65 research outputs found
Description logics of context
We introduce Description Logics of Context (DLCs)—an extension of Description Logics (DLs) for context-based reasoning. Our approach descends from J. McCarthy's tradition of treating contexts as formal objects over which one can quantify and express first-order properties. DLCs are founded in two-dimensional possible world semantics, where one dimension represents a usual object domain and the other a domain of contexts, and accommodate two interacting DL languages—the object and the context language—interpreted over their respective domains. Effectively, DLCs comprise a family of two-sorted , two-dimensional combinations of pairs of DLs. We argue that this setup ensures a well-grounded, generic framework for capturing and studying mechanisms of contextualization in the DL paradigm. As the main technical contribution, we prove 2ExpTime-completeness of the satisfiability problem in the maximally expressive DLC, based on the DL forumla . As an interesting corollary, we show that under certain conditions this result holds also for a range of two-dimensional DLs, including the prominent forumla
Combining DL-LiteNbool with branching time: a gentle marriage
We study combinations of the description logic DL-Lite_{bool}^N with the branching temporal logics CTL* and CTL. We analyse two types of combinations, both with rigid roles: (i) temporal operators are applied to concepts and to ABox assertions, and (ii) temporal operators are applied to concepts and Boolean combinations of concept inclusions and ABox assertions. For the resulting logics, we present algorithms for the satisfiability problem and (mostly tight) complexity bounds ranging from ExpTime to 3ExpTime
Beyond the grounding bottleneck: Datalog techniques for inference in probabilistic logic programs
State-of-the-art inference approaches in probabilistic logic programming
typically start by computing the relevant ground program with respect to the
queries of interest, and then use this program for probabilistic inference
using knowledge compilation and weighted model counting. We propose an
alternative approach that uses efficient Datalog techniques to integrate
knowledge compilation with forward reasoning with a non-ground program. This
effectively eliminates the grounding bottleneck that so far has prohibited the
application of probabilistic logic programming in query answering scenarios
over knowledge graphs, while also providing fast approximations on classical
benchmarks in the field
Quantified Markov logic networks
Markov Logic Networks (MLNs) are well-suited for expressing statistics such as “with high probability a smoker knows another smoker” but not for expressing statements such as “there is a smoker who knows most other smokers”, which is necessary for modeling, e.g. influencers in social networks. To overcome this shortcoming, we study quantified MLNs which generalize MLNs by introducing statistical universal quantifiers, allowing to express also the latter type of statistics in a principled way. Our main technical contribution is to show that the standard reasoning tasks in quantified MLNs, maximum a posteriori and marginal inference, can be reduced to their respective MLN counterparts in polynomial time
Complexity of branching temporal description logics
We study branching-time temporal description logics (TDLs) based on the DLs ALC and EL and the temporal logics CTL and CTL*. The main contributions are algorithms for satisfiability that are more direct than existing approaches, and (mostly) tight elementary complexity bounds that range from PTIME to 2EXPTIME and 3EXPTIME. A careful use of tree automata techniques allows us to obtain transparent and uniform algorithms, avoiding to deal directly with the intricacies of CTL*
On metric temporal description logics
We introduce metric temporal description logics (mTDLs) as combinations of the classical description logic ALC with (a) LTLbin, an extension of the temporal logic LTL with succinctly represented intervals, and (b) metric temporal logic MTL, extending LTLbin with capabilities to quantitatively reason about time delays. Our main contributions are algorithms and tight complexity bounds for the satisfiability problem in these mTDLs: For mTDLs based on (fragments of) LTLbin, we establish complexity bounds ranging from EXPTIME to 2EXPSPACE. For mTDLs based on (fragments of) MTL interpreted over the naturals, we establish complexity bounds ranging from EXPSPACE to 2EXPSPACE
Reverse engineering queries in ontology-enriched systems: the case of expressive horn description logic ontologies
We introduce the query-by-example (QBE) paradigm for query answering in the presence of ontologies. Intuitively, QBE permits non-expert users to explore the data by providing examples of the information they (do not) want, which the system then generalizes into a query. Formally, we study the following question: given a knowledge base and sets of positive and negative examples, is there a query that returns all positive but none of the negative examples? We focus on description logic knowledge bases with ontologies formulated in Horn-ALCI and (unions of) conjunctive queries. Our main contributions are characterizations, algorithms and tight complexity bounds for QBE
Lightweight description logics and branching time: a troublesome marriage
We study branching-time temporal description logics
(BTDLs) based on the temporal logic CTL in the presence of
rigid (time-invariant) roles and general TBoxes. There is evidence
that, if full CTL is combined with the classical ALC
in this way, reasoning becomes undecidable. In this paper,
we begin by substantiating this claim, establishing undecidability
for a fragment of this combination. In view of this
negative result, we then investigate BTDLs that emerge from
combining fragments of CTL with lightweight DLs from the
EL and DL-Lite families. We show that even rather inexpressive
BTDLs based on EL exhibit very high complexity.
Most notably, we identify two convex fragments which are
undecidable and hard for non-elementary time, respectively.
For BTDLs based on DL-LiteN
bool, we obtain tight complexity
bounds that range from PSPACE to EXPTIME
ALC_ALC: A context description logic
We develop a novel description logic (DL) for representing
and reasoning with contextual knowledge. Our approach descends from
McCarthy’s tradition of treating contexts as formal objects over which
one can quantify and express first-order properties. As a foundation we
consider several common product-like combinations of DLs with multimodal
logics and adopt the prominent (Kn)ALC. We then extend it with
a second sort of vocabulary for describing contexts, i.e., objects of the
second dimension. In this way, we obtain a two-sorted, two-dimensional
combination of a pair of DLs ALC, called ALCALC. As our main technical
result, we show that the satisfiability problem in this logic, as well as in
its proper fragment (Kn)ALC with global TBoxes and local roles, is 2ExpTime-
complete. Hence, the surprising conclusion is that the significant
increase in the expressiveness of ALCALC due to adding the vocabulary
comes for no substantial price in terms of its worst-case complexity
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