Catarina Dutilh-Novaes , VU Amsterdam
Eberhard Guhe , Harvard-Yenching Institute/Fudan University
The thesis that logic and metaphysics are entangled is cashed out as: logic and metaphysics have to be developed simultaneously -- to develop logic one needs to develop metaphysics and to develop metaphysics one needs to develop logic. In particular, to develop logic, one needs logical and abstract objects of some sort: sentence and symbol types (not tokens), truth-values, possible worlds, properties or the extensions of properties, natural numbers (as conceived by Frege), etc. I try to show that one must simultaneously develop a theory of these metaphysical objects while one is formulating the foundations of logic.
Edward Zalta , Stanford
Elaine Pimentel , Universidade Federal do Rio Grande do Norte
Frank Sautter , Universidade Federal de Santa Maria
Often referred to as 'the mathematics of dynamical, state-based systems', coalgebra claims to provide a compositional and uniform framework to specify, analyse and reason about state and behaviour in computing. This lecture addresses this claim by discussing why Coalgebra matters for the design of models and logics for computational phenomena. To a great extent, in this domain one in interested in properties that are preserved along the system's evolution, the so-called `business rules', as well as in `future warranties', stating that e.g. some desirable outcome will be eventually produced. Both classes are examples of modal assertions, i.e. properties that are to be interpreted across a transition system capturing the system's dynamics. The relevance of modal reasoning in computing is witnessed by the fact that most university syllabi in the area include some incursion into modal logic, in particular in its temporal variants. The novelty is that, as it happens with the notions of transition, behaviour, or observational equivalence, modalities in Coalgebra acquire a shape . That is, they become parametric on whatever type of behaviour, and corresponding coinduction scheme, seems appropriate for addressing the problem at hand.
In this context, the lecture revisits Coalgebra from a computational perspective, focussing on models, their composition and behavioural properties.An effort will be made to help building up the right intuitions, often at the expense of a completely self-contained exposition.
Luis Soares Barbosa , Universidade do Minho
In recent years, many dynamic logics have been proposed in fields like Computer Science, Phylosophy, Physics and Formal Biology. In this talk, we discuss three broad categories where dynamic logics have been developed: dynamic logics for program/process specification, dynamic Logics for reasoning about actions in AI, multi-agent epistemic logic and dynamic epistemic logics. First, we present some standard extension of Propositional Dynamic Logic. Second, we introduce a Dynamic Logic in which the programs are terms in some process algebras: CCS (Calculus for Communicating Systems) and pi-Calculus specifications. We discuss how to match the notion of bisimulation between two processes in CCS with the notion of logically equivalent processes in PDL. Finally, we briefly discuss other possibilities to extend PDL, for instance adding data structure, with Petri nets and with fuzzy programs.
Mario Benevides , Universidade Federal do Rio de Janeiro
There are many reasons to study logic, but the one which we shall discuss in this talk is the use of logic to model thought processes in mathematics and to obtain new theorems as a consequence. One of the most beautiful instances of this is the first order logic which can be used to prove and unify many theorems in mathematics. For example, the compactness of first order logic has numerous applications, from Ramsey’s theorem on. Yet, there are many mathematical processes which first order logic is not sufficient to express, for example even the notion of convergence of real sequences needs an infinite conjunction to be expressed in logical terms. Therefore one needs to study the so called strong logics, with more expressive power. Gaining in expressibility often means losing the pleasing properties that we are used to have in the first order case, such as compactness. Yet, surprisingly, there are certain very strong compactness results happening at unexpectedly high cardinals: singular cardinals, the smallest of which is aleph_omega. We try to explain this phenomenon in terms of strong logics.
Mirna Dzamonja , University of East Anglia