Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.

This paper proposes a feasible variation of approximate grid-based path-planning methods, which have been replaced with probabilistic methods nowadays, due mainly to their impracticality in high-dimensional spaces. Our aim is to demonstrate that, with an incremental exploration of the CSpace by means of Interpolated walk primitives and ANY-Time algorithms, we can generate – online – high-quality solutions that can be compared with probabilistic methods and can even improve some aspects, such as the completeness. Computational time, path smoothness, path clearance, and path distance are the qualifiers used to evaluate the path planner. These quality factors are critical in robotics. In fact, in both mobile and industrial robots, the computational time is a primary requirement to work online, the clearance gives security to the movements of the robot, and the smoothness can prolong the life of the mechanical components. Our method has been compared to probabilistic path planners, with the feasibility and benefits of our algorithm being proved in terms of the quality factors aforementioned.