Nested Aggregates in Answer Sets: An Application to a Priori Optimization

TL;DR

This paper extends answer set programming to handle nested multiple aggregates over multiple variables, enabling advanced reasoning and optimization in complex problems like the Probabilistic Traveling Salesman Problem.

Contribution

It introduces a formal framework for nested aggregates in answer set programming and demonstrates its application to a complex optimization problem.

Findings

Successfully modeled the Probabilistic Traveling Salesman Problem using nested aggregates.

Showed the applicability of the extended answer set programming to real-world optimization tasks.

Enhanced reasoning capabilities in answer set programming with nested aggregates.

Abstract

We allow representing and reasoning in the presence of nested multiple aggregates over multiple variables and nested multiple aggregates over functions involving multiple variables in answer sets, precisely, in answer set optimization programming and in answer set programming. We show the applicability of the answer set optimization programming with nested multiple aggregates and the answer set programming with nested multiple aggregates to the Probabilistic Traveling Salesman Problem, a fundamental a priori optimization problem in Operation Research.