International Conference on Logic Programming and Nonmonotonic Reasoning

LPNMR 2015: Logic Programming and Nonmonotonic Reasoning pp 488-501 | Cite as

ASPMT(QS): Non-Monotonic Spatial Reasoning with Answer Set Programming Modulo Theories

  • Przemysław Andrzej Wałęga
  • Mehul Bhatt
  • Carl Schultz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9345)

Abstract

The systematic modelling of dynamic spatial systems [9] is a key requirement in a wide range of application areas such as comonsense cognitive robotics, computer-aided architecture design, dynamic geographic information systems. We present ASPMT(QS), a novel approach and fully-implemented prototype for non-monotonic spatial reasoning —a crucial requirement within dynamic spatial systems– based on Answer Set Programming Modulo Theories (ASPMT). ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Sat Modulo Theories (SMT) instances in order to compute stable models by means of SMT solvers. We formalise and implement concepts of default spatial reasoning and spatial frame axioms using choice formulas. Spatial reasoning is performed by encoding spatial relations as systems of polynomial constraints, and solving via SMT with the theory of real nonlinear arithmetic. We empirically evaluate ASPMT(QS) in comparison with other prominent contemporary spatial reasoning systems. Our results show that ASPMT(QS) is the only existing system that is capable of reasoning about indirect spatial effects (i.e. addressing the ramification problem), and integrating geometric and qualitative spatial information within a non-monotonic spatial reasoning context.

Keywords

Non-monotonic spatial reasoning Answer set programming modulo theories Declarative spatial reasoning 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Przemysław Andrzej Wałęga
    • 1
  • Mehul Bhatt
    • 2
  • Carl Schultz
    • 2
  1. 1.Institute of PhilosophyUniversity of WarsawWarsawPoland
  2. 2.Department of Computer ScienceUniversity of BremenBremenGermany

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