20,709 research outputs found
A Declarative Semantics for CLP with Qualification and Proximity
Uncertainty in Logic Programming has been investigated during the last
decades, dealing with various extensions of the classical LP paradigm and
different applications. Existing proposals rely on different approaches, such
as clause annotations based on uncertain truth values, qualification values as
a generalization of uncertain truth values, and unification based on proximity
relations. On the other hand, the CLP scheme has established itself as a
powerful extension of LP that supports efficient computation over specialized
domains while keeping a clean declarative semantics. In this paper we propose a
new scheme SQCLP designed as an extension of CLP that supports qualification
values and proximity relations. We show that several previous proposals can be
viewed as particular cases of the new scheme, obtained by partial
instantiation. We present a declarative semantics for SQCLP that is based on
observables, providing fixpoint and proof-theoretical characterizations of
least program models as well as an implementation-independent notion of goal
solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10
Complementary Lipschitz continuity results for the distribution of intersections or unions of independent random sets in finite discrete spaces
We prove that intersections and unions of independent random sets in finite
spaces achieve a form of Lipschitz continuity. More precisely, given the
distribution of a random set , the function mapping any random set
distribution to the distribution of its intersection (under independence
assumption) with is Lipschitz continuous with unit Lipschitz constant if
the space of random set distributions is endowed with a metric defined as the
norm distance between inclusion functionals also known as commonalities.
Moreover, the function mapping any random set distribution to the distribution
of its union (under independence assumption) with is Lipschitz continuous
with unit Lipschitz constant if the space of random set distributions is
endowed with a metric defined as the norm distance between hitting
functionals also known as plausibilities.
Using the epistemic random set interpretation of belief functions, we also
discuss the ability of these distances to yield conflict measures. All the
proofs in this paper are derived in the framework of Dempster-Shafer belief
functions. Let alone the discussion on conflict measures, it is straightforward
to transcribe the proofs into the general (non necessarily epistemic) random
set terminology
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