  Extending the popular Answer Set Programming (ASP) paradigm by introspective
reasoning capacities has received increasing interest within the last years.
Particular attention is given to the formalism of epistemic logic programs
(ELPs) where standard rules are equipped with modal operators which allow to
express conditions on literals for being known or possible, i.e., contained in
all or some answer sets, respectively. ELPs thus deliver multiple collections
of answer sets, known as world views. Employing ELPs for reasoning problems so
far has mainly been restricted to standard decision problems (complexity
analysis) and enumeration (development of systems) of world views. In this
paper, we take a next step and contribute to epistemic logic programming in two
ways: First, we establish quantitative reasoning for ELPs, where the acceptance
of a certain set of literals depends on the number (proportion) of world views
that are compatible with the set. Second, we present a novel system that is
capable of efficiently solving the underlying counting problems required to
answer such quantitative reasoning problems. Our system exploits the
graph-based measure treewidth and works by iteratively finding and refining
(graph) abstractions of an ELP program. On top of these abstractions, we apply
dynamic programming that is combined with utilizing existing search-based
solvers like (e)clingo for hard combinatorial subproblems that appear during
solving. It turns out that our approach is competitive with existing systems
that were introduced recently. This work is under consideration for acceptance
in TPLP.
