Modular HEX-Programs

The goal of this project is to develop formalisms and reasoning methods for powerful reasoning systems for modular, possibly distributed logic programs, which are based on declarative knowledge representation. Especially, logic programs under the answer set semantics are used to realize languages and tools for extending and developing current approaches to modularity in knowledge bases, such that they can be evaluated locally or in a distributed manner. A special focus was on the study of suitable models and algorithms for inconsistent and for various reasons incomplete information in this setting. Reasoning methods, that rely on semantic approximations, have been developed in order to evaluate such logic programs more efficiently. On top of that, we have developed suitable reasoning platforms for modular, possibly distributed logic program, using previously developed approaches to extended reasoning methods. The present project has tackled the issue of modularity in logic program by (i) a novel semantics for modular nonmonotonic logic programs (MLPs) that we devised which allows for mutual recursion between program modules (a natural property that previously defined semantics had been missing); (ii) the semantic properties of MLPs, their computational complexity, and characterizations in terms of classical models; (iii) design of efficient reasoning algorithms for fragments of MLPs that allows to evaluate them in a top-down fashion; (iv) novel optimization technique for logic programs based on domain decomposition techniques. Furthermore, in the setting of distributed modularity aspects, the present project tackled the issue by (i) developing a basic algorithm to evaluate Distributed Nonmonotonic Multi-Context Systems (DMCS); (ii) we investigated optimizations of our basic algorithm under the availability of topology information of the system; (iii) we addressed the role of symmetry detection and symmetry breaking in DMCS to speed up the distributed evaluation process; (iv) we dealt with incompleteness by further extended the MCS formalization to a dynamic setting where the interlinkage between local knowledge bases is not fixed at design time. Instantiations of the system are only determined/approximated at runtime by configuration based on quality-based criteria. The approaches have been implemented in research prototypes, and experimental evaluations showed promising results. Moreover, these prototypes have been used to implement applications in the context of modular and distributed knowledge representation.