200 research outputs found
Verification of Query Completeness over Processes [Extended Version]
Data completeness is an essential aspect of data quality, and has in turn a
huge impact on the effective management of companies. For example, statistics
are computed and audits are conducted in companies by implicitly placing the
strong assumption that the analysed data are complete. In this work, we are
interested in studying the problem of completeness of data produced by business
processes, to the aim of automatically assessing whether a given database query
can be answered with complete information in a certain state of the process. We
formalize so-called quality-aware processes that create data in the real world
and store it in the company's information system possibly at a later point.Comment: Extended version of a paper that was submitted to BPM 201
Query Stability in Monotonic Data-Aware Business Processes [Extended Version]
Organizations continuously accumulate data, often according to some business
processes. If one poses a query over such data for decision support, it is
important to know whether the query is stable, that is, whether the answers
will stay the same or may change in the future because business processes may
add further data. We investigate query stability for conjunctive queries. To
this end, we define a formalism that combines an explicit representation of the
control flow of a process with a specification of how data is read and inserted
into the database. We consider different restrictions of the process model and
the state of the system, such as negation in conditions, cyclic executions,
read access to written data, presence of pending process instances, and the
possibility to start fresh process instances. We identify for which facet
combinations stability of conjunctive queries is decidable and provide
encodings into variants of Datalog that are optimal with respect to the
worst-case complexity of the problem.Comment: This report is the extended version of a paper accepted at the 19th
International Conference on Database Theory (ICDT 2016), March 15-18, 2016 -
Bordeaux, Franc
Unification in monoidal theories is solving linear equations over semirings
Although for numerous equational theories unification algorithms have been developed there is still a lack of general methods. In this paper we apply algebraic techniques to the study of a whole class of theories, which we call monoidal. Our approach leads to general results on the structure of unification algorithms and the unification type of such theories. An equational theory is monoidal if it contains a binary operation which is associative and commutative, an identity for the binary operation, and an arbitrary number of unary symbols which are homomorphisms for the binary operation and the identity. Monoidal theories axiomatize varieties of abelian monoids. Examples are the theories of abelian monoids (AC), idempotent abelian monoids (ACI), and abelian groups. To every monoidal theory we associate a semiring. Intuitively, semirings are rings without subtraction. We show that every unification problem in a monoidal theory can be translated into a system of linear equations over the corresponding semiring. More specifically, problems without free constants are translated into homogeneous equations. For problems with free constants inhomogeneous equations have to be solved in addition. Exploiting the correspondence between unification and linear algebra we give algebraic characterizations of the unification type of a theory. In particular, we show that with respect to unification without constants monoidal theories are either unitary or nullary. Applying Hilbert\u27s Basis Theorem we prove that theories of groups with commuting homomorphisms are unitary with respect to unification with and without constants
The Unification Hierarchy is Undecidable
In unification theory, equational theories can be classified according to the existence and cardinality of minimal complete solution sets for equation systems. For unitary, finitary, and infinitary theories minimal complete solution sets always exist and are singletons, finite, or possibly infinite sets, respectively. In nullary theories, minimal complete sets do not exist for some equation systems. These classes form the unification hierarchy.
We show that it is not possible to decide where a given equational theory resides in the unification hierarchy. Moreover, it is proved that for some classes this problem is not even recursively enumerable
Subsumption algorithms for concept languages
We investigate the subsumption problem in logic-based knowledge representation languages of the KL-ONE family and give decision procedures. All our languages contain as a kernel the logical connectives conjunction, disjunction, and negation for concepts, as well as role quantification. The algorithms are rule-based and can be understood as variants of tableaux calculus with a special control strategy. In the first part of the paper, we add number restrictions and conjunction of roles to the kernel language. We show that subsumption in this language is decidable, and we investigate sublanguages for which the problem of deciding subsumption is PSPACE-complete. In the second part, we amalgamate the kernel language with feature descriptions as used in computational linguistics. We show that feature descriptions do not increase the complexity of the subsumption problem
Adding homomorphisms to commutative/monoidal theories or : how algebra can help in equational unification
Two approaches to equational unification can be distinguished. The syntactic approach relies heavily on the syntactic structure of the identities that define the equational theory. The semantic approach exploits the structure of the algebras that satisfy the theory. With this paper we pursue the semantic approach to unification. We consider the class of theories for which solving unification problems is equivalent to solving systems of linear equations over a semiring. This class has been introduced by the authors independently of each other as commutative theories (Baader) and monoidal theories (Nutt). The class encompasses important examples like the theories of abelian monoids, idempotent abelian monoids, and abelian groups. We identify a large subclass of commutative/monoidal theories that are of unification type zero by studying equations over the corresponding semiring. As a second result, we show with methods from linear algebra that unitary and finitary commutative/monoidal theories do not change their unification type when they are augmented by a finite monoid of homomorphisms, and how algorithms for the extended theory can be obtained from algorithms for the basic theory. The two results illustrate how using algebraic machinery can lead to general results and elegant proofs in unification theory
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
On abduction and answer generation through constrained resolution
Recently, extensions of constrained logic programming and constrained resolution for theorem proving have been introduced, that consider constraints, which are interpreted under an open world assumption. We discuss relationships between applications of these approaches for query answering in knowledge base systems on the one hand and abduction-based hypothetical reasoning on the other hand. We show both that constrained resolution can be used as an operationalization of (some limited form of) abduction and that abduction is the logical status of an answer generation process through constrained resolution, ie., it is an abductive but not a deductive form of reasoning
- …