arXiv subjects

Ana Ozaki

Publications and source records attributed to Ana Ozaki.

34 records · Page 2Linked to original sources

arXiv2022

Extracting Rules from Neural Networks with Partial Interpretations

We investigate the problem of extracting rules, expressed in Horn logic, from neural network models. Our work is based on the exact learning model, in which a learner interacts with a teacher (the neural network model) via queries in order to learn an abstract target concept, which in our case is a set of Horn rules. We consider partial interpretations to formulate the queries. These can be understood as a representation of the world where part of the knowledge regarding the truthiness of propositions is unknown. We employ Angluin s algorithm for learning Horn rules via queries and evaluate our strategy empirically.

cs.LG↗

arXiv2022

Mining EL Bases with Adaptable Role Depth

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining EL bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining EL bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all EL concept inclusions holding in the interpretation, not only the ones up to a fixed role depth.

cs.LO↗

arXiv2022

Revising Ontologies via Models: The ALC-formula Case

Most approaches for repairing description logic (DL) ontologies aim at changing the axioms as little as possible while solving inconsistencies, incoherences and other types of undesired behaviours. As in Belief Change, these issues are often specified using logical formulae. Instead, in the new setting for updating DL ontologies that we propose here, the input for the change is given by a model which we want to add or remove. The main goal is to minimise the loss of information, without concerning with the syntactic structure. This new setting is motivated by scenarios where an ontology is built automatically and needs to be refined or updated. In such situations, the syntactical form is often irrelevant and the incoming information is not necessarily given as a formula. We define general operations and conditions on which they are applicable, and instantiate our approach to the case of ALC-formulae.

cs.LO↗

arXiv2022

First-order Temporal Logic on Finite Traces: Semantic Properties, Decidable Fragments, and Applications

Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and synthesis of programs, as well as in knowledge representation and reasoning. In this paper, we focus on first-order temporal logic on finite traces. We first investigate preservation of equivalences and satisfiability of formulas between finite and infinite traces, by providing a set of semantic and syntactic conditions to guarantee when the distinction between reasoning in the two cases can be blurred. Moreover, we show that the satisfiability problem on finite traces for several decidable fragments of first-order temporal logic is ExpSpace-complete, as in the infinite trace case, while it decreases to NExpTime when finite traces bounded in the number of instants are considered. This leads also to new complexity results for temporal description logics over finite traces. Finally, we investigate applications to planning and verification, in particular by establishing connections with the notions of insensitivity to infiniteness and safety from the literature.

cs.LO↗

arXiv2021

Geometric Models for (Temporally) Attributed Description Logics

In the search for knowledge graph embeddings that could capture ontological knowledge, geometric models of existential rules have been recently introduced. It has been shown that convex geometric regions capture the so-called quasi-chained rules. Attributed description logics (DL) have been defined to bridge the gap between DL languages and knowledge graphs, whose facts often come with various kinds of annotations that may need to be taken into account for reasoning. In particular, temporally attributed DLs are enriched by specific attributes whose semantics allows for some temporal reasoning. Considering that geometric models and (temporally) attributed DLs are promising tools designed for knowledge graphs, this paper investigates their compatibility, focusing on the attributed version of a Horn dialect of the DL-Lite family. We first adapt the definition of geometric models to attributed DLs and show that every satisfiable ontology has a convex geometric model. Our second contribution is a study of the impact of temporal attributes. We show that a temporally attributed DL may not have a convex geometric model in general but we can recover geometric satisfiability by imposing some restrictions on the use of the temporal attributes.

