97,152 research outputs found
Using small MUSes to explain how to solve pen and paper puzzles
Pen and paper puzzles like Sudoku, Futoshiki and Skyscrapers are hugely popular. Solving such puzzles can be a trivial task for modern AI systems. However, most AI systems solve problems using a form of backtracking, while people try to avoid backtracking as much as possible. This means that existing AI systems do not output explanations about their reasoning that are meaningful to people. We present Demystify, a tool which allows puzzles to be expressed in a high-level constraint programming language and uses MUSes to allow us to produce descriptions of steps in the puzzle solving. We give several improvements to the existing techniques for solving puzzles with MUSes, which allow us to solve a range of significantly more complex puzzles and give higher quality explanations. We demonstrate the effectiveness and generality of Demystify by comparing its results to documented strategies for solving a range of pen and paper puzzles by hand, showing that our technique can find many of the same explanations.Publisher PD
Combination of convex theories: Modularity, deduction completeness, and explanation
AbstractDecision procedures are key components of theorem provers and constraint satisfaction systems. Their modular combination is of prime interest for building efficient systems, but their effective use is often limited by poor interface capabilities, when such procedures only provide a simple “sat/unsat” answer. In this paper, we develop a framework to design cooperation schemas between such procedures while maintaining modularity of their interfaces. First, we use the framework to specify and prove the correctness of classic combination schemas by Nelson–Oppen and Shostak. Second, we introduce the concept of deduction complete satisfiability procedures, we show how to build them for large classes of theories, then we provide a schema to modularly combine them. Third, we consider the problem of modularly constructing explanations for combinations by re-using available proof-producing procedures for the component theories
3D reduction of the N-body Bethe-Salpeter equation
We perform a 3D reduction of the two-fermion Bethe-Salpeter equation, by
series expansion around a positive-energy instantaneous approximation of the
Bethe-Salpeter kernel, followed by another series expansion at the 3D level in
order to get a manifestly hermitian 3D potential. It turns out that this
potential does not depend on the choice of the starting approximation of the
kernel anymore, and can be written in a very compact form. This result can also
be obtained directly by starting with an approximation of the free propagator,
based on integrals in the relative energies instead of the more usual
delta-constraint. Furthermore, the method can be generalized to a system of N
particles, consisting in any combination of bosons and fermions. As an example,
we write the 3D equation for systems of two or three fermions exchanging
photons, in Feynman or Coulomb's gauge.Comment: 22 pages, 3 figures in one single ps file. In the first revision, the
self-energy corrections to the propagator have been taken into account. The
three figures were gathered in a single ps file instead of three eps. In this
second revision (after submission to Nuclear Physics A and refereeing) some
explanations have been added, plus a new subsection about the scattering of a
particle by a bound stat
Value withdrawal explanations: a theoretical tool for programming environments
Constraint logic programming combines declarativity and efficiency thanks to
constraint solvers implemented for specific domains. Value withdrawal
explanations have been efficiently used in several constraints programming
environments but there does not exist any formalization of them. This paper is
an attempt to fill this lack. Furthermore, we hope that this theoretical tool
could help to validate some programming environments. A value withdrawal
explanation is a tree describing the withdrawal of a value during a domain
reduction by local consistency notions and labeling. Domain reduction is
formalized by a search tree using two kinds of operators: operators for local
consistency notions and operators for labeling. These operators are defined by
sets of rules. Proof trees are built with respect to these rules. For each
removed value, there exists such a proof tree which is the withdrawal
explanation of this value.Comment: 14 pages; Alexandre Tessier, editor; WLPE 2002,
http://xxx.lanl.gov/abs/cs.SE/020705
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Meta-Constraints: to aid interaction and to provide explanations
We explore the use of meta-constraints as a way of providing explanations to the user. Meta-constraints can provide a summary of the state of the CPS, and thus form a way of leaving out a large amount of detail that would be unhelpful to the user when dealing with a large problem. The ideas are illustrated through the problem of University students selecting modules for their studies
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