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Non-monotonic spatial reasoning with answer set programming modulo theories*

Published online by Cambridge University Press:  30 August 2016

Spatial Reasoning ( The DesignSpace Group, Germany ( University of Warsaw, Warsaw, Poland University of Münster, Münster, Germany University of Bremen, Bremen, Germany (e-mail:,,
Spatial Reasoning ( The DesignSpace Group, Germany ( University of Warsaw, Warsaw, Poland University of Münster, Münster, Germany University of Bremen, Bremen, Germany (e-mail:,,
Spatial Reasoning ( The DesignSpace Group, Germany ( University of Warsaw, Warsaw, Poland University of Münster, Münster, Germany University of Bremen, Bremen, Germany (e-mail:,,


The systematic modelling of dynamic spatial systems is a key requirement in a wide range of application areas such as commonsense cognitive robotics, computer-aided architecture design, and dynamic geographic information systems. We present Answer Set Programming Modulo Theories (ASPMT)(QS), a novel approach and fully implemented prototype for non-monotonic spatial reasoning — a crucial requirement within dynamic spatial systems — based on ASPMT. ASPMT(QS) consists of a (qualitative) spatial representation module (QS) and a method for turning tight ASPMT instances into Satisfiability 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. Spatial reasoning is performed by encoding spatial relations as systems of polynomial constraints, and solving via SMT with the theory of real non-linear arithmetic. We empirically evaluate ASPMT(QS) in comparison with other contemporary spatial reasoning systems both within and outside the context of logic programming. ASPMT(QS) is currently the only existing system that is capable of reasoning about indirect spatial effects (i.e., addressing the ramification problem), and integrating geometric and QS information within a non-monotonic spatial reasoning context.

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This is an extended version of a paper presented at the Logic Programming and Nonmonotonic Reasoning Conference (LPNMR 2015), invited as a rapid communication in TPLP. The authors acknowledge the assistance of the conference program chairs Giovambattista Ianni and Miroslaw Truszczynski.

This paper comes with an online appendix containing Appendices A-H. The online appendix is available via the supplementary materials link from the TPLP web-site.


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