5,801 research outputs found
Working with ARMs: Complexity Results on Atomic Representations of Herbrand Models
AbstractAn atomic representation of a Herbrand model (ARM) is a finite set of (not necessarily ground) atoms over a given Herbrand universe. Each ARM represents a possibly infinite Herbrand interpretation. This concept has emerged independently in different branches of computer science as a natural and useful generalization of the concept of finite Herbrand interpretation. It was shown that several recursively decidable problems on finite Herbrand models (or interpretations) remain decidable on ARMs.The following problems are essential when working with ARMs: Deciding the equivalence of two ARMs, deciding subsumption between ARMs, and evaluating clauses over ARMs. These problems were shown to be decidable, but their computational complexity has remained obscure so far. The previously published decision algorithms require exponential space. In this paper, we prove that all mentioned problems are coNP-complete
Unification in the Description Logic EL
The Description Logic EL has recently drawn considerable attention since, on
the one hand, important inference problems such as the subsumption problem are
polynomial. On the other hand, EL is used to define large biomedical
ontologies. Unification in Description Logics has been proposed as a novel
inference service that can, for example, be used to detect redundancies in
ontologies. The main result of this paper is that unification in EL is
decidable. More precisely, EL-unification is NP-complete, and thus has the same
complexity as EL-matching. We also show that, w.r.t. the unification type, EL
is less well-behaved: it is of type zero, which in particular implies that
there are unification problems that have no finite complete set of unifiers.Comment: 31page
Logical Reduction of Metarules
International audienceMany forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called derivation reduction, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperform subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times
Specific-to-General Learning for Temporal Events with Application to Learning Event Definitions from Video
We develop, analyze, and evaluate a novel, supervised, specific-to-general
learner for a simple temporal logic and use the resulting algorithm to learn
visual event definitions from video sequences. First, we introduce a simple,
propositional, temporal, event-description language called AMA that is
sufficiently expressive to represent many events yet sufficiently restrictive
to support learning. We then give algorithms, along with lower and upper
complexity bounds, for the subsumption and generalization problems for AMA
formulas. We present a positive-examples--only specific-to-general learning
method based on these algorithms. We also present a polynomial-time--computable
``syntactic'' subsumption test that implies semantic subsumption without being
equivalent to it. A generalization algorithm based on syntactic subsumption can
be used in place of semantic generalization to improve the asymptotic
complexity of the resulting learning algorithm. Finally, we apply this
algorithm to the task of learning relational event definitions from video and
show that it yields definitions that are competitive with hand-coded ones
Repairing Ontologies via Axiom Weakening.
Ontology engineering is a hard and error-prone task, in which
small changes may lead to errors, or even produce an inconsistent
ontology. As ontologies grow in size, the need for automated
methods for repairing inconsistencies while preserving
as much of the original knowledge as possible increases.
Most previous approaches to this task are based on removing
a few axioms from the ontology to regain consistency.
We propose a new method based on weakening these axioms
to make them less restrictive, employing the use of refinement
operators. We introduce the theoretical framework for
weakening DL ontologies, propose algorithms to repair ontologies
based on the framework, and provide an analysis of
the computational complexity. Through an empirical analysis
made over real-life ontologies, we show that our approach
preserves significantly more of the original knowledge of the
ontology than removing axioms
Semantic Matchmaking as Non-Monotonic Reasoning: A Description Logic Approach
Matchmaking arises when supply and demand meet in an electronic marketplace,
or when agents search for a web service to perform some task, or even when
recruiting agencies match curricula and job profiles. In such open
environments, the objective of a matchmaking process is to discover best
available offers to a given request. We address the problem of matchmaking from
a knowledge representation perspective, with a formalization based on
Description Logics. We devise Concept Abduction and Concept Contraction as
non-monotonic inferences in Description Logics suitable for modeling
matchmaking in a logical framework, and prove some related complexity results.
We also present reasonable algorithms for semantic matchmaking based on the
devised inferences, and prove that they obey to some commonsense properties.
Finally, we report on the implementation of the proposed matchmaking framework,
which has been used both as a mediator in e-marketplaces and for semantic web
services discovery
Decidable Reasoning in Terminological Knowledge Representation Systems
Terminological knowledge representation systems (TKRSs) are tools for
designing and using knowledge bases that make use of terminological languages
(or concept languages). We analyze from a theoretical point of view a TKRS
whose capabilities go beyond the ones of presently available TKRSs. The new
features studied, often required in practical applications, can be summarized
in three main points. First, we consider a highly expressive terminological
language, called ALCNR, including general complements of concepts, number
restrictions and role conjunction. Second, we allow to express inclusion
statements between general concepts, and terminological cycles as a particular
case. Third, we prove the decidability of a number of desirable TKRS-deduction
services (like satisfiability, subsumption and instance checking) through a
sound, complete and terminating calculus for reasoning in ALCNR-knowledge
bases. Our calculus extends the general technique of constraint systems. As a
byproduct of the proof, we get also the result that inclusion statements in
ALCNR can be simulated by terminological cycles, if descriptive semantics is
adopted.Comment: See http://www.jair.org/ for any accompanying file
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