1,872 research outputs found
Counting Complexity for Reasoning in Abstract Argumentation
In this paper, we consider counting and projected model counting of
extensions in abstract argumentation for various semantics. When asking for
projected counts we are interested in counting the number of extensions of a
given argumentation framework while multiple extensions that are identical when
restricted to the projected arguments count as only one projected extension. We
establish classical complexity results and parameterized complexity results
when the problems are parameterized by treewidth of the undirected
argumentation graph. To obtain upper bounds for counting projected extensions,
we introduce novel algorithms that exploit small treewidth of the undirected
argumentation graph of the input instance by dynamic programming (DP). Our
algorithms run in time double or triple exponential in the treewidth depending
on the considered semantics. Finally, we take the exponential time hypothesis
(ETH) into account and establish lower bounds of bounded treewidth algorithms
for counting extensions and projected extension.Comment: Extended version of a paper published at AAAI-1
Taxonomy for Humans or Computers? Cognitive Pragmatics for Big Data
Criticism of big data has focused on showing that more is not necessarily better, in the sense that data may lose their value when taken out of context and aggregated together. The next step is to incorporate an awareness of pitfalls for aggregation into the design of data infrastructure and institutions. A common strategy minimizes aggregation errors by increasing the precision of our conventions for identifying and classifying data. As a counterpoint, we argue that there are pragmatic trade-offs between precision and ambiguity that are key to designing effective solutions for generating big data about biodiversity. We focus on the importance of theory-dependence as a source of ambiguity in taxonomic nomenclature and hence a persistent challenge for implementing a single, long-term solution to storing and accessing meaningful sets of biological specimens. We argue that ambiguity does have a positive role to play in scientific progress as a tool for efficiently symbolizing multiple aspects of taxa and mediating between conflicting hypotheses about their nature. Pursuing a deeper understanding of the trade-offs and synthesis of precision and ambiguity as virtues of scientific language and communication systems then offers a productive next step for realizing sound, big biodiversity data services
Where Fail-Safe Default Logics Fail
Reiter's original definition of default logic allows for the application of a
default that contradicts a previously applied one. We call failure this
condition. The possibility of generating failures has been in the past
considered as a semantical problem, and variants have been proposed to solve
it. We show that it is instead a computational feature that is needed to encode
some domains into default logic
Constructive Geometry and the Parallel Postulate
Euclidean geometry consists of straightedge-and-compass constructions and
reasoning about the results of those constructions. We show that Euclidean
geometry can be developed using only intuitionistic logic. We consider three
versions of Euclid's parallel postulate: Euclid's own formulation in his
Postulate 5; Playfair's 1795 version, and a new version we call the strong
parallel postulate. These differ in that Euclid's version and the new version
both assert the existence of a point where two lines meet, while Playfair's
version makes no existence assertion. Classically, the models of Euclidean
(straightedge-and-compass) geometry are planes over Euclidean fields. We prove
a similar theorem for constructive Euclidean geometry, by showing how to define
addition and multiplication without a case distinction about the sign of the
arguments. With intuitionistic logic, there are two possible definitions of
Euclidean fields, which turn out to correspond to the different versions of the
parallel axiom. In this paper, we completely settle the questions about
implications between the three versions of the parallel postulate: the strong
parallel postulate easily implies Euclid 5, and in fact Euclid 5 also implies
the strong parallel postulate, although the proof is lengthy, depending on the
verification that Euclid 5 suffices to define multiplication geometrically. We
show that Playfair does not imply Euclid 5, and we also give some other
independence results. Our independence proofs are given without discussing the
exact choice of the other axioms of geometry; all we need is that one can
interpret the geometric axioms in Euclidean field theory. The proofs use Kripke
models of Euclidean field theories based on carefully constructed rings of
real-valued functions.Comment: 114 pages, 39 figure
Geospatial Narratives and their Spatio-Temporal Dynamics: Commonsense Reasoning for High-level Analyses in Geographic Information Systems
The modelling, analysis, and visualisation of dynamic geospatial phenomena
has been identified as a key developmental challenge for next-generation
Geographic Information Systems (GIS). In this context, the envisaged
paradigmatic extensions to contemporary foundational GIS technology raises
fundamental questions concerning the ontological, formal representational, and
(analytical) computational methods that would underlie their spatial
information theoretic underpinnings.
We present the conceptual overview and architecture for the development of
high-level semantic and qualitative analytical capabilities for dynamic
geospatial domains. Building on formal methods in the areas of commonsense
reasoning, qualitative reasoning, spatial and temporal representation and
reasoning, reasoning about actions and change, and computational models of
narrative, we identify concrete theoretical and practical challenges that
accrue in the context of formal reasoning about `space, events, actions, and
change'. With this as a basis, and within the backdrop of an illustrated
scenario involving the spatio-temporal dynamics of urban narratives, we address
specific problems and solutions techniques chiefly involving `qualitative
abstraction', `data integration and spatial consistency', and `practical
geospatial abduction'. From a broad topical viewpoint, we propose that
next-generation dynamic GIS technology demands a transdisciplinary scientific
perspective that brings together Geography, Artificial Intelligence, and
Cognitive Science.
Keywords: artificial intelligence; cognitive systems; human-computer
interaction; geographic information systems; spatio-temporal dynamics;
computational models of narrative; geospatial analysis; geospatial modelling;
ontology; qualitative spatial modelling and reasoning; spatial assistance
systemsComment: ISPRS International Journal of Geo-Information (ISSN 2220-9964);
Special Issue on: Geospatial Monitoring and Modelling of Environmental
Change}. IJGI. Editor: Duccio Rocchini. (pre-print of article in press
To Preference via Entrenchment
We introduce a simple generalization of Gardenfors and Makinson's epistemic
entrenchment called partial entrenchment. We show that preferential inference
can be generated as the sceptical counterpart of an inference mechanism defined
directly on partial entrenchment.Comment: 16 page
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