21,841 research outputs found
Operational Semantics of Resolution and Productivity in Horn Clause Logic
This paper presents a study of operational and type-theoretic properties of
different resolution strategies in Horn clause logic. We distinguish four
different kinds of resolution: resolution by unification (SLD-resolution),
resolution by term-matching, the recently introduced structural resolution, and
partial (or lazy) resolution. We express them all uniformly as abstract
reduction systems, which allows us to undertake a thorough comparative analysis
of their properties. To match this small-step semantics, we propose to take
Howard's System H as a type-theoretic semantic counterpart. Using System H, we
interpret Horn formulas as types, and a derivation for a given formula as the
proof term inhabiting the type given by the formula. We prove soundness of
these abstract reduction systems relative to System H, and we show completeness
of SLD-resolution and structural resolution relative to System H. We identify
conditions under which structural resolution is operationally equivalent to
SLD-resolution. We show correspondence between term-matching resolution for
Horn clause programs without existential variables and term rewriting.Comment: Journal Formal Aspect of Computing, 201
A Type-Theoretic Approach to Structural Resolution
Structural resolution (or S-resolution) is a newly proposed alternative to
SLD-resolution that allows a systematic separation of derivations into
term-matching and unification steps. Productive logic programs are those for
which term-matching reduction on any query must terminate. For productive
programs with coinductive meaning, finite term-rewriting reductions can be seen
as measures of observation in an infinite derivation. Ability of handling
corecursion in a productive way is an attractive computational feature of
S-resolution.
In this paper, we make first steps towards a better conceptual understanding
of operational properties of S-resolution as compared to SLD-resolution. To
this aim, we propose a type system for the analysis of both SLD-resolution and
S-resolution.
We formulate S-resolution and SLD-resolution as reduction systems, and show
their soundness relative to the type system. One of the central methods of this
paper is realizability transformation, which makes logic programs productive
and non-overlapping. We show that S-resolution and SLD-resolution are only
equivalent for programs with these two properties.Comment: LOPSTR 201
Entangling two atoms in spatially separated cavities through both photon emission and absorption processes
We consider a system consisting of a -type atom and a V-type atom,
which are individually trapped in two spatially separated cavities that are
connected by an optical fibre. We show that an extremely entangled state of the
two atoms can be deterministically generated through both photon emission of
the -type atom and photon absorption of the V-type atom in an ideal
situation. The influence of various decoherence processes such as spontaneous
emission and photon loss on the fidelity of the entangled state is also
investigated. We find that the effect of photon leakage out of the fibre on the
fidelity can be greatly diminished in some special cases. As regards the effect
of spontaneous emission and photon loss from the cavities, we find that the
present scheme with a fidelity higher than 0.98 may be realized under current
experiment conditions.Comment: 12 pages, 4 figure
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