1,315 research outputs found
Complexity Results for Modal Dependence Logic
Modal dependence logic was introduced recently by V\"a\"an\"anen. It enhances
the basic modal language by an operator =(). For propositional variables
p_1,...,p_n, =(p_1,...,p_(n-1);p_n) intuitively states that the value of p_n is
determined by those of p_1,...,p_(n-1). Sevenster (J. Logic and Computation,
2009) showed that satisfiability for modal dependence logic is complete for
nondeterministic exponential time. In this paper we consider fragments of modal
dependence logic obtained by restricting the set of allowed propositional
connectives. We show that satisfibility for poor man's dependence logic, the
language consisting of formulas built from literals and dependence atoms using
conjunction, necessity and possibility (i.e., disallowing disjunction), remains
NEXPTIME-complete. If we only allow monotone formulas (without negation, but
with disjunction), the complexity drops to PSPACE-completeness. We also extend
V\"a\"an\"anen's language by allowing classical disjunction besides dependence
disjunction and show that the satisfiability problem remains NEXPTIME-complete.
If we then disallow both negation and dependence disjunction, satistiability is
complete for the second level of the polynomial hierarchy. In this way we
completely classify the computational complexity of the satisfiability problem
for all restrictions of propositional and dependence operators considered by
V\"a\"an\"anen and Sevenster.Comment: 22 pages, full version of CSL 2010 pape
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Characterizing Representation of Temporal Data Visualization
Designing visualizations for exploration of temporal data requires several choices based on aspects of time and visual representation. Previous taxonomies have described existing visualizations based on these aspects without relating the visual representations. We propose to characterize existing visualization techniques based on both semantic aspects of time and visual representations. Our design space helps to identify how these different visual representations relate and give the possibility to combine attributes of representation from different techniques. We compare two examples of visualizations from the literature based on our taxonomy
Changing a semantics: opportunism or courage?
The generalized models for higher-order logics introduced by Leon Henkin, and
their multiple offspring over the years, have become a standard tool in many
areas of logic. Even so, discussion has persisted about their technical status,
and perhaps even their conceptual legitimacy. This paper gives a systematic
view of generalized model techniques, discusses what they mean in mathematical
and philosophical terms, and presents a few technical themes and results about
their role in algebraic representation, calibrating provability, lowering
complexity, understanding fixed-point logics, and achieving set-theoretic
absoluteness. We also show how thinking about Henkin's approach to semantics of
logical systems in this generality can yield new results, dispelling the
impression of adhocness. This paper is dedicated to Leon Henkin, a deep
logician who has changed the way we all work, while also being an always open,
modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on
his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and
Alonso, E., 201
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Exploring Temporal Granularities with Visualization
Time can be expressed and aggregated into concepts called granularities. Granularities are defined in a structure with their rules of conversion that may take the form of trees or graphs, thus it’s possible to design tools that dynamically explore different granularities that might reveal patterns hidden in other levels. We described an intial investigation of the use of interactive visualization techniques for that purpose and define future work to be done
Dependence Logic with Generalized Quantifiers: Axiomatizations
We prove two completeness results, one for the extension of dependence logic
by a monotone generalized quantifier Q with weak interpretation, weak in the
meaning that the interpretation of Q varies with the structures. The second
result considers the extension of dependence logic where Q is interpreted as
"there exists uncountable many." Both of the axiomatizations are shown to be
sound and complete for FO(Q) consequences.Comment: 17 page
Approximation of holomorphic mappings on strongly pseudoconvex domains
Let D be a relatively compact strongly pseudoconvex domain in a Stein
manifold, and let Y be a complex manifold. We prove that the set A(D,Y),
consisting of all continuous maps from the closure of D to Y which are
holomorphic in D, is a complex Banach manifold. When D is the unit disc in C
(or any other topologically trivial strongly pseudoconvex domain in a Stein
manifold), A(D,Y) is locally modeled on the Banach space A(D,C^n)=A(D)^n with
n=dim Y. Analogous results hold for maps which are holomorphic in D and of
class C^r up to the boundary for any positive integer r. We also establish the
Oka property for sections of continuous or smooth fiber bundles over the
closure of D which are holomorphic over D and whose fiber enjoys the Convex
approximation property. The main analytic technique used in the paper is a
method of gluing holomorphic sprays over Cartan pairs in Stein manifolds, with
control up to the boundary, which was developed in our paper "Holomorphic
curves in complex manifolds" (Duke Math. J. 139 (2007), no. 2, 203--253)
A Paraconsistent Higher Order Logic
Classical logic predicts that everything (thus nothing useful at all) follows
from inconsistency. A paraconsistent logic is a logic where an inconsistency
does not lead to such an explosion, and since in practice consistency is
difficult to achieve there are many potential applications of paraconsistent
logics in knowledge-based systems, logical semantics of natural language, etc.
Higher order logics have the advantages of being expressive and with several
automated theorem provers available. Also the type system can be helpful. We
present a concise description of a paraconsistent higher order logic with
countable infinite indeterminacy, where each basic formula can get its own
indeterminate truth value (or as we prefer: truth code). The meaning of the
logical operators is new and rather different from traditional many-valued
logics as well as from logics based on bilattices. The adequacy of the logic is
examined by a case study in the domain of medicine. Thus we try to build a
bridge between the HOL and MVL communities. A sequent calculus is proposed
based on recent work by Muskens.Comment: Originally in the proceedings of PCL 2002, editors Hendrik Decker,
Joergen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/). Correcte
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