349 research outputs found
Belief Revision in Expressive Knowledge Representation Formalisms
We live in an era of data and information, where an immeasurable amount of discoveries, findings, events, news, and transactions are generated every second. Governments, companies, or individuals have to employ and process all that data for knowledge-based decision-making (i.e. a decision-making process that uses predetermined criteria to measure and ensure the optimal outcome for a specific topic), which then prompt them to view the knowledge as valuable resource. In this knowledge-based view, the capability to create and utilize knowledge is the key source of an organization or individual’s competitive advantage. This dynamic nature of knowledge leads us to the study of belief revision (or belief change), an area which emerged from work in philosophy and then impacted further developments in computer science and artificial intelligence.
In belief revision area, the AGM postulates by Alchourrón, Gärdenfors, and Makinson continue to represent a cornerstone in research related to belief change. Katsuno and Mendelzon (K&M) adopted the AGM postulates for changing belief bases and characterized AGM belief base revision in propositional logic over finite signatures. In this thesis, two research directions are considered. In the first, by considering the semantic point of view, we generalize K&M’s approach to the setting of (multiple) base revision in arbitrary Tarskian logics, covering all logics with a classical model-theoretic semantics and hence a wide variety of logics used in knowledge representation and beyond. Our generic formulation applies to various notions of “base”, such as belief sets, arbitrary or finite sets of sentences, or single sentences.
The core result is a representation theorem showing a two-way correspondence between AGM base revision operators and certain “assignments”: functions mapping belief bases to total — yet not transitive — “preference” relations between interpretations. Alongside, we present a companion result for the case when the AGM postulate of syntax-independence is abandoned. We also provide a characterization of all logics for which our result can be strengthened to assignments producing transitive preference relations (as in K&M’s original work), giving rise to two more representation theorems for such logics, according to syntax dependence vs. independence. The second research direction in this thesis explores two approaches for revising description logic knowledge bases under fixed-domain semantics, namely model-based approach and individual-based approach. In this logical setting, models of the knowledge bases can be enumerated and can be computed to produce the revision result, semantically. We show a characterization of the AGM revision operator for this logic and present a concrete model-based revision approach via distance between interpretations. In addition, by weakening the KB based on certain domain elements, a novel individual-based revision operator is provided as an alternative approach
OWL Reasoners still useable in 2023
In a systematic literature and software review over 100 OWL reasoners/systems
were analyzed to see if they would still be usable in 2023. This has never been
done in this capacity. OWL reasoners still play an important role in knowledge
organisation and management, but the last comprehensive surveys/studies are
more than 8 years old. The result of this work is a comprehensive list of 95
standalone OWL reasoners and systems using an OWL reasoner. For each item,
information on project pages, source code repositories and related
documentation was gathered. The raw research data is provided in a Github
repository for anyone to use
Finite-Cliquewidth Sets of Existential Rules: Toward a General Criterion for Decidable yet Highly Expressive Querying
In our pursuit of generic criteria for decidable ontology-based querying, we introduce finite-cliquewidth sets (fcs) of existential rules, a model-theoretically defined class of rule sets, inspired by the cliquewidth measure from graph theory. By a generic argument, we show that fcs ensures decidability of entailment for a sizable class of queries (dubbed DaMSOQs) subsuming conjunctive queries (CQs). The fcs class properly generalizes the class of finite-expansion sets (fes), and for signatures of arity ? 2, the class of bounded-treewidth sets (bts). For higher arities, bts is only indirectly subsumed by fcs by means of reification. Despite the generality of fcs, we provide a rule set with decidable CQ entailment (by virtue of first-order-rewritability) that falls outside fcs, thus demonstrating the incomparability of fcs and the class of finite-unification sets (fus). In spite of this, we show that if we restrict ourselves to single-headed rule sets over signatures of arity ? 2, then fcs subsumes fus
Answering regular path queries mediated by unrestricted SQ ontologies
A prime application of description logics is ontology-mediated query answering, with the query language often reaching far beyond instance queries. Here, we investigate this task for positive existential two-way regular path queries and ontologies formulated in the expressive description logic , where denotes the extension of the basic description logic with transitive roles () and qualified number restrictions () which can be unrestrictedly applied to both non-transitive and transitive roles (). Notably, the latter is usually forbidden in expressive description logics. As the main contribution, we show decidability of ontology-mediated query answering in that setting and establish tight complexity bounds, namely 2ExpTime-completeness in combined complexity and coNP-completeness in data complexity. Since the lower bounds are inherited from the fragment , we concentrate on providing upper bounds. As main technical tools we establish a tree-like countermodel property and a characterization of when a query is not satisfied in a tree-like interpretation. Together, these results allow us to use an automata-based approach to query answering
Saturation-based Boolean conjunctive query answering and rewriting for the guarded quantification fragments
Query answering is an important problem in AI, database and knowledge
representation. In this paper, we develop saturation-based Boolean conjunctive
query answering and rewriting procedures for the guarded, the loosely guarded
and the clique-guarded fragments. Our query answering procedure improves
existing resolution-based decision procedures for the guarded and the loosely
guarded fragments and this procedure solves Boolean conjunctive query answering
problems for the guarded, the loosely guarded and the clique-guarded fragments.
