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A Complete Classification of Tractability in RCC-5
TLDR
This work investigates the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning and identifies all maximal tractable subalgebras which are four in total. Expand
Twenty-One Large Tractable Subclasses of Allen's Algebra
TLDR
Nine more maximal tractable subclasses of Allen's interval algebra are presented, in addition to their previously reported ORD-Horn subclass, and the path consistency algorithm is shown to decide satisfiability of interval networks using any of the algebras. Expand
Computational Complexity of Relating Time Points with Intervals
TLDR
Vilain's point–interval algebra is identified as a subalgebra in Meiri's approach to temporal reasoning, which combines reasoning about metric and qualitative temporal constraints over both time points and time intervals. Expand
A Complete Classification of Tractability in Allen's Algebra Relative to Subsets of Basic Relations
TLDR
The conclusion is that no tractable subalgebra dial is not known in the literature can contain more than the three basic relations (≡), (b) and ( b⪰ ), which means that concerning algebras for specifying complete knowledge about temporal information, there is no hope of finding yet unknown classes with much expressivity. Expand
Maximal Tractable Subclasses of Allen's Interval Algebra: Preliminary Report
This paper continues Nebel and Burckert's investigation of Allen's interval algebra by presenting nine more maximal tractable subclasses of the algebra (provided that P ≠ N P), in addition to theirExpand
Reasoning About Set Constraints Applied to Tractable Inference in Intuitionistic Logic
TLDR
This paper identifies a new class of set constraints where checking satissability is tractable (i.e. polynomial-time) and shows how to use this tractability result for constructing a new tractable fragment of intuitionistic logic. Expand
A Complete Classiication of Tractability in the Spatial Theory Rcc-5
We investigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satissability problem for RCC-5 is known to beExpand
Eight Maximal Tractable Subclasses of Allen's Algebra with Metric Time
TLDR
Eight new maximal tractable subclasses of Allen's interval algebra are presented, some of them subsuming previously reported tractable algebras that allow for metric temporal constraints on interval starting or ending points, using the recent framework of Horn DLRs. Expand
Towards a Complete Classification of Tractability in Allen's Algebra
TLDR
The conclusion is that no tractable subalgebra that is not known in the literature can contain more than the three basic relations (≡), (b) and (b-), which means there is no hope of finding yet unknown classes with much expressivity. Expand
Reasoning about Action in Polynomial Time
TLDR
A temporal logic with a restriction for which deciding satisfiability is tractable, a tractable extension for reasoning about action, and NP-completeness results for the unrestricted problems are presented. Expand
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