608 research outputs found
Least Generalizations and Greatest Specializations of Sets of Clauses
The main operations in Inductive Logic Programming (ILP) are generalization
and specialization, which only make sense in a generality order. In ILP, the
three most important generality orders are subsumption, implication and
implication relative to background knowledge. The two languages used most often
are languages of clauses and languages of only Horn clauses. This gives a total
of six different ordered languages. In this paper, we give a systematic
treatment of the existence or non-existence of least generalizations and
greatest specializations of finite sets of clauses in each of these six ordered
sets. We survey results already obtained by others and also contribute some
answers of our own. Our main new results are, firstly, the existence of a
computable least generalization under implication of every finite set of
clauses containing at least one non-tautologous function-free clause (among
other, not necessarily function-free clauses). Secondly, we show that such a
least generalization need not exist under relative implication, not even if
both the set that is to be generalized and the background knowledge are
function-free. Thirdly, we give a complete discussion of existence and
non-existence of greatest specializations in each of the six ordered languages.Comment: See http://www.jair.org/ for any accompanying file
A Transformation-based Implementation for CLP with Qualification and Proximity
Uncertainty in logic programming has been widely investigated in the last
decades, leading to multiple extensions of the classical LP paradigm. However,
few of these are designed as extensions of the well-established and powerful
CLP scheme for Constraint Logic Programming. In a previous work we have
proposed the SQCLP (proximity-based qualified constraint logic programming)
scheme as a quite expressive extension of CLP with support for qualification
values and proximity relations as generalizations of uncertainty values and
similarity relations, respectively. In this paper we provide a transformation
technique for transforming SQCLP programs and goals into semantically
equivalent CLP programs and goals, and a practical Prolog-based implementation
of some particularly useful instances of the SQCLP scheme. We also illustrate,
by showing some simple-and working-examples, how the prototype can be
effectively used as a tool for solving problems where qualification values and
proximity relations play a key role. Intended use of SQCLP includes flexible
information retrieval applications.Comment: 49 pages, 5 figures, 1 table, preliminary version of an article of
the same title, published as Technical Report SIC-4-10, Universidad
Complutense, Departamento de Sistemas Inform\'aticos y Computaci\'on, Madrid,
Spai
Inductive Logic Programming in Databases: from Datalog to DL+log
In this paper we address an issue that has been brought to the attention of
the database community with the advent of the Semantic Web, i.e. the issue of
how ontologies (and semantics conveyed by them) can help solving typical
database problems, through a better understanding of KR aspects related to
databases. In particular, we investigate this issue from the ILP perspective by
considering two database problems, (i) the definition of views and (ii) the
definition of constraints, for a database whose schema is represented also by
means of an ontology. Both can be reformulated as ILP problems and can benefit
from the expressive and deductive power of the KR framework DL+log. We
illustrate the application scenarios by means of examples. Keywords: Inductive
Logic Programming, Relational Databases, Ontologies, Description Logics, Hybrid
Knowledge Representation and Reasoning Systems. Note: To appear in Theory and
Practice of Logic Programming (TPLP).Comment: 30 pages, 3 figures, 2 tables
Anti-Unification of Unordered Goals
Anti-unification in logic programming refers to the process of capturing common syntactic structure among given goals, computing a single new goal that is more general called a generalization of the given goals. Finding an arbitrary common generalization for two goals is trivial, but looking for those common generalizations that are either as large as possible (called largest common generalizations) or as specific as possible (called most specific generalizations) is a non-trivial optimization problem, in particular when goals are considered to be unordered sets of atoms. In this work we provide an in-depth study of the problem by defining two different generalization relations. We formulate a characterization of what constitutes a most specific generalization in both settings. While these generalizations can be computed in polynomial time, we show that when the number of variables in the generalization needs to be minimized, the problem becomes NP-hard. We subsequently revisit an abstraction of the largest common generalization when anti-unification is based on injective variable renamings, and prove that it can be computed in polynomially bounded time
Classification and representation of types in TDL
TDL is a typed feature-based representation language and inference system, specifically designed to support highly lexicalized constraint-based grammar theories. Type definitions in TDL consist of type and feature constraints over the full Boolean connectives together with coreferences, thus making TDL Turing-complete. TDL provides open- and closed-world reasoning over types. Working with partially as well as with fully expanded types is possible. Efficient reasoning in TDL is accomplished through specialized modules. In this paper, we will highlight the type/inheritance hierarchy module of TDL and show how we represent conjunctively and disjunctively defined types. Negated types and incompatible types are handled by specialized bottom symbols. Redefining a type only leads to the redefinition of the dependent types, and not to the redefinition of the whole grammar/lexicon. Undefined types are nothing special. Reasoning over the type hierarchy is partially realized by a bit vector encoding of types, similar to the one used in Aït-Kaci\u27s LOGIN. However, the underlying semantics does not harmonize with the open-world assumption of TDL. Thus, we have to generalize the GLB/LUB operation to account for this fact. The system, as presented in the paper, has been fully implemented in Common Lisp and is an integrated part of a large NL system. It has been installed and successfully employed at other sites and runs on various platforms
A workbench to develop ILP systems
Tese de mestrado integrado. Engenharia Informática e Computação. Faculdade de Engenharia. Universidade do Porto. 201
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