8,932 research outputs found
Step-Indexed Logical Relations for Probability (long version)
It is well-known that constructing models of higher-order probabilistic
programming languages is challenging. We show how to construct step-indexed
logical relations for a probabilistic extension of a higher-order programming
language with impredicative polymorphism and recursive types. We show that the
resulting logical relation is sound and complete with respect to the contextual
preorder and, moreover, that it is convenient for reasoning about concrete
program equivalences. Finally, we extend the language with dynamically
allocated first-order references and show how to extend the logical relation to
this language. We show that the resulting relation remains useful for reasoning
about examples involving both state and probabilistic choice.Comment: Extended version with appendix of a FoSSaCS'15 pape
On the Implementation of the Probabilistic Logic Programming Language ProbLog
The past few years have seen a surge of interest in the field of
probabilistic logic learning and statistical relational learning. In this
endeavor, many probabilistic logics have been developed. ProbLog is a recent
probabilistic extension of Prolog motivated by the mining of large biological
networks. In ProbLog, facts can be labeled with probabilities. These facts are
treated as mutually independent random variables that indicate whether these
facts belong to a randomly sampled program. Different kinds of queries can be
posed to ProbLog programs. We introduce algorithms that allow the efficient
execution of these queries, discuss their implementation on top of the
YAP-Prolog system, and evaluate their performance in the context of large
networks of biological entities.Comment: 28 pages; To appear in Theory and Practice of Logic Programming
(TPLP
Probabilistic theories with purification
We investigate general probabilistic theories in which every mixed state has
a purification, unique up to reversible channels on the purifying system. We
show that the purification principle is equivalent to the existence of a
reversible realization of every physical process, namely that every physical
process can be regarded as arising from a reversible interaction of the system
with an environment, which is eventually discarded. From the purification
principle we also construct an isomorphism between transformations and
bipartite states that possesses all structural properties of the
Choi-Jamiolkowski isomorphism in quantum mechanics. Such an isomorphism allows
one to prove most of the basic features of quantum mechanics, like e.g.
existence of pure bipartite states giving perfect correlations in independent
experiments, no information without disturbance, no joint discrimination of all
pure states, no cloning, teleportation, no programming, no bit commitment,
complementarity between correctable channels and deletion channels,
characterization of entanglement-breaking channels as measure-and-prepare
channels, and others, without resorting to the mathematical framework of
Hilbert spaces.Comment: Differing from the journal version, this version includes a table of
contents and makes extensive use of boldface type to highlight the contents
of the main theorems. It includes a self-contained introduction to the
framework of general probabilistic theories and a discussion about the role
of causality and local discriminabilit
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
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