Based on this query answering procedure, we also introduce a novel
saturation-based query rewriting procedure for these guarded fragments. Unlike
mainstream query answering and rewriting methods, our procedures derive a
compact and reusable saturation, namely a closure of formulas, to handle the
challenge of querying for distributed datasets. This paper lays the theoretical
foundations for the first automated deduction decision procedures for Boolean
conjunctive query answering and the first saturation-based Boolean conjunctive
query rewriting in the guarded, the loosely guarded and the clique-guarded
fragments
Ontology-Based Query Answering for Probabilistic Temporal Data: Extended Version
We investigate ontology-based query answering for data that are both temporal and probabilistic, which might occur in contexts such as stream reasoning or situation recognition with uncertain data. We present a framework that allows to represent temporal probabilistic data, and introduce a query language with which complex temporal and probabilistic patterns can be described. Specifically, this language combines conjunctive queries with operators from linear time logic as well as probability operators. We analyse the complexities of evaluating queries in this language in various settings. While in some cases, combining the temporal and the probabilistic dimension in such a way comes at the cost of increased complexity, we also determine cases for which this increase can be avoided.This is an extended version of the article to appear in the proceedings of AAAI 2019
Using Model Theory to Find Decidable and Tractable Description Logics with Concrete Domains
Concrete domains have been introduced in the area of Description Logic (DL) to enable reference to concrete objects (such as numbers) and predefined predicates on these objects (such as numerical comparisons) when defining concepts. Unfortunately, in the presence of general concept inclusions (GCIs), which are supported by all modern DL systems, adding concrete domains may easily lead to undecidability.
To regain decidability of the DL ALC in the presence of GCIs, quite strong restrictions, called ω-admissibility, were imposed on the concrete domain. On the one hand, we generalize the notion of ω-admissibility from concrete domains with only binary predicates to concrete domains with predicates of arbitrary arity. On the other hand, we relate ω-admissibility to well-known notions from model theory. In particular, we show that finitely bounded homogeneous structures yield ω-admissible concrete domains. This allows us to show ω-admissibility of concrete domains using existing results from model theory.
When integrating concrete domains into lightweight DLs of the EL family, achieving decidability of reasoning is not enough. One wants the resulting DL to be tractable. This can be achieved by using so-called p-admissible concrete domains and restricting the interaction between the DL and the concrete domain. We investigate p-admissibility from an algebraic point of view. Again, this yields strong algebraic tools for demonstrating p-admissibility. In particular, we obtain an expressive numerical p-admissible concrete domain based on the rational numbers. Although ω-admissibility and p-admissibility are orthogonal conditions that are almost exclusive, our algebraic characterizations of these two properties allow us to locate an infinite class of p-admissible concrete domains whose integration into ALC yields
decidable DLs.
DL systems that can handle concrete domains allow their users to employ a fixed set of predicates of one or more fixed concrete domains when modelling concepts.
They do not provide their users with means for defining new predicates, let alone new concrete domains. The good news is that finitely bounded homogeneous structures offer precisely that. We show that integrating concrete domains based on finitely bounded homogeneous structures into ALC yields decidable DLs even if we allow predicates specified by first-order formulas. This class of structures also provides effective means for defining new ω-admissible concrete domains with at most binary predicates. The bad news is that defining ω-admissible concrete domains with predicates of higher arities is computationally hard. We obtain two new lower bounds for this meta-problem, but leave its decidability open. In contrast, we prove that there is no algorithm that would facilitate defining p-admissible concrete domains already for binary signatures.:1. Introduction . . . 1
2. Preliminaries . . . 5
3. Description Logics with Concrete Domains . . . 9
3.1. Basic definitions and undecidability results . . . 9
3.2. Decidable and tractable DLs with concrete domains . . . 16
4. A Model-Theoretic Analysis of ω-Admissibility . . . 23
4.1. Homomorphism ω-compactness via ω-categoricity . . . 23
4.2. Patchworks via homogeneity . . . 24
4.3. JDJEPD via decomposition into orbits . . . 27
4.4. Upper bounds via finite boundedness . . . 28
4.5. ω-admissible finitely bounded homogeneous structures . . . 32
4.6. ω-admissible homogeneous cores with a decidable CSP . . . 34
4.7. Coverage of the developed sufficient conditions . . . 36
4.8. Closure properties: homogeneity & finite boundedness . . . 39
5. A Model-Theoretic Analysis of p-Admissibility . . . 47
5.1. Convexity via square embeddings . . . 47
5.2. Convex ω-categorical structures . . . 50
5.3. Convex numerical structures . . . 52
5.4. Ages defined by forbidden substructures . . . 54
5.5. Ages defined by forbidden homomorphic images . . . 56
5.6. (Non-)closure properties of convexity . . . 59
6. Towards user-definable concrete domains . . . 61
6.1. A proof-theoretic perspective . . . 65
6.2. Universal Horn sentences and the JEP . . . 66
6.3. Universal sentences and the AP: the Horn case . . . 77
6.4. Universal sentences and the AP: the general case . . . 90
7. Conclusion . . . 99
7.1. Contributions and future outlook . . . 99
A. Concrete Domains without Equality . . . 103
Bibliography . . . 107
List of figures . . . 115
Alphabetical Index . . . 11
Maybe Eventually? Towards Combining Temporal and Probabilistic Description Logics and Queries: Extended Version
We present some initial results on ontology-based query answering with description logic ontologies that may employ temporal and probabilistic operators on concepts and axioms. Speci_cally, we consider description logics extended with operators from linear temporal logic (LTL), as well as subjective probability operators, and an extended query language in which conjunctive queries can be combined using these operators. We first show some complexity results for the setting in which either only temporal operators or only probabilistic operators may be used, both in the ontology and in the query, and then show a 2ExpSpace lower bound for the setting in which both types of operators can be used together.This is an extended version of an article accepted at Description Logics 2019
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