4 research outputs found
Allen's Interval Algebra Makes the Difference
Allen's Interval Algebra constitutes a framework for reasoning about temporal
information in a qualitative manner. In particular, it uses intervals, i.e.,
pairs of endpoints, on the timeline to represent entities corresponding to
actions, events, or tasks, and binary relations such as precedes and overlaps
to encode the possible configurations between those entities. Allen's calculus
has found its way in many academic and industrial applications that involve,
most commonly, planning and scheduling, temporal databases, and healthcare. In
this paper, we present a novel encoding of Interval Algebra using answer-set
programming (ASP) extended by difference constraints, i.e., the fragment
abbreviated as ASP(DL), and demonstrate its performance via a preliminary
experimental evaluation. Although our ASP encoding is presented in the case of
Allen's calculus for the sake of clarity, we suggest that analogous encodings
can be devised for other point-based calculi, too.Comment: Part of DECLARE 19 proceeding
A Multivariate Complexity Analysis of Qualitative Reasoning Problems
Qualitative reasoning is an important subfield of artificial intelligence
where one describes relationships with qualitative, rather than numerical,
relations. Many such reasoning tasks, e.g., Allen's interval algebra, can be
solved in time, but single-exponential running times
are currently far out of reach. In this paper we consider
single-exponential algorithms via a multivariate analysis consisting of a
fine-grained parameter (e.g., the number of variables) and a coarse-grained
parameter expected to be relatively small. We introduce the classes FPE and
XE of problems solvable in , respectively , time,
and prove several fundamental properties of these classes. We proceed by
studying temporal reasoning problems and (1) show that the Partially Ordered
Time problem of effective width is solvable in time and is thus
included in XE, and (2) that the network consistency problem for Allen's
interval algebra with no interval overlapping with more than others is
solvable in time and is included in FPE. Our
multivariate approach is in no way limited to these to specific problems and
may be a generally useful approach for obtaining single-exponential algorithms
On neighbourhood singleton-style consistencies for qualitative spatial and temporal reasoning
Given a qualitative constraint network (QCN), a singleton-style consistency focuses on each base relation (atom) of a constraint separately, rather than the entire constraint altogether. This local consistency is essential for tackling fundamental reasoning problems associated with QCNs, such as minimal labeling, but can suffer from redundant constraint checks, especially when checks occur far from where the pruning usually takes place. In this paper, we propose singleton-style consistencies that are applied just on the neighbourhood of a singleton-checked constraint instead of the whole network. We make a theoretical comparison with existing consistencies and consequently prove some properties of the new ones. Further, we propose algorithms to enforce our consistencies, as well as parsimonious variants thereof, that are more efficient in practice than the state of the art. An experimental evaluation with random and structured QCNs of Allen's Interval Algebra in the phase transition region demonstrates the potential of our approach.acceptedVersionPeer reviewe