106,645 research outputs found
Learning definite Horn formulas from closure queries
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be learnable under different query learning settings, such as learning from membership and equivalence queries or learning from entailment. We propose yet a different type of query: the closure query. Closure queries are a natural extension of membership queries and also a variant, appropriate in the context of definite Horn formulas, of the so-called correction queries. We present an algorithm that learns conjunctions of definite Horn clauses in polynomial time, using closure and equivalence queries, and show how it relates to the canonical Guigues–Duquenne basis for implicational systems. We also show how the different query models mentioned relate to each other by either showing full-fledged reductions by means of query simulation (where possible), or by showing their connections in the context of particular algorithms that use them for learning definite Horn formulas.Peer ReviewedPostprint (author's final draft
Equivalences, Identities, Symmetric Differences, and Congruences in Orthomodular Lattices
It is shown that operations of equivalence cannot serve for building algebras
which would induce orthomodular lattices as the operations of implication can.
Several properties of equivalence operations have been investigated.
Distributivity of equivalence terms and several other 3 variable expressions
involving equivalence terms have been proved to hold in any orthomodular
lattice. Symmetric differences have been shown to reduce to complements of
equivalence terms. Some congruence relations related to equivalence operations
and symmetric differences have been considered.Comment: 13 pages, 1 figure, 1 table; To be published in International Journal
of Theoretical Physics, Vol. 42, No. 12 (2003); Web page:
http://m3k.grad.hr/pavici
On the Usability of Probably Approximately Correct Implication Bases
We revisit the notion of probably approximately correct implication bases
from the literature and present a first formulation in the language of formal
concept analysis, with the goal to investigate whether such bases represent a
suitable substitute for exact implication bases in practical use-cases. To this
end, we quantitatively examine the behavior of probably approximately correct
implication bases on artificial and real-world data sets and compare their
precision and recall with respect to their corresponding exact implication
bases. Using a small example, we also provide qualitative insight that
implications from probably approximately correct bases can still represent
meaningful knowledge from a given data set.Comment: 17 pages, 8 figures; typos added, corrected x-label on graph
Mapping-equivalence and oid-equivalence of single-function object-creating conjunctive queries
Conjunctive database queries have been extended with a mechanism for object
creation to capture important applications such as data exchange, data
integration, and ontology-based data access. Object creation generates new
object identifiers in the result, that do not belong to the set of constants in
the source database. The new object identifiers can be also seen as Skolem
terms. Hence, object-creating conjunctive queries can also be regarded as
restricted second-order tuple-generating dependencies (SO tgds), considered in
the data exchange literature.
In this paper, we focus on the class of single-function object-creating
conjunctive queries, or sifo CQs for short. We give a new characterization for
oid-equivalence of sifo CQs that is simpler than the one given by Hull and
Yoshikawa and places the problem in the complexity class NP. Our
characterization is based on Cohen's equivalence notions for conjunctive
queries with multiplicities. We also solve the logical entailment problem for
sifo CQs, showing that also this problem belongs to NP. Results by Pichler et
al. have shown that logical equivalence for more general classes of SO tgds is
either undecidable or decidable with as yet unknown complexity upper bounds.Comment: This revised version has been accepted on 11 January 2016 for
publication in The VLDB Journa
Topological representation for monadic implication algebras
In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.Fil: Abad, Manuel. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: Cimadamore, Cecilia Rossana. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - BahĂa Blanca. Instituto de Matemática BahĂa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahĂa Blanca; ArgentinaFil: DĂaz Varela, JosĂ© Patricio. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico Conicet - BahĂa Blanca. Instituto de Matemática BahĂa Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática BahĂa Blanca; Argentin
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