For some computational problems (e.g., product configuration, planning, diagnosis, query answering, phylogeny reconstruction), computing a set of similar/diverse solutions may be desirable for better decision-making. With this motivation, we have studied several decision/optimization versions of this problem in the context of Answer set programming (ASP), analyzed their computational complexity, and introduced offline/online methods to compute similar/diverse solutions of such computational problems with respect to a given distance function. All these methods rely on the idea of computing solutions to a problem by means of finding the answer sets for an ASP program that describes the problem. The offline methods compute all solutions of a problem in advance using the ASP formulation of the problem with an existing ASP solver, like clasp, and then identify similar/diverse solutions using some clustering methods (possibly in ASP as well). The online methods compute similar/diverse solutions of a problem following one of the three approaches: by reformulating the ASP representation of the problem to compute similar/diverse solutions at once using an existing ASP solver; by computing similar/diverse solutions iteratively (one after the other) using an existing ASP solver; by modifying the search algorithm of an ASP solver to compute similar/diverse solutions incrementally. All these methods are sound; the offline method and the first online method are complete whereas the others are not. We have modified clasp to implement the last online method and called it clasp-nk. In the first two online methods, the given distance function is represented in ASP; in the last one, however, it is implemented in C++. We have shown the applicability and the effectiveness of these methods using clasp or clasp-nk on two sorts of problems with different distance measures: on a real-world problem in phylogenetics (i.e., reconstruction of similar/diverse phylogenies for Indo-European languages), and on several planning problems in a well-known domain (i.e., Blocks World). We have observed that in terms of computational efficiency (both time and space), the last online method outperforms the others; also, it allows us to compute similar/diverse solutions when the distance function cannot be represented in ASP (e.g., due to some mathematical functions not supported by the ASP solvers) but can be easily implemented in C++.

Answer set programming (ASP) is a form of declarative programming that allows to succinctly formulate and efficiently solve complex problems. An intuitive extension of this formalism is communicating ASP, in which multiple ASP programs collaborate to solve the problem at hand. However, the expressiveness of communicating ASP has not been thoroughly studied. In this paper, we present a systematic study of the additional expressiveness offered by allowing ASP programs to communicate. First, we consider a simple form of communication where programs are only allowed to ask questions to each other. For the most part, we deliberately consider only simple programs, i.e. programs for which computing the answer sets is in P. We find that the problem of deciding whether a literal is in some answer set of a communicating ASP program using simple communication is NP-hard. In other words, due to the ability of these simple ASP programs to communicate and collaborate, we move up a step in the polynomial hierarchy. Second, we modify the communication mechanism to also allow us to focus on a sequence of communicating programs, where each program in the sequence may successively remove some of the remaining models. This mimics a network of leaders, where the first leader has the first say and may remove models that he or she finds unsatisfactory. Using this particular communication mechanism allows us to capture the entire polynomial hierarchy. This means, in particular, that communicating ASP could be used to solve problems that are above the second level of polynomial hierarchy, such as some forms of abductive reasoning as well as PSPACE-complete problems such as STRIPS planning.

Open Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this paper, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where knowledge bases and FoLPs coexist, and we show that reasoning with such knowledge bases can be reduced to reasoning with FoLPs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, thus providing a genuine alternative approach to current integration approaches of ontologies and rules.