6,255 research outputs found
Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of
ICLP 2015
Recent advances in knowledge compilation introduced techniques to compile
\emph{positive} logic programs into propositional logic, essentially exploiting
the constructive nature of the least fixpoint computation. This approach has
several advantages over existing approaches: it maintains logical equivalence,
does not require (expensive) loop-breaking preprocessing or the introduction of
auxiliary variables, and significantly outperforms existing algorithms.
Unfortunately, this technique is limited to \emph{negation-free} programs. In
this paper, we show how to extend it to general logic programs under the
well-founded semantics.
We develop our work in approximation fixpoint theory, an algebraical
framework that unifies semantics of different logics. As such, our algebraical
results are also applicable to autoepistemic logic, default logic and abstract
dialectical frameworks
Connectionist Theory Refinement: Genetically Searching the Space of Network Topologies
An algorithm that learns from a set of examples should ideally be able to
exploit the available resources of (a) abundant computing power and (b)
domain-specific knowledge to improve its ability to generalize. Connectionist
theory-refinement systems, which use background knowledge to select a neural
network's topology and initial weights, have proven to be effective at
exploiting domain-specific knowledge; however, most do not exploit available
computing power. This weakness occurs because they lack the ability to refine
the topology of the neural networks they produce, thereby limiting
generalization, especially when given impoverished domain theories. We present
the REGENT algorithm which uses (a) domain-specific knowledge to help create an
initial population of knowledge-based neural networks and (b) genetic operators
of crossover and mutation (specifically designed for knowledge-based networks)
to continually search for better network topologies. Experiments on three
real-world domains indicate that our new algorithm is able to significantly
increase generalization compared to a standard connectionist theory-refinement
system, as well as our previous algorithm for growing knowledge-based networks.Comment: See http://www.jair.org/ for any accompanying file
On Spatial Conjunction as Second-Order Logic
Spatial conjunction is a powerful construct for reasoning about dynamically
allocated data structures, as well as concurrent, distributed and mobile
computation. While researchers have identified many uses of spatial
conjunction, its precise expressive power compared to traditional logical
constructs was not previously known. In this paper we establish the expressive
power of spatial conjunction. We construct an embedding from first-order logic
with spatial conjunction into second-order logic, and more surprisingly, an
embedding from full second order logic into first-order logic with spatial
conjunction. These embeddings show that the satisfiability of formulas in
first-order logic with spatial conjunction is equivalent to the satisfiability
of formulas in second-order logic. These results explain the great expressive
power of spatial conjunction and can be used to show that adding unrestricted
spatial conjunction to a decidable logic leads to an undecidable logic. As one
example, we show that adding unrestricted spatial conjunction to two-variable
logic leads to undecidability. On the side of decidability, the embedding into
second-order logic immediately implies the decidability of first-order logic
with a form of spatial conjunction over trees. The embedding into spatial
conjunction also has useful consequences: because a restricted form of spatial
conjunction in two-variable logic preserves decidability, we obtain that a
correspondingly restricted form of second-order quantification in two-variable
logic is decidable. The resulting language generalizes the first-order theory
of boolean algebra over sets and is useful in reasoning about the contents of
data structures in object-oriented languages.Comment: 16 page
Symbolic Exact Inference for Discrete Probabilistic Programs
The computational burden of probabilistic inference remains a hurdle for
applying probabilistic programming languages to practical problems of interest.
In this work, we provide a semantic and algorithmic foundation for efficient
exact inference on discrete-valued finite-domain imperative probabilistic
programs. We leverage and generalize efficient inference procedures for
Bayesian networks, which exploit the structure of the network to decompose the
inference task, thereby avoiding full path enumeration. To do this, we first
compile probabilistic programs to a symbolic representation. Then we adapt
techniques from the probabilistic logic programming and artificial intelligence
communities in order to perform inference on the symbolic representation. We
formalize our approach, prove it sound, and experimentally validate it against
existing exact and approximate inference techniques. We show that our inference
approach is competitive with inference procedures specialized for Bayesian
networks, thereby expanding the class of probabilistic programs that can be
practically analyzed
The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty
Many real world domains require the representation of a measure of
uncertainty. The most common such representation is probability, and the
combination of probability with logic programs has given rise to the field of
Probabilistic Logic Programming (PLP), leading to languages such as the
Independent Choice Logic, Logic Programs with Annotated Disjunctions (LPADs),
Problog, PRISM and others. These languages share a similar distribution
semantics, and methods have been devised to translate programs between these
languages. The complexity of computing the probability of queries to these
general PLP programs is very high due to the need to combine the probabilities
of explanations that may not be exclusive. As one alternative, the PRISM system
reduces the complexity of query answering by restricting the form of programs
it can evaluate. As an entirely different alternative, Possibilistic Logic
Programs adopt a simpler metric of uncertainty than probability. Each of these
approaches -- general PLP, restricted PLP, and Possibilistic Logic Programming
-- can be useful in different domains depending on the form of uncertainty to
be represented, on the form of programs needed to model problems, and on the
scale of the problems to be solved. In this paper, we show how the PITA system,
which originally supported the general PLP language of LPADs, can also
efficiently support restricted PLP and Possibilistic Logic Programs. PITA
relies on tabling with answer subsumption and consists of a transformation
along with an API for library functions that interface with answer subsumption
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