  UDIL (unified descriptive intensional logic) aims to be an alternative and
improved version of Bealer's logic fulfilling the goal of unifying Bealer's
systems T1 and T2 together with adding features to deal with definite
descriptions and singular terms and their related philosophical problems (there
are interesting connections to Zalta's more restricted parallel second-order
version in his book \emph{Axiomatic Metaphysics}). UDIL also allows a much
shorter and transparent proof of soundness, in particular with regards to a
notoriously difficult preliminary lemma. UDIL stands out as being both formally
and philosophically distinct from mainstream approaches to intensionality. One
motivation for UDIL is to contribute to the Leibnizean goal of a formal
philosophy, that is, a philosophy in which arguments and proofs are carried out
entirely within a formal system.

Logic