2,515 research outputs found
Topological Schemas of Memory Spaces
Hippocampal cognitive map---a neuronal representation of the spatial
environment---is broadly discussed in the computational neuroscience literature
for decades. More recent studies point out that hippocampus plays a major role
in producing yet another cognitive framework that incorporates not only
spatial, but also nonspatial memories---the memory space. However, unlike
cognitive maps, memory spaces have been barely studied from a theoretical
perspective. Here we propose an approach for modeling hippocampal memory spaces
as an epiphenomenon of neuronal spiking activity. First, we suggest that the
memory space may be viewed as a finite topological space---a hypothesis that
allows treating both spatial and nonspatial aspects of hippocampal function on
equal footing. We then model the topological properties of the memory space to
demonstrate that this concept naturally incorporates the notion of a cognitive
map. Lastly, we suggest a formal description of the memory consolidation
process and point out a connection between the proposed model of the memory
spaces to the so-called Morris' schemas, which emerge as the most compact
representation of the memory structure.Comment: 24 pages, 8 Figures, 1 Suppl. Figur
Class Association Rules Mining based Rough Set Method
This paper investigates the mining of class association rules with rough set
approach. In data mining, an association occurs between two set of elements
when one element set happen together with another. A class association rule set
(CARs) is a subset of association rules with classes specified as their
consequences. We present an efficient algorithm for mining the finest class
rule set inspired form Apriori algorithm, where the support and confidence are
computed based on the elementary set of lower approximation included in the
property of rough set theory. Our proposed approach has been shown very
effective, where the rough set approach for class association discovery is much
simpler than the classic association method.Comment: 10 pages, 2 figure
Dual Logic Concepts based on Mathematical Morphology in Stratified Institutions: Applications to Spatial Reasoning
Several logical operators are defined as dual pairs, in different types of
logics. Such dual pairs of operators also occur in other algebraic theories,
such as mathematical morphology. Based on this observation, this paper proposes
to define, at the abstract level of institutions, a pair of abstract dual and
logical operators as morphological erosion and dilation. Standard quantifiers
and modalities are then derived from these two abstract logical operators.
These operators are studied both on sets of states and sets of models. To cope
with the lack of explicit set of states in institutions, the proposed abstract
logical dual operators are defined in an extension of institutions, the
stratified institutions, which take into account the notion of open sentences,
the satisfaction of which is parametrized by sets of states. A hint on the
potential interest of the proposed framework for spatial reasoning is also
provided.Comment: 36 page
Infinite Probabilistic Databases
Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009).
We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics.
It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries
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
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