13,250 research outputs found
Translating between Horn Representations and their Characteristic Models
Characteristic models are an alternative, model based, representation for
Horn expressions. It has been shown that these two representations are
incomparable and each has its advantages over the other. It is therefore
natural to ask what is the cost of translating, back and forth, between these
representations. Interestingly, the same translation questions arise in
database theory, where it has applications to the design of relational
databases. This paper studies the computational complexity of these problems.
Our main result is that the two translation problems are equivalent under
polynomial reductions, and that they are equivalent to the corresponding
decision problem. Namely, translating is equivalent to deciding whether a given
set of models is the set of characteristic models for a given Horn expression.
We also relate these problems to the hypergraph transversal problem, a well
known problem which is related to other applications in AI and for which no
polynomial time algorithm is known. It is shown that in general our translation
problems are at least as hard as the hypergraph transversal problem, and in a
special case they are equivalent to it.Comment: See http://www.jair.org/ for any accompanying file
Interpreting Embedding Models of Knowledge Bases: A Pedagogical Approach
Knowledge bases are employed in a variety of applications from natural
language processing to semantic web search; alas, in practice their usefulness
is hurt by their incompleteness. Embedding models attain state-of-the-art
accuracy in knowledge base completion, but their predictions are notoriously
hard to interpret. In this paper, we adapt "pedagogical approaches" (from the
literature on neural networks) so as to interpret embedding models by
extracting weighted Horn rules from them. We show how pedagogical approaches
have to be adapted to take upon the large-scale relational aspects of knowledge
bases and show experimentally their strengths and weaknesses.Comment: presented at 2018 ICML Workshop on Human Interpretability in Machine
Learning (WHI 2018), Stockholm, Swede
Holographic Embeddings of Knowledge Graphs
Learning embeddings of entities and relations is an efficient and versatile
method to perform machine learning on relational data such as knowledge graphs.
In this work, we propose holographic embeddings (HolE) to learn compositional
vector space representations of entire knowledge graphs. The proposed method is
related to holographic models of associative memory in that it employs circular
correlation to create compositional representations. By using correlation as
the compositional operator HolE can capture rich interactions but
simultaneously remains efficient to compute, easy to train, and scalable to
very large datasets. In extensive experiments we show that holographic
embeddings are able to outperform state-of-the-art methods for link prediction
in knowledge graphs and relational learning benchmark datasets.Comment: To appear in AAAI-1
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
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