalizations to private actions, combining information change with factual change, and so on. I will point out some relations with AGM belief revision, with Moore-sentences (p is true and you don't know that p) and with knowability (is everything knowable? no!). The topic remains much in the limelight, latest developments are about protocols, and quantifying over information change, and protocol synthesis/planning. I will give a sprinkling of such topics as well.
Richard L. Epstein
Advanced Reasoning Forum
Modern formal logic is based on the assumption that the world is made up of things and propositions are about the relations or properties of things. Starting with some hints in our ordinary language, I will show how we can devise a formal logic to reason instead about the world as process-mass. Clarifying that view with a formal language and logic raises questions about how grammar shapes our perceptions of the world and our morality.
Normative conflicts are situations in which an agent ought to do each of several things but cannot do them all. They seem an all too frequent part of anyone's life. Yet standard deontic logic declares them to be logically impossible. Hence we look to adapt the standard principles to develop a logic of normative concepts that can accommodate such conflicts. Here I present the problems posed by normative conflicts, and how difficult they seem to be. Then I introduce some promising new results that apply the framework of Adaptive Logic to these problems. I will close, however, with a critical look at those results, and question how adequate they really are. This will point to some broader, more philosophical questions about what one expects of systems of philosophical logic, and especially systems for nonmonotonic or defeasible reasoning.
Deontic Logic (Adapted) for Normative Conflicts
Department of Philosophy, Willamette University
The astoundingly fast development of Ramsey theory has uncovered its deep connections with several other areas of mathematics such as logic, set theory, topological dynamics, functional analysis and, of course, combinatorial theory. We will survey some aspects of the theory, from its origins to some recent advancements and open questions.
In recent years there has been considerable activity in generalizing
to continuous settings techniques from logic (set theory and model
theory) that were initially devised for discrete settings. Several
model-theoretic frameworks have been proposed, independently, as
formalisms for continuous logic (Chang-Keisler, Henson, Ben Yaacov
and Usvyatsov); however, these have turned out to be equivalent.
I will state a maximality theorem that, among other things,
characterizes these logics and explains why the equivalence that
has been observed so far is not a mere coincidence.
Our result covers not only to the already proposed formalisms,
but a wide range of logics, namely, logics for which certain
topologies are regular.
The results that I will present have been obtained jointly with Xavier Caicedo and Jonathan Brucks.
The Brazilian Embassies and Consulates abroad maintain updated web sites, that provide information about visas and entry requirements, such as immunizations, depending on where you are coming from, as well as other practical information and health tips. Please take some time to review the entry requirements to avoid unpleasant surprises.