There are crying needs for a new semantics which extends the
methodology of denotational semantics and domain theory to the
challenges in analyzing computation today. If semantics is to
encompass operational concerns adequately it has to be an {\em
intensional} theory, capturing the {\em ways} in which computation
proceeds and not merely input and output. The evidence for this comes
from: sequential programming, where \eg~game semantics informs
operational semantics; interactive/distributed computation, where
\eg~analysis of security protocols often relies on clever encryption
to ensure desired event dependencies; from anomalies, as in
nondeterministic dataflow, where intensionality is forced in order to
achieve a compositional semantics. This intensionality would
immediately set the next generation of semantics apart from
traditional domain theory and denotational semantics. Once achieved it
would make the current distinctions between operational and
denotational semantics disappear; a denotation would carry its
operational semantics. But what form should the next generation of
semantics take? This talk will outline beginning ideas and an ERC
research programme to find out.