1,544 research outputs found
Subsumption Algorithms for Three-Valued Geometric Resolution
In our implementation of geometric resolution, the most costly operation is
subsumption testing (or matching): One has to decide for a three-valued,
geometric formula, if this formula is false in a given interpretation. The
formula contains only atoms with variables, equality, and existential
quantifiers. The interpretation contains only atoms with constants. Because the
atoms have no term structure, matching for geometric resolution is hard. We
translate the matching problem into a generalized constraint satisfaction
problem, and discuss several approaches for solving it efficiently, one direct
algorithm and two translations to propositional SAT. After that, we study
filtering techniques based on local consistency checking. Such filtering
techniques can a priori refute a large percentage of generalized constraint
satisfaction problems. Finally, we adapt the matching algorithms in such a way
that they find solutions that use a minimal subset of the interpretation. The
adaptation can be combined with every matching algorithm. The techniques
presented in this paper may have applications in constraint solving independent
of geometric resolution.Comment: This version was revised on 18.05.201
Induction of Interpretable Possibilistic Logic Theories from Relational Data
The field of Statistical Relational Learning (SRL) is concerned with learning
probabilistic models from relational data. Learned SRL models are typically
represented using some kind of weighted logical formulas, which make them
considerably more interpretable than those obtained by e.g. neural networks. In
practice, however, these models are often still difficult to interpret
correctly, as they can contain many formulas that interact in non-trivial ways
and weights do not always have an intuitive meaning. To address this, we
propose a new SRL method which uses possibilistic logic to encode relational
models. Learned models are then essentially stratified classical theories,
which explicitly encode what can be derived with a given level of certainty.
Compared to Markov Logic Networks (MLNs), our method is faster and produces
considerably more interpretable models.Comment: Longer version of a paper appearing in IJCAI 201
Query Answering in Probabilistic Data and Knowledge Bases
Probabilistic data and knowledge bases are becoming increasingly important in academia and industry. They are continuously extended with new data, powered by modern information extraction tools that associate probabilities with knowledge base facts. The state of the art to store and process such data is founded on probabilistic database systems, which are widely and successfully employed. Beyond all the success stories, however, such systems still lack the fundamental machinery to convey some of the valuable knowledge hidden in them to the end user, which limits their potential applications in practice. In particular, in their classical form, such systems are typically based on strong, unrealistic limitations, such as the closed-world assumption, the closed-domain assumption, the tuple-independence assumption, and the lack of commonsense knowledge. These limitations do not only lead to unwanted consequences, but also put such systems on weak footing in important tasks, querying answering being a very central one. In this thesis, we enhance probabilistic data and knowledge bases with more realistic data models, thereby allowing for better means for querying them. Building on the long endeavor of unifying logic and probability, we develop different rigorous semantics for probabilistic data and knowledge bases, analyze their computational properties and identify sources of (in)tractability and design practical scalable query answering algorithms whenever possible. To achieve this, the current work brings together some recent paradigms from logics, probabilistic inference, and database theory
Focusing ATMS Problem-Solving: A Formal Approach
The Assumption-based Truth Maintenance System (ATMS) is a general and powerful problem-solving tool in AI. Unfortunately, its generality usually entails a high computational cost. In this paper, we study how a general notion of cost function can be incorporated into the design of an algorithm for focusing the ATMS, called BF-ATMS. The BF-ATMS algorithm explores a search space of size polynomial in the number of assumptions, even for problems which are proven to have exponential size labels. Experimental results indicate significant speedups over the standard ATMS for such problems. In addition to its improved efficiency, the BF-ATMS algorithm retains the multiple-context capability of an ATMS, and the important properties of consistency, minimality, soundness, as well as the property of bounded completeness. The usefulness of the new algorithm is demonstrated by its application to the task of consistency-based diagnosis, where dramatic efficiency improvements, with respect to the standard solution technique, are obtained
On Polynomial Sized MDP Succinct Policies
Policies of Markov Decision Processes (MDPs) determine the next action to
execute from the current state and, possibly, the history (the past states).
When the number of states is large, succinct representations are often used to
compactly represent both the MDPs and the policies in a reduced amount of
space. In this paper, some problems related to the size of succinctly
represented policies are analyzed. Namely, it is shown that some MDPs have
policies that can only be represented in space super-polynomial in the size of
the MDP, unless the polynomial hierarchy collapses. This fact motivates the
study of the problem of deciding whether a given MDP has a policy of a given
size and reward. Since some algorithms for MDPs work by finding a succinct
representation of the value function, the problem of deciding the existence of
a succinct representation of a value function of a given size and reward is
also considered
Logical settings for concept learning from incomplete examples in First Order Logic
We investigate here concept learning from incomplete examples. Our first
purpose is to discuss to what extent logical learning settings have to be
modified in order to cope with data incompleteness. More precisely we are
interested in extending the learning from interpretations setting introduced by
L. De Raedt that extends to relational representations the classical
propositional (or attribute-value) concept learning from examples framework. We
are inspired here by ideas presented by H. Hirsh in a work extending the
Version space inductive paradigm to incomplete data. H. Hirsh proposes to
slightly modify the notion of solution when dealing with incomplete examples: a
solution has to be a hypothesis compatible with all pieces of information
concerning the examples. We identify two main classes of incompleteness. First,
uncertainty deals with our state of knowledge concerning an example. Second,
generalization (or abstraction) deals with what part of the description of the
example is sufficient for the learning purpose. These two main sources of
incompleteness can be mixed up when only part of the useful information is
known. We discuss a general learning setting, referred to as "learning from
possibilities" that formalizes these ideas, then we present a more specific
learning setting, referred to as "assumption-based learning" that cope with
examples which uncertainty can be reduced when considering contextual
information outside of the proper description of the examples. Assumption-based
learning is illustrated on a recent work concerning the prediction of a
consensus secondary structure common to a set of RNA sequences
Stochastic Constraint Programming
To model combinatorial decision problems involving uncertainty and
probability, we introduce stochastic constraint programming. Stochastic
constraint programs contain both decision variables (which we can set) and
stochastic variables (which follow a probability distribution). They combine
together the best features of traditional constraint satisfaction, stochastic
integer programming, and stochastic satisfiability. We give a semantics for
stochastic constraint programs, and propose a number of complete algorithms and
approximation procedures. Finally, we discuss a number of extensions of
stochastic constraint programming to relax various assumptions like the
independence between stochastic variables, and compare with other approaches
for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial
Intelligenc
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