The multi-agent path finding (MAPF) problem is a combinatorial search problem that aims at finding paths for multiple agents (e.g., robots) in an environment (e.g., an autonomous warehouse) such that no two agents collide with each other, and subject to some constraints on the lengths of paths. We consider a general version of MAPF, called mMAPF, that involves multi-modal transportation modes (e.g., due to velocity constraints) and consumption of different types of resources (e.g., batteries). The real-world applications of mMAPF require flexibility (e.g., solving variations of mMAPF) as well as explainability. Our earlier studies on mMAPF have focused on the former challenge of flexibility. In this study, we focus on the latter challenge of explainability, and introduce a method for generating explanations for queries regarding the feasibility and optimality of solutions, the nonexistence of solutions, and the observations about solutions. Our method is based on answer set programming.

In this paper we develop a concept aware multi-preferential semantics for dealing with typicality in description logics, where preferences are associated with concepts, starting from a collection of ranked TBoxes containing defeasible concept inclusions. Preferences are combined to define a preferential interpretation in which defeasible inclusions can be evaluated. The construction of the concept-aware multipreference semantics is related to Brewka’s framework for qualitative preferences. We exploit Answer Set Programming (in particular, asprin) to achieve defeasible reasoning under the multipreference approach for the lightweight description logic ξ$\mathcal L_ \bot ^ + $.

In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining a formal proof showing that the answer sets of a given (non-ground) logic program P correctly correspond to the solutions to the problem encoded by P, regardless of the problem instance. To this aim, we use a formal specification language based on ASP modules, so that each module can be proved to capture some informal aspect of the problem in an isolated way. This specification language relies on a novel definition of (possibly nested, first order) program modules that may incorporate local hidden atoms at different levels. Then, verifying the logic program P amounts to prove some kind of equivalence between P and its modular specification.

In sequent calculi, cut elimination is a property that guarantees that any provable formula can be proven analytically. For example, Gentzen’s classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. In this paper, we use coinductive Horn clause theories to show that cut is not eliminable in a coinductive extension of LJ, a system we call CLJ. We derive two further practical results from this study. We show that CoLP by Gupta et al. gives rise to cut-free proofs in CLJ with fixpoint terms, and we formulate and implement a novel method of coinductive theory exploration that provides several heuristics for discovery of cut formulae in CLJ.

For planning an assembly of a product from a given set of parts, robots necessitate certain cognitive skills: high-level planning is needed to decide the order of actuation actions, while geometric reasoning is needed to check the feasibility of these actions. For collaborative assembly tasks with humans, robots require further cognitive capabilities, such as commonsense reasoning, sensing, and communication skills, not only to cope with the uncertainty caused by incomplete knowledge about the humans’ behaviors but also to ensure safer collaborations. We propose a novel method for collaborative assembly planning under uncertainty, that utilizes hybrid conditional planning extended with commonsense reasoning and a rich set of communication actions for collaborative tasks. Our method is based on answer set programming. We show the applicability of our approach in a real-world assembly domain, where a bi-manual Baxter robot collaborates with a human teammate to assemble furniture.

We elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation.

Generalising and re-using knowledge learned while solving one problem instance has been neglected by state-of-the-art answer set solvers. We suggest a new approach that generalises learned nogoods for re-use to speed-up the solving of future problem instances. Our solution combines well-known ASP solving techniques with deductive logic-based machine learning. Solving performance can be improved by adding learned non-ground constraints to the original program. We demonstrate the effects of our method by means of realistic examples, showing that our approach requires low computational cost to learn constraints that yield significant performance benefits in our test cases. These benefits can be seen with ground-and-solve systems as well as lazy-grounding systems. However, ground-and-solve systems suffer from additional grounding overheads, induced by the additional constraints in some cases. By means of conflict minimization, non-minimal learned constraints can be reduced. This can result in significant reductions of grounding and solving efforts, as our experiments show.