  Search-optimization problems are plentiful in scientific and engineering
domains. Artificial intelligence has long contributed to the development of
search algorithms and declarative programming languages geared towards solving
and modeling search-optimization problems. Automated reasoning and knowledge
representation are the subfields of AI that are particularly vested in these
developments. Many popular automated reasoning paradigms provide users with
languages supporting optimization statements. Recall integer linear
programming, MaxSAT, optimization satisfiability modulo theory, and
(constraint) answer set programming. These paradigms vary significantly in
their languages in ways they express quality conditions on computed solutions.
Here we propose a unifying framework of so called extended weight systems that
eliminates syntactic distinctions between paradigms. They allow us to see
essential similarities and differences between optimization statements provided
by distinct automated reasoning languages. We also study formal properties of
the proposed systems that immediately translate into formal properties of
paradigms that can be captured within our framework. Under consideration in
Theory and Practice of Logic Programming (TPLP).
