50,514 research outputs found
Non-elementary proper forcing
We introduce a simplified framework for ord-transitive models and Shelah's
non elementary proper (nep) theory. We also introduce a new construction for
the countable support nep iteration
Characterizing Quantifier Extensions of Dependence Logic
We characterize the expressive power of extensions of Dependence Logic and
Independence Logic by monotone generalized quantifiers in terms of quantifier
extensions of existential second-order logic.Comment: 9 page
Complexity of Prioritized Default Logics
In default reasoning, usually not all possible ways of resolving conflicts
between default rules are acceptable. Criteria expressing acceptable ways of
resolving the conflicts may be hardwired in the inference mechanism, for
example specificity in inheritance reasoning can be handled this way, or they
may be given abstractly as an ordering on the default rules. In this article we
investigate formalizations of the latter approach in Reiter's default logic.
Our goal is to analyze and compare the computational properties of three such
formalizations in terms of their computational complexity: the prioritized
default logics of Baader and Hollunder, and Brewka, and a prioritized default
logic that is based on lexicographic comparison. The analysis locates the
propositional variants of these logics on the second and third levels of the
polynomial hierarchy, and identifies the boundary between tractable and
intractable inference for restricted classes of prioritized default theories
Dendroidal sets as models for homotopy operads
The homotopy theory of infinity-operads is defined by extending Joyal's
homotopy theory of infinity-categories to the category of dendroidal sets. We
prove that the category of dendroidal sets is endowed with a model category
structure whose fibrant objects are the infinity-operads (i.e. dendroidal inner
Kan complexes). This extends the theory of infinity-categories in the sense
that the Joyal model category structure on simplicial sets whose fibrant
objects are the infinity-categories is recovered from the model category
structure on dendroidal sets by simply slicing over the point.Comment: This is essentially the published version, except that we added an
erratum at the end of the paper concerning the behaviour of cofibrations with
respect to the tensor product of dendroidal set
Inseparable local uniformization
It is known since the works of Zariski in early 40ies that desingularization
of varieties along valuations (called local uniformization of valuations) can
be considered as the local part of the desingularization problem. It is still
an open problem if local uniformization exists in positive characteristic and
dimension larger than three. In this paper, we prove that Zariski local
uniformization of algebraic varieties is always possible after a purely
inseparable extension of the field of rational functions, i.e. any valuation
can be uniformized by a purely inseparable alteration.Comment: 66 pages, final version, the paper was seriously revise
Non-normal modalities in variants of Linear Logic
This article presents modal versions of resource-conscious logics. We
concentrate on extensions of variants of Linear Logic with one minimal
non-normal modality. In earlier work, where we investigated agency in
multi-agent systems, we have shown that the results scale up to logics with
multiple non-minimal modalities. Here, we start with the language of
propositional intuitionistic Linear Logic without the additive disjunction, to
which we add a modality. We provide an interpretation of this language on a
class of Kripke resource models extended with a neighbourhood function: modal
Kripke resource models. We propose a Hilbert-style axiomatization and a
Gentzen-style sequent calculus. We show that the proof theories are sound and
complete with respect to the class of modal Kripke resource models. We show
that the sequent calculus admits cut elimination and that proof-search is in
PSPACE. We then show how to extend the results when non-commutative connectives
are added to the language. Finally, we put the logical framework to use by
instantiating it as logics of agency. In particular, we propose a logic to
reason about the resource-sensitive use of artefacts and illustrate it with a
variety of examples
Classification of Two-dimensional Local Conformal Nets with c<1 and 2-cohomology Vanishing for Tensor Categories
We classify two-dimensional local conformal nets with parity symmetry and
central charge less than 1, up to isomorphism. The maximal ones are in a
bijective correspondence with the pairs of A-D-E Dynkin diagrams with the
difference of their Coxeter numbers equal to 1. In our previous classification
of one-dimensional local conformal nets, Dynkin diagrams D_{2n+1} and E_7 do
not appear, but now they do appear in this classification of two-dimensional
local conformal nets. Such nets are also characterized as two-dimensional local
conformal nets with mu-index equal to 1 and central charge less than 1. Our
main tool, in addition to our previous classification results for
one-dimensional nets, is 2-cohomology vanishing for certain tensor categories
related to the Virasoro tensor categories with central charge less than 1.Comment: 40 pages, LaTeX 2
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