6,157 research outputs found
A map of dependencies among three-valued logics
International audienceThree-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value
Functional Dependencies in OWL ABox
Functional Dependency (FD) has been extensively studied in database theory. Most recently there have been some works investigating the implications of extending Description Logics with functional dependencies. In particular the OWL ontology language offers the functional property property allowing simple functional dependency to be specified. As it turns out, more complex FD specified as concept constructors has been proved to lead to undecidability in the general case, which restricts its usage as part of TBOX. This paper departs from previous ones by restricting FDs applicability to instances in the ABOX. We specify FD as a new constructor, an OWL concept. FD instances are mapped to Horn clauses and evaluated against the ABOX according to userâs desired behavior. The latter allows users to determine whether FDs should be interpreted as constraints, assertions or views. Our approach gives ontology users data guarantees usually found in databases, integrated with the ontology conceptual model
Equality-friendly well-founded semantics and applications to description logics
We tackle the problem of deïŹning a well-founded semantics (WFS) for Datalog rules with existentially quantiïŹed variables in their heads and nega- tions in their bodies. In particular, we provide a WFS for the recent Datalog± family of ontology languages, which covers several important description logics (DLs). To do so, we generalize Datalog± by non-stratiïŹed nonmonotonic nega- tion in rule bodies, and we deïŹne a WFS for this generalization via guarded ïŹxed point logic. We refer to this approach as equality-friendly WFS, since it has the advantage that it does not make the unique name assumption (UNA); this brings it close to OWL and its proïŹles as well as typical DLs, which also do not make the UNA. We prove that for guarded Datalog± with negation under the equality- friendly WFS, conjunctive query answering is decidable, and we provide precise complexity results for this problem. From these results, we obtain precise deïŹ- nitions of the standard WFS extensions of EL and of members of the DL-Lite family, as well as corresponding complexity results for query answering
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
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