1,260 research outputs found
Fusions of Description Logics and Abstract Description Systems
Fusions are a simple way of combining logics. For normal modal logics,
fusions have been investigated in detail. In particular, it is known that,
under certain conditions, decidability transfers from the component logics to
their fusion. Though description logics are closely related to modal logics,
they are not necessarily normal. In addition, ABox reasoning in description
logics is not covered by the results from modal logics. In this paper, we
extend the decidability transfer results from normal modal logics to a large
class of description logics. To cover different description logics in a uniform
way, we introduce abstract description systems, which can be seen as a common
generalization of description and modal logics, and show the transfer results
in this general setting
On Fibring Semantics for BDI Logics
This study examines BDI logics in the context of Gabbay's fibring semantics. We show that dovetailing (a special form of fibring) can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach's incestual schema G^[a, b, c, d]. Further we exemplify the constraints required on fibring function to capture the semantics of interactions among modalities. The advantages of having a fibred approach is discussed in the final section
Worst-case Optimal Query Answering for Greedy Sets of Existential Rules and Their Subclasses
The need for an ontological layer on top of data, associated with advanced
reasoning mechanisms able to exploit the semantics encoded in ontologies, has
been acknowledged both in the database and knowledge representation
communities. We focus in this paper on the ontological query answering problem,
which consists of querying data while taking ontological knowledge into
account. More specifically, we establish complexities of the conjunctive query
entailment problem for classes of existential rules (also called
tuple-generating dependencies, Datalog+/- rules, or forall-exists-rules. Our
contribution is twofold. First, we introduce the class of greedy
bounded-treewidth sets (gbts) of rules, which covers guarded rules, and their
most well-known generalizations. We provide a generic algorithm for query
entailment under gbts, which is worst-case optimal for combined complexity with
or without bounded predicate arity, as well as for data complexity and query
complexity. Secondly, we classify several gbts classes, whose complexity was
unknown, with respect to combined complexity (with both unbounded and bounded
predicate arity) and data complexity to obtain a comprehensive picture of the
complexity of existential rule fragments that are based on diverse guardedness
notions. Upper bounds are provided by showing that the proposed algorithm is
optimal for all of them
Towards Resolution-based Reasoning for Connected Logics
AbstractThe method of connecting logics has gained a lot of attention in the knowledge representation and ontology communities because of its intuitive semantics and natural support for modular KR, its generality, and its robustness concerning decidability preservation. However, so far no dedicated automated reasoning solutions have been developed, and the only reasoning available was via translation into sufficiently expressive logics. In this paper, we present a simple modalised version of basic E-connections, and develop a sound, complete, and terminating resolution-based reasoning procedure. The approach is modular and can be extended to more expressive versions of E-connections
Clausal Resolution for Modal Logics of Confluence
We present a clausal resolution-based method for normal multimodal logics of
confluence, whose Kripke semantics are based on frames characterised by
appropriate instances of the Church-Rosser property. Here we restrict attention
to eight families of such logics. We show how the inference rules related to
the normal logics of confluence can be systematically obtained from the
parametrised axioms that characterise such systems. We discuss soundness,
completeness, and termination of the method. In particular, completeness can be
modularly proved by showing that the conclusions of each newly added inference
rule ensures that the corresponding conditions on frames hold. Some examples
are given in order to illustrate the use of the method.Comment: 15 pages, 1 figure. Preprint of the paper accepted to IJCAR 201
Complete Additivity and Modal Incompleteness
In this paper, we tell a story about incompleteness in modal logic. The story
weaves together a paper of van Benthem, `Syntactic aspects of modal
incompleteness theorems,' and a longstanding open question: whether every
normal modal logic can be characterized by a class of completely additive modal
algebras, or as we call them, V-BAOs. Using a first-order reformulation of the
property of complete additivity, we prove that the modal logic that starred in
van Benthem's paper resolves the open question in the negative. In addition,
for the case of bimodal logic, we show that there is a naturally occurring
logic that is incomplete with respect to V-BAOs, namely the provability logic
GLB. We also show that even logics that are unsound with respect to such
algebras do not have to be more complex than the classical propositional
calculus. On the other hand, we observe that it is undecidable whether a
syntactically defined logic is V-complete. After these results, we generalize
the Blok Dichotomy to degrees of V-incompleteness. In the end, we return to van
Benthem's theme of syntactic aspects of modal incompleteness
Dynamic Change Evaluation for Ontology Evolution in the Semantic Web
Changes in an ontology may have a disruptive impact on any system using it. This impact may depend on structural changes such as introduction or removal of concept definitions, or it may be related to a change in the expected performance of the reasoning tasks. As the number of systems using ontologies is expected to increase, and given the open nature of the Semantic Web, introduction of new ontologies and modifications to existing ones are to be expected. Dynamically handling such changes, without requiring human intervention, becomes crucial. This paper presents a framework that isolates groups of related axioms in an OWL ontology, so that a change in one or more axioms can be automatically localised to a part of the ontology
Towards a non monotonic description logics model
In order to deal with the Ontology Change problem and considering an environment where Description Logics (DLs) are used to describe ontologies, the question of how to integrate distributed ontologies appears to be in touch with Belief Revision since DL terminologies may define same concept descriptions of a not necessarily same world model. A possible alternative to reason about these concepts is to generate unique concept descriptions in a different terminology. This new terminology needs to be consistently created, trying to deal with the minimal change problem, and moreover, yielding a non-monotonic layer to express ontological knowledge in order to be further updated with new distributed ontologies.VII Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI
Ten virtues of structured graphs
This paper extends the invited talk by the first author about the virtues
of structured graphs. The motivation behind the talk and this paper relies on our
experience on the development of ADR, a formal approach for the design of styleconformant,
reconfigurable software systems. ADR is based on hierarchical graphs
with interfaces and it has been conceived in the attempt of reconciling software architectures
and process calculi by means of graphical methods. We have tried to
write an ADR agnostic paper where we raise some drawbacks of flat, unstructured
graphs for the design and analysis of software systems and we argue that hierarchical,
structured graphs can alleviate such drawbacks
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