Extending the popular answer set programming 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, that is, 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.

Answer-Set Programming (ASP) has seen tremendous progress over the last two decades and is nowadays successfully applied in many real-world domains. However, for certain types of problems, the well-known ASP grounding bottleneck still causes severe problems. This becomes virulent when grounding of rules, where the variables have to be replaced by constants, leads to a ground pro- gram that is too huge to be processed by the ASP solver. In this work, we tackle this problem by a novel method that decouples non-ground atoms in rules in order to delegate the evaluation of rule bodies to the solving process. Our procedure translates a non-ground normal program into a ground disjunctive program that is exponential only in the maximum predicate arity, and thus polynomial if this arity is assumed to be bounded by a constant. We demonstrate the feasibility of this new method experimentally by comparing it to standard ASP technology in terms of grounding size, grounding time and total runtime.

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 deci- sion problems (complexity analysis) and enumeration (development of systems) of world views. In this paper, we first 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 capable of efficiently solving the underlying counting problems required for quantitative reasoning. Our system exploits the graph-based measure treewidth by iteratively finding (graph) abstractions of ELPs.

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