nonmonotonic reasoning

This paper presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to $\Delta^P_3$-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof. Furthermore, we illustrate the general architecture of the DLV system which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.

Many systems that exhibit nonmonotonic behavior have been described and studied already in the literature. The general notion of nonmonotonic reasoning, though, has almost always been described only negatively, by the property it does not enjoy, i.e. monotonicity. We study here general patterns of nonmonotonic reasoning and try to isolate properties that could help us map the field of nonmonotonic reasoning by reference to positive properties. We concentrate on a number of families of nonmonotonic consequence relations, defined in the style of Gentzen. Both proof-theoretic and semantic points of view are developed in parallel. The former point of view was pioneered by D. Gabbay, while the latter has been advocated by Y. Shoham in. Five such families are defined and characterized by representation theorems, relating the two points of view. One of the families of interest, that of preferential relations, turns out to have been studied by E. Adams. The "preferential" models proposed here are a much stronger tool than Adams' probabilistic semantics. The basic language used in this paper is that of propositional logic. The extension of our results to first order predicate calculi and the study of the computational complexity of the decision problems described in this paper will be treated in another paper.

Domain-specific heuristics are an essential technique for solving combinatorial problems efficiently. Current approaches to integrate domain-specific heuristics with Answer Set Programming (ASP) are unsatisfactory when dealing with heuristics that are specified non-monotonically on the basis of partial assignments. Such heuristics frequently occur in practice, for example, when picking an item that has not yet been placed in bin packing. Therefore, we present novel syntax and semantics for declarative specifications of domain-specific heuristics in ASP. Our approach supports heuristic statements that depend on the partial assignment maintained during solving, which has not been possible before. We provide an implementation in ALPHA that makes ALPHA the first lazy-grounding ASP system to support declaratively specified domain-specific heuristics. Two practical example domains are used to demonstrate the benefits of our proposal. Additionally, we use our approach to implement informed search with A*, which is tackled within ASP for the first time. A* is applied to two further search problems. The experiments confirm that combining lazy-grounding ASP solving and our novel heuristics can be vital for solving industrial-size problems.