6 research outputs found
Consequence-based Reasoning for Description Logics with Disjunction, Inverse Roles, Number Restrictions, and Nominals
We present a consequence-based calculus for concept subsumption and
classification in the description logic ALCHOIQ, which extends ALC with role
hierarchies, inverse roles, number restrictions, and nominals. By using
standard transformations, our calculus extends to SROIQ, which covers all of
OWL 2 DL except for datatypes. A key feature of our calculus is its
pay-as-you-go behaviour: unlike existing algorithms, our calculus is worst-case
optimal for all the well-known proper fragments of ALCHOIQ, albeit not for the
full logic
On the Correspondence Between Monotonic Max-Sum GNNs and Datalog
Although there has been significant interest in applying machine learning
techniques to structured data, the expressivity (i.e., a description of what
can be learned) of such techniques is still poorly understood. In this paper,
we study data transformations based on graph neural networks (GNNs). First, we
note that the choice of how a dataset is encoded into a numeric form
processable by a GNN can obscure the characterisation of a model's
expressivity, and we argue that a canonical encoding provides an appropriate
basis. Second, we study the expressivity of monotonic max-sum GNNs, which cover
a subclass of GNNs with max and sum aggregation functions. We show that, for
each such GNN, one can compute a Datalog program such that applying the GNN to
any dataset produces the same facts as a single round of application of the
program's rules to the dataset. Monotonic max-sum GNNs can sum an unbounded
number of feature vectors which can result in arbitrarily large feature values,
whereas rule application requires only a bounded number of constants. Hence,
our result shows that the unbounded summation of monotonic max-sum GNNs does
not increase their expressive power. Third, we sharpen our result to the
subclass of monotonic max GNNs, which use only the max aggregation function,
and identify a corresponding class of Datalog programs
On the correspondence between monotonic max-sum GNNs and Datalog
Although there has been significant interest in applying machine learning techniques to structured data, the expressivity (i.e., a description of what can be learned) of such techniques is still poorly understood. In this paper, we study data transformations based on graph neural networks (GNNs). First, we note that the choice of how a dataset is encoded into a numeric form processable by a GNN can obscure the characterisation of a model's expressivity, and we argue that a canonical encoding provides an appropriate basis. Second, we study the expressivity of monotonic max-sum GNNs, which cover a subclass of GNNs with max and sum aggregation functions. We show that, for each such GNN, one can compute a Datalog program such that applying the GNN to any dataset produces the same facts as a single round of application of the program's rules to the dataset. Monotonic max-sum GNNs can sum an unbounded number of feature vectors which can result in arbitrarily large feature values, whereas rule application requires only a bounded number of constants. Hence, our result shows that the unbounded summation of monotonic max-sum GNNs does not increase their expressive power. Third, we sharpen our result to the subclass of monotonic max GNNs, which use only the max aggregation function, and identify a corresponding class of Datalog programs
The Stable Model Semantics of Datalog with Metric Temporal Operators
We introduce negation under the stable model semantics in DatalogMTL - a
temporal extension of Datalog with metric temporal operators. As a result, we
obtain a rule language which combines the power of answer set programming with
the temporal dimension provided by metric operators. We show that, in this
setting, reasoning becomes undecidable over the rational timeline, and
decidable in EXPSPACE in data complexity over the integer timeline. We also
show that, if we restrict our attention to forward-propagating programs,
reasoning over the integer timeline becomes PSPACE-complete in data complexity,
and hence, no harder than over positive programs; however, reasoning over the
rational timeline in this fragment remains undecidable. Under consideration in
Theory and Practice of Logic Programming (TPLP).Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Consequence-based reasoning for the Description Logic SROIQ
Consequence-based (CB) reasoners combine ideas from resolution and
(hyper)tableau calculi to solve the problem of ontology classification in
Description Logics (DLs). Existing CB reasoners, however, are only capable of handling DLs without nominals (such as SRIQ), or DLs without
disjunction (such as Horn-SROIQ). In this thesis, we present a novel
CB calculus for concept subsumption in the DL ALCHOIQ+, a logic
that extends ALC with role hierarchies, inverse roles, number restrictions, and nominals. To the best of our knowledge, ours is the first CB
calculus for an NExpTime-complete DL. By using standard transformations, our calculus extends to SROIQ, which covers all of OWL 2 DL
except for datatypes. A key feature of our calculus is its pay-as-you-go behaviour: the calculus is worst-case optimal for many well-known fragments of ALCHOIQ+, including ELH, Horn-ALCHOIQ+, and ALCHIQ+. Furthermore, the calculus is worst-case time exponential for the full logic ALCHOIQ+, except for cases where nominals, inverse roles, and number restrictions interact simultaneously, which are very rare in practice. Our calculus can also decide DL reasoning problems other than subsumption, such as ontology classification, instance retrieval, and realisation. We have implemented our calculus as an extension of the reasoner Sequoia, which previously supported ontology classification for SRIQ. Our implementation includes novel optimisation techniques that overcome some of the performance limitations affecting the previous version. We have carried out an empirical evaluation of our implementation which shows that the performance of Sequoia is competitive with other state-of-the-art systems. Our results also show that Sequoia nicely complements tableau-based reasoners, as it can more easily classify some ontologies. Thus, the calculus and implementation presented in this thesis provide an important addition to the repertoire of reasoning techniques and practical systems for expressive DLs
Explainable GNN-based models over knowledge graphs
Graph Neural Networks (GNNs) are often used to realise learnable transformations of graph data. While effective in practice, GNNs make predictions via numeric manipulations in an embedding space, so their output cannot be easily explained symbolically. In this paper, we propose a new family of GNN-based transformations of graph data that can be trained effectively, but where all predictions can be explained symbolically as logical inferences in Datalog—a well-known knowledge representation formalism. Specifically, we show how to encode an input knowledge graph into a graph with numeric feature vectors, process this graph using a GNN, and decode the result into an output knowledge graph. We use a new class of \emph{monotonic} GNNs (MGNNs) to ensure that this process is equivalent to a round of application of a set of Datalog rules. We also show that, given an arbitrary MGNN, we can extract automatically a set of rules that completely characterises the transformation. We evaluate our approach by applying it to classification tasks in knowledge graph completion