@phdthesis{Ostrowski2018, author = {Ostrowski, Max}, title = {Modern constraint answer set solving}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-407799}, school = {Universit{\"a}t Potsdam}, pages = {135}, year = {2018}, abstract = {Answer Set Programming (ASP) is a declarative problem solving approach, combining a rich yet simple modeling language with high-performance solving capabilities. Although this has already resulted in various applications, certain aspects of such applications are more naturally modeled using variables over finite domains, for accounting for resources, fine timings, coordinates, or functions. Our goal is thus to extend ASP with constraints over integers while preserving its declarative nature. This allows for fast prototyping and elaboration tolerant problem descriptions of resource related applications. The resulting paradigm is called Constraint Answer Set Programming (CASP). We present three different approaches for solving CASP problems. The first one, a lazy, modular approach combines an ASP solver with an external system for handling constraints. This approach has the advantage that two state of the art technologies work hand in hand to solve the problem, each concentrating on its part of the problem. The drawback is that inter-constraint dependencies cannot be communicated back to the ASP solver, impeding its learning algorithm. The second approach translates all constraints to ASP. Using the appropriate encoding techniques, this results in a very fast, monolithic system. Unfortunately, due to the large, explicit representation of constraints and variables, translation techniques are restricted to small and mid-sized domains. The third approach merges the lazy and the translational approach, combining the strength of both while removing their weaknesses. To this end, we enhance the dedicated learning techniques of an ASP solver with the inferences of the translating approach in a lazy way. That is, the important knowledge is only made explicit when needed. By using state of the art techniques from neighboring fields, we provide ways to tackle real world, industrial size problems. By extending CASP to reactive solving, we open up new application areas such as online planning with continuous domains and durations.}, language = {en} }