10,807 research outputs found
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
Spatial database implementation of fuzzy region connection calculus for analysing the relationship of diseases
Analyzing huge amounts of spatial data plays an important role in many
emerging analysis and decision-making domains such as healthcare, urban
planning, agriculture and so on. For extracting meaningful knowledge from
geographical data, the relationships between spatial data objects need to be
analyzed. An important class of such relationships are topological relations
like the connectedness or overlap between regions. While real-world
geographical regions such as lakes or forests do not have exact boundaries and
are fuzzy, most of the existing analysis methods neglect this inherent feature
of topological relations. In this paper, we propose a method for handling the
topological relations in spatial databases based on fuzzy region connection
calculus (RCC). The proposed method is implemented in PostGIS spatial database
and evaluated in analyzing the relationship of diseases as an important
application domain. We also used our fuzzy RCC implementation for fuzzification
of the skyline operator in spatial databases. The results of the evaluation
show that our method provides a more realistic view of spatial relationships
and gives more flexibility to the data analyst to extract meaningful and
accurate results in comparison with the existing methods.Comment: ICEE201
Arguments Whose Strength Depends on Continuous Variation
Both the traditional Aristotelian and modern symbolic approaches to logic have seen logic in terms of discrete symbol processing. Yet there are several kinds of argument whose validity depends on some topological notion of continuous variation, which is not well captured by discrete symbols. Examples include extrapolation and slippery slope arguments, sorites, fuzzy logic, and those involving closeness of possible worlds. It is argued that the natural first attempts to analyze these notions and explain their relation to reasoning fail, so that ignorance of their nature is profound
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