arXiv subjects

Rafael Peñaloza

Publications and source records attributed to Rafael Peñaloza.

31 records · Page 2Linked to original sources

arXiv2020

Reasoning with Contextual Knowledge and Influence Diagrams

Influence diagrams (IDs) are well-known formalisms extending Bayesian networks to model decision situations under uncertainty. Although they are convenient as a decision theoretic tool, their knowledge representation ability is limited in capturing other crucial notions such as logical consistency. We complement IDs with the light-weight description logic (DL) EL to overcome such limitations. We consider a setup where DL axioms hold in some contexts, yet the actual context is uncertain. The framework benefits from the convenience of using DL as a domain knowledge representation language and the modelling strength of IDs to deal with decisions over contexts in the presence of contextual uncertainty. We define related reasoning problems and study their computational complexity.

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arXiv2020

Axiom Pinpointing

Axiom pinpointing refers to the task of finding the specific axioms in an ontology which are responsible for a consequence to follow. This task has been studied, under different names, in many research areas, leading to a reformulation and reinvention of techniques. In this work, we present a general overview to axiom pinpointing, providing the basic notions, different approaches for solving it, and some variations and applications which have been considered in the literature. This should serve as a starting point for researchers interested in related problems, with an ample bibliography for delving deeper into the details.

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arXiv2019

Temporal Logics Over Finite Traces with Uncertainty (Technical Report)

Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of uncertainty which cannot be handled with classical logics. We thus propose a new probabilistic temporal logic over finite traces using superposition semantics, where all possible evolutions are possible, until observed. We study the properties of the logic and provide automata-based mechanisms for deriving probabilistic inferences from its formulas. We then study a fragment of the logic with better computational properties. Notably, formulas in this fragment can be discovered from event log data using off-the-shelf existing declarative process discovery techniques.

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arXiv2018

Cutting Diamonds: Temporal DLs with Probabilistic Distributions over Data

Recent work has studied a probabilistic extension of the temporal logic LTL that refines the eventuality (or diamond) constructor with a probability distribution on when will this eventuality be satisfied. In this paper, we adapt this notion to a well established temporal extension of DL-Lite, allowing the new probabilistic constructor only in the ABox assertions. We investigate the satisfiability problem of this new temporal DL over equiparametric geometric distributions.

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arXiv2018

Query Answering for Rough EL Ontologies (Extended Technical Report)

Querying large datasets with incomplete and vague data is still a challenge. Ontology-based query answering extends standard database query answering by background knowledge from an ontology to augment incomplete data. We focus on ontologies written in rough description logics (DLs), which allow to represent vague knowledge by partitioning the domain of discourse into classes of indiscernible elements. In this paper, we extend the combined approach for ontology-based query answering to a variant of the DL EL augmented with rough concept constructors. We show that this extension preserves the good computational properties of classical EL and can be implemented by standard database systems.

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arXiv2018

Repairing Description Logic Ontologies by Weakening Axioms

The classical approach for repairing a Description Logic ontology O in the sense of removing an unwanted consequence $α$ is to delete a minimal number of axioms from O such that the resulting ontology O' does not have the consequence $α$. However, the complete deletion of axioms may be too rough, in the sense that it may also remove consequences that are actually wanted. To alleviate this problem, we propose a more gentle way of repair in which axioms are not necessarily deleted, but only weakened. On the one hand, we investigate general properties of this gentle repair method. On the other hand, we propose and analyze concrete approaches for weakening axioms expressed in the Description Logic EL.

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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.

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arXiv2017

A Decidable Very Expressive Description Logic for Databases (Extended Version)

We introduce $\mathcal{DLR}^+$, an extension of the n-ary propositionally closed description logic $\mathcal{DLR}$ to deal with attribute-labelled tuples (generalising the positional notation), projections of relations, and global and local objectification of relations, able to express inclusion, functional, key, and external uniqueness dependencies. The logic is equipped with both TBox and ABox axioms. We show how a simple syntactic restriction on the appearance of projections sharing common attributes in a $\mathcal{DLR}^+$ knowledge base makes reasoning in the language decidable with the same computational complexity as $\mathcal{DLR}$. The obtained $\mathcal{DLR}^\pm$ n-ary description logic is able to encode more thoroughly conceptual data models such as EER, UML, and ORM.

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arXiv2017

Towards Statistical Reasoning in Description Logics over Finite Domains (Full Version)

We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical consequences of these proportions. After introducing some general reasoning problems and analyzing their properties, we present first algorithms and complexity results for reasoning in some fragments of Statistical $\mathcal{ALC}$.

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arXiv2016

Probabilistic Reasoning in the Description Logic ALCP with the Principle of Maximum Entropy (Full Version)

A central question for knowledge representation is how to encode and handle uncertain knowledge adequately. We introduce the probabilistic description logic ALCP that is designed for representing context-dependent knowledge, where the actual context taking place is uncertain. ALCP allows the expression of logical dependencies on the domain and probabilistic dependencies on the possible contexts. In order to draw probabilistic conclusions, we employ the principle of maximum entropy. We provide reasoning algorithms for this logic, and show that it satisfies several desirable properties of probabilistic logics.

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arXiv2015

Answering Fuzzy Conjunctive Queries over Finitely Valued Fuzzy Ontologies

Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of degrees of truth. To answer such queries, we extend a well-known technique that reduces the fuzzy ontology to a classical one, and use classical DL reasoners as a black box. We improve the complexity of previous reduction techniques for finitely valued fuzzy DLs, which allows us to prove tight complexity results for answering certain kinds of fuzzy CQs. We conclude with an experimental evaluation of a prototype implementation, showing the feasibility of our approach.

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arXiv2015

Reasoning in Infinitely Valued G-IALCQ

Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable in the presence of a negation constructor and general concept inclusion axioms. One exception to this negative result are FDLs whose semantics is based on the infinitely valued Gödel t-norm (G). In this paper, we extend previous decidability results for G-IALC to deal also with qualified number restrictions. Our novel approach is based on a combination of the known crispification technique for finitely valued FDLs and the automata-based procedure originally developed for reasoning in G-IALC. The proposed approach combines the advantages of these two methods, while removing their respective drawbacks.

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arXiv2015

Dynamic Bayesian Ontology Languages

Many formalisms combining ontology languages with uncertainty, usually in the form of probabilities, have been studied over the years. Most of these formalisms, however, assume that the probabilistic structure of the knowledge remains static over time. We present a general approach for extending ontology languages to handle time-evolving uncertainty represented by a dynamic Bayesian network. We show how reasoning in the original language and dynamic Bayesian inferences can be exploited for effective reasoning in our framework.

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