19,595 research outputs found
Topological Foundations of Cognitive Science
A collection of papers presented at the First International Summer Institute in Cognitive Science, University at Buffalo, July 1994, including the following papers:
** Topological Foundations of Cognitive Science, Barry Smith
** The Bounds of Axiomatisation, Graham White
** Rethinking Boundaries, Wojciech Zelaniec
** Sheaf Mereology and Space Cognition, Jean Petitot
** A Mereotopological Definition of 'Point', Carola Eschenbach
** Discreteness, Finiteness, and the Structure of Topological Spaces, Christopher Habel
** Mass Reference and the Geometry of Solids, Almerindo E. Ojeda
** Defining a 'Doughnut' Made Difficult, N .M. Gotts
** A Theory of Spatial Regions with Indeterminate Boundaries, A.G. Cohn and N.M. Gotts
** Mereotopological Construction of Time from Events, Fabio Pianesi and Achille C. Varzi
** Computational Mereology: A Study of Part-of Relations for Multi-media Indexing, Wlodek Zadrozny and Michelle Ki
A Complete Classification of Tractability in 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
satisfiability problem for RCC-5 is known to be NP-complete but not much is
known about its approximately four billion subclasses. We provide a complete
classification of satisfiability for all these subclasses into polynomial and
NP-complete respectively. In the process, we identify all maximal tractable
subalgebras which are four in total.Comment: See http://www.jair.org/ for an online appendix and other files
accompanying this articl
Assessing the impact of representational and contextual problem features on student use of right-hand rules
Students in introductory physics struggle with vector algebra and these
challenges are often associated with contextual and representational features
of the problems. Performance on problems about cross product direction is
particularly poor and some research suggests that this may be primarily due to
misapplied right-hand rules. However, few studies have had the resolution to
explore student use of right-hand rules in detail. This study reviews
literature in several disciplines, including spatial cognition, to identify ten
contextual and representational problem features that are most likely to
influence performance on problems requiring a right-hand rule. Two quantitative
measures of performance (correctness and response time) and two qualitative
measures (methods used and type of errors made) were used to explore the impact
of these problem features on student performance. Quantitative results are
consistent with expectations from the literature, but reveal that some features
(such as the type of reasoning required and the physical awkwardness of using a
right-hand rule) have a greater impact than others (such as whether the vectors
are placed together or separate). Additional insight is gained by the
qualitative analysis, including identifying sources of difficulty not
previously discussed in the literature and revealing that the use of
supplemental methods, such as physically rotating the paper, can mitigate
errors associated with certain features
Stochastic Invariants for Probabilistic Termination
Termination is one of the basic liveness properties, and we study the
termination problem for probabilistic programs with real-valued variables.
Previous works focused on the qualitative problem that asks whether an input
program terminates with probability~1 (almost-sure termination). A powerful
approach for this qualitative problem is the notion of ranking supermartingales
with respect to a given set of invariants. The quantitative problem
(probabilistic termination) asks for bounds on the termination probability. A
fundamental and conceptual drawback of the existing approaches to address
probabilistic termination is that even though the supermartingales consider the
probabilistic behavior of the programs, the invariants are obtained completely
ignoring the probabilistic aspect.
In this work we address the probabilistic termination problem for
linear-arithmetic probabilistic programs with nondeterminism. We define the
notion of {\em stochastic invariants}, which are constraints along with a
probability bound that the constraints hold. We introduce a concept of {\em
repulsing supermartingales}. First, we show that repulsing supermartingales can
be used to obtain bounds on the probability of the stochastic invariants.
Second, we show the effectiveness of repulsing supermartingales in the
following three ways: (1)~With a combination of ranking and repulsing
supermartingales we can compute lower bounds on the probability of termination;
(2)~repulsing supermartingales provide witnesses for refutation of almost-sure
termination; and (3)~with a combination of ranking and repulsing
supermartingales we can establish persistence properties of probabilistic
programs.
We also present results on related computational problems and an experimental
evaluation of our approach on academic examples.Comment: Full version of a paper published at POPL 2017. 20 page
Reasoning about Cardinal Directions between Extended Objects
Direction relations between extended spatial objects are important
commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model,
known as Cardinal Direction Calculus (CDC), for representing direction
relations between connected plane regions. CDC is perhaps the most expressive
qualitative calculus for directional information, and has attracted increasing
interest from areas such as artificial intelligence, geographical information
science, and image retrieval. Given a network of CDC constraints, the
consistency problem is deciding if the network is realizable by connected
regions in the real plane. This paper provides a cubic algorithm for checking
consistency of basic CDC constraint networks, and proves that reasoning with
CDC is in general an NP-Complete problem. For a consistent network of basic CDC
constraints, our algorithm also returns a 'canonical' solution in cubic time.
This cubic algorithm is also adapted to cope with cardinal directions between
possibly disconnected regions, in which case currently the best algorithm is of
time complexity O(n^5)
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