Spring Semester
These are the pages of the Logic Seminar at the Università degli Studi di Milano and the Università degli Studi dell'Insubria.
The Logic Seminar
Welcome to the web pages of the Logic Seminar at the Università degli Studi di Milano and the Università degli Studi dell'Insubria.
The Seminar usually meets every other week during both the autumn and the spring semester, currently on Mondays. The exact date, time, and place of each meeting are annonunced on these pages.
There are two types of talks at the Seminar. First, we invite visiting researchers, colleagues, or graduate students to give talks on their own research activity. Second, during each semester we run a proper seminar on a given subject that is of interest to a group of participants. Usually, the participants are not experts on that subject, but wish to learn more about it. The participants then take turns in preparing one- or two-hour talks on a specific topic within the chosen subject. The subject we have chosen for the Spring Semester 2008-2009 is Topos Theory. The same series will also be ongoing during the Autumn and Spring Semesters 2009-2010.
Next Talk
15 May 2012, 11.00, Dipartimenti DSI/DiCo, sala riunioni (primo piano)
Dr. Achille Frigeri,
Dipartimento di Matematica "Francesco Brioschi",
Politecnico di Milano,
Time modalities over many-valued logics
In the last two decades, many attempts to "fuzzify" temporal logics have been proposed. The existing approaches are based on the
idea of replacing classical connectives or propositions with their fuzzy
counterparts. However, none of them have tried to fuzzify the temporal
modalities and the semantics of temporal operators is still crisp. For example, the semantics of temporal modality "always" is in general defined
as the fuzzy conjunction of all the evaluations of its argument at each
time instant. However, a single violation of its argument makes the evaluation of the whole formula false, exactly as for the classical semantics
of "always" in LTL. The need to deeply fuzzify temporal operators is being pushed by the increasing importance of adaptive systems and smart
appliances. As a matter of facts, these systems may need to tolerate
small violations or be aware of the satisfaction degree of their requirements for assessing their performance or for re-configuration purposes.
In these cases the possibility of expressing fuzziness on time in temporal
modalities becomes crucial. To this aim, we propose FTL (Fuzzy-time
Temporal Logic), a temporal framework to express vagueness on time,
by starting either from propositional logic or fuzzy logic. It extends the
classical fuzzy version of LTL, by adding temporal modalities that allow
the designers to express properties such as "almost always" and "soon".
In this paper we formally describe this framework, by discussing some
of the possible different languages that can be derived from it and their
relationship with other languages, such as LTL and its fuzzy version.
(joint work with Liliana Pasquale and Paola Spoletini)