5 research outputs found
Symmetry-breaking Answer Set Solving
In the context of Answer Set Programming, this paper investigates
symmetry-breaking to eliminate symmetric parts of the search space and,
thereby, simplify the solution process. We propose a reduction of disjunctive
logic programs to a coloured digraph such that permutational symmetries can be
constructed from graph automorphisms. Symmetries are then broken by introducing
symmetry-breaking constraints. For this purpose, we formulate a preprocessor
that integrates a graph automorphism system. Experiments demonstrate its
computational impact.Comment: Proceedings of ICLP'10 Workshop on Answer Set Programming and Other
Computing Paradig
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Labellings for assumption-based and abstract argumentation
The semantics of Assumption-Based Argumentation (ABA) frameworks are traditionally characterised as assumption extensions, i.e. sets of accepted assumptions. Assumption labellings are an alternative way to express the semantics of flat ABA frameworks, where one of the labels in, out, or undec is assigned to each assumption. They are beneficial for applications where it is important to distinguish not only between accepted and non-accepted assumptions, but further divide the non-accepted assumptions into those which are clearly rejected and those which are neither accepted nor rejected and thus undecided. We prove one-to-one correspondences between assumption labellings and extensions for the admissible, grounded, complete, preferred, ideal, semi-stable and stable semantics. We also show how the definition of assumption labellings for flat ABA frameworks can be extended to assumption labellings for any (flat and non-flat) ABA framework, enabling reasoning with a wider range of scenarios. Since flat ABA frameworks are structured instances of Abstract Argumentation (AA) frameworks, we furthermore investigate the relation between assumption labellings for flat ABA frameworks and argument labellings for AA frameworks. Building upon prior work on complete assumption and argument labellings, we prove one-to-one correspondences between grounded, preferred, ideal, and stable assumption and argument labellings, and a one-to-many correspondence between admissible assumption and argument labellings. Inspired by the notion of admissible assumption labellings we introduce committed admissible argument labellings for AA frameworks, which correspond more closely to admissible assumption labellings of ABA frameworks than admissible argument labellings do