cs.LO↗

arXiv2021

On Free Description Logics with Definite Descriptions

Definite descriptions are phrases of the form 'the $x$ such that $φ$', used to refer to single entities in a context. They are often more meaningful to users than individual names alone, in particular when modelling or querying data over ontologies. We investigate free description logics with both individual names and definite descriptions as terms of the language, while also accounting for their possible lack of denotation. We focus on the extensions of $\mathcal{ALC}$ and, respectively, $\mathcal{EL}$ with nominals, the universal role, and definite descriptions. We show that standard reasoning in these extensions is not harder than in the original languages, and we characterise the expressive power of concepts relative to first-order formulas using a suitable notion of bisimulation. Moreover, we lay the foundations for automated support for definite descriptions generation by studying the complexity of deciding the existence of definite descriptions for an individual under an ontology. Finally, we provide a polynomial-time reduction of reasoning in other free description logic languages based on dual-domain semantics to the case of partial interpretations.

cs.LO↗

arXiv2021

Learning Description Logic Ontologies. Five Approaches. Where Do They Stand?

The quest for acquiring a formal representation of the knowledge of a domain of interest has attracted researchers with various backgrounds into a diverse field called ontology learning. We highlight classical machine learning and data mining approaches that have been proposed for (semi-)automating the creation of description logic (DL) ontologies. These are based on association rule mining, formal concept analysis, inductive logic programming, computational learning theory, and neural networks. We provide an overview of each approach and how it has been adapted for dealing with DL ontologies. Finally, we discuss the benefits and limitations of each of them for learning DL ontologies.

cs.AI↗

arXiv2021

On the Complexity of Learning Description Logic Ontologies

Ontologies are a popular way of representing domain knowledge, in particular, knowledge in domains related to life sciences. (Semi-)automating the process of building an ontology has attracted researchers from different communities into a field called "Ontology Learning". We provide a formal specification of the exact and the probably approximately correct learning models from computational learning theory. Then, we recall from the literature complexity results for learning lightweight description logic (DL) ontologies in these models. Finally, we highlight other approaches proposed in the literature for learning DL ontologies.

cs.AI↗

arXiv2020

Automated Reasoning in Temporal DL-Lite

This paper investigates the feasibility of automated reasoning over temporal DL-Lite (TDL-Lite) knowledge bases (KBs). We test the usage of off-the-shelf LTL reasoners to check satisfiability of TDL-Lite KBs. In particular, we test the robustness and the scalability of reasoners when dealing with TDL-Lite TBoxes paired with a temporal ABox. We conduct various experiments to analyse the performance of different reasoners by randomly generating TDL-Lite KBs and then measuring the running time and the size of the translations. Furthermore, in an effort to make the usage of TDL-Lite KBs a reality, we present a fully fledged tool with a graphical interface to design them. Our interface is based on conceptual modelling principles and it is integrated with our translation tool and a temporal reasoner.

cs.AI↗

arXiv2020

Learning Query Inseparable ELH Ontologies

We investigate the complexity of learning query inseparable ELH ontologies in a variant of Angluin's exact learning model. Given a fixed data instance A* and a query language Q, we are interested in computing an ontology H that entails the same queries as a target ontology T on A*, that is, H and T are inseparable w.r.t. A* and Q. The learner is allowed to pose two kinds of questions. The first is `Does (T,A)\models q?', with A an arbitrary data instance and q and query in Q. An oracle replies this question with `yes' or `no'. In the second, the learner asks `Are H and T inseparable w.r.t. A* and Q?'. If so, the learning process finishes, otherwise, the learner receives (A*,q) with q in Q, (T,A*)\models q and (H,A*)\not\models q (or vice-versa). Then, we analyse conditions in which query inseparability is preserved if A* changes. Finally, we consider the PAC learning model and a setting where the algorithms learn from a batch of classified data, limiting interactions with the oracles.

cs.AI↗

arXiv2020

On the Learnability of Possibilistic Theories

We investigate learnability of possibilistic theories from entailments in light of Angluin's exact learning model. We consider cases in which only membership, only equivalence, and both kinds of queries can be posed by the learner. We then show that, for a large class of problems, polynomial time learnability results for classical logic can be transferred to the respective possibilistic extension. In particular, it follows from our results that the possibilistic extension of propositional Horn theories is exactly learnable in polynomial time. As polynomial time learnability in the exact model is transferable to the classical probably approximately correct model extended with membership queries, our work also establishes such results in this model.

