Mathematical Fuzzy Logic in the foundations of uncertain reasoning

``Fuzzy methods'' are currently ubiquitous in many economic applications,
especially to business and marketing. In philosophy ``fuzzy logic'' has
long been discussed in connection with vagueness and its linguistic
consequences. Both areas have played an important role and ultimately
brought about a number of contributions envisaged by the early works in
``fuzzy sets''.

Over the past two decades, much work has been done to connect the early
contributions to the wider logical landscape, resulting in what has been
eventually termed Mathematical Fuzzy Logic. As a branch of mathematical
logic, MFL developed its own tools and methods which partly advanced
our understanding of many-valued logics, and partly lead to new logical
systems.

I will begin by pointing out two examples of how MFL helps us framing
the discussion on central concepts in philosophy, (graded truth) and
decision theory (convexity). Building on those, I will then suggest
that a number of foundational problems in the social sciences lend
themselves to being tackled from the MFL perspective (rather from the
``fuzzy methods'' perspectives.) The question then becomes: How does
MFL helps us rethink the foundations of reasoning and decision-making
under uncertainty?