cs.LO↗

arXiv2019

Enriching Ontology-based Data Access with Provenance (Extended Version)

Ontology-based data access (OBDA) is a popular paradigm for querying heterogeneous data sources by connecting them through mappings to an ontology. In OBDA, it is often difficult to reconstruct why a tuple occurs in the answer of a query. We address this challenge by enriching OBDA with provenance semirings, taking inspiration from database theory. In particular, we investigate the problems of (i) deciding whether a provenance annotated OBDA instance entails a provenance annotated conjunctive query, and (ii) computing a polynomial representing the provenance of a query entailed by a provenance annotated OBDA instance. Differently from pure databases, in our case these polynomials may be infinite. To regain finiteness, we consider idempotent semirings, and study the complexity in the case of DL-Lite ontologies. We implement Task (ii) in a state-of-the-art OBDA system and show the practical feasibility of the approach through an extensive evaluation against two popular benchmarks.

cs.DB↗

arXiv2019

Learning Ontologies with Epistemic Reasoning: The EL Case

We investigate the problem of learning description logic ontologies from entailments via queries, using epistemic reasoning. We introduce a new learning model consisting of epistemic membership and example queries and show that polynomial learnability in this model coincides with polynomial learnability in Angluin's exact learning model with membership and equivalence queries. We then instantiate our learning framework to EL and show some complexity results for an epistemic extension of EL where epistemic operators can be applied over the axioms. Finally, we transfer known results for EL ontologies and its fragments to our learning model based on epistemic reasoning.

cs.AI↗

arXiv2018

Consequence-Based Axiom Pinpointing

Axiom pinpointing refers to the problem of finding the axioms in an ontology that are relevant for understanding a given entailment or consequence. One approach for axiom pinpointing, known as glass-box, is to modify a classical decision procedure for the entailments into a method that computes the solutions for the pinpointing problem. Recently, consequence-based decision procedures have been proposed as a promising alternative for tableaux-based reasoners for standard ontology languages. In this work, we present a general framework to extend consequence-based algorithms with axiom pinpointing.

cs.LO↗

arXiv2017

Exact Learning of Lightweight Description Logic Ontologies

We study the problem of learning description logic (DL) ontologies in Angluin et al.'s framework of exact learning via queries. We admit membership queries ("is a given subsumption entailed by the target ontology?") and equivalence queries ("is a given ontology equivalent to the target ontology?"). We present three main results: (1) ontologies formulated in (two relevant versions of) the description logic DL-Lite can be learned with polynomially many queries of polynomial size; (2) this is not the case for ontologies formulated in the description logic EL, even when only acyclic ontologies are admitted; and (3) ontologies formulated in a fragment of EL related to the web ontology language OWL 2 RL can be learned in polynomial time. We also show that neither membership nor equivalence queries alone are sufficient in cases (1) and (3).

cs.LG↗

arXiv2016

New Steps on the Exact Learning of CNF

A major problem in computational learning theory is whether the class of formulas in conjunctive normal form (CNF) is efficiently learnable. Although it is known that this class cannot be polynomially learned using either membership or equivalence queries alone, it is open whether CNF can be polynomially learned using both types of queries. One of the most important results concerning a restriction of the class CNF is that propositional Horn formulas are polynomial time learnable in Angluin's exact learning model with membership and equivalence queries. In this work we push this boundary and show that the class of multivalued dependency formulas (MVDF) is polynomially learnable from interpretations. We then provide a notion of reduction between learning problems in Angluin's model, showing that a transformation of the algorithm suffices to efficiently learn multivalued database dependencies from data relations. We also show via reductions that our main result extends well known previous results and allows us to find alternative solutions for them.

cs.LG↗