167 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 individualâs 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 AlchourrĂłn, GĂ€rdenfors, 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&Mâs 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 âbaseâ, 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 âassignmentsâ: functions mapping belief bases to total â yet not transitive â âpreferenceâ 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&Mâs 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
Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic
This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvistâs B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL
, in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established
Combining Query Rewriting and Knowledge Graph Embeddings for Complex Query Answering
The field of complex query answering using Knowledge Graphs (KGs) has seen substantial advancements in recent years, primarily through the utilization of Knowledge Graph Embeddings (KGEs). However, these methodologies often stumble when faced with intricate query structures that involve multiple entities and relationships. This thesis primarily investigates the potential of integrating query rewriting techniques into the KGE query answering process to improve performance in such situations. Guided by a TBox, a schema that describes the concepts and relationships in the data from Description Logics, query rewriting translates a query into a union of rewritten queries that can potentially widen the prediction scope for KGEs. The thesis uses the PerfectRef algorithm for facilitating query rewriting, aiming to maximize the scope of query response and enhance prediction capabilities. Two distinct datasets were employed in the study: The Family Dataset, a subset of Wikidata, and DBPedia15k, a subset of DBPedia. The effectiveness of the proposed methodology was evaluated against these datasets using different KGE models, in our case TransE, DistMult, BoxE, RotatE, and CompGCN. The results demonstrate a notable improvement in complex query answering when query rewriting is used for both The Family dataset and DBPedia15k. Furthermore, the amalgamation of query rewriting and KGE predictions yielded a performance boost for The Family dataset. However, the same was not observed for DBPedia15k, likely due to discrepancies and errors present within DBPedia15k compared to the Full DBPedia KG used for validation in our framework. This research suggests that query rewriting, as a pre-processing step for KGE prediction, can enhance the performance of complex query answering, mainly when the dataset is not fully entailed. This study provides important insights into the potential and limitations of integrating query rewriting with KGEs. It may serve as a guidepost for future research to improve the complex query answering when a TBox is available.Masteroppgave i informatikkINF399MAMN-PROGMAMN-IN
Putting ABox Updates into Action
When trying to apply recently developed approaches for updating Description Logic ABoxes in the context of an action programming language, one encounters two problems. First, updates generate so-called Boolean ABoxes, which cannot be handled by traditional Description Logic reasoners. Second, iterated update operations result in very large Boolean ABoxes, which, however, contain a huge amount of redundant information. In this paper, we address both issues from a practical point of view
Updating Description Logic ABoxes
Aus dem Abstract:
Description logic (DL) ABoxes are a tool for describing the state of affairs in an application domain. In this paper, we consider the problem of updating ABoxes when the state changes. We assume that changes are described at an atomic level, i.e., in terms of possibly negated ABox assertions that involve only atomic concepts and roles. We analyze such basic ABox updates in several standard DLs by investigating whether the updated ABox can be expressed in these DLs and, if so, whether it is computable and what is its size
Extending the Description Logic ÏEL(deg) with Acyclic TBoxes
In a previous paper, we have introduced an extension of the lightweight Description Logic EL that allows us to define concepts in an approximate way. For this purpose, we have defined a graded membership function deg, which for each individual and concept yields a number in the interval [0; 1] expressing the degree to which the individual belongs to the concept. Threshold concepts C~t for ~ 2 â {, â„} then collect all the individuals that belong to C with degree ~ t. We have then investigated the complexity of reasoning in the Description Logic ÏEL(deg), which is obtained from EL by adding such threshold concepts. In the present paper, we extend these results, which were obtained for reasoning without TBoxes, to the case of reasoning w.r.t. acyclic TBoxes. Surprisingly, this is not as easy as might have been expected. On the one hand, one must be quite careful to define acyclic TBoxes such that they still just introduce abbreviations for complex concepts, and thus can be unfolded. On the other hand, it turns out that, in contrast to the case of EL, adding acyclic TBoxes to ÏEL(deg) increases the complexity of reasoning by at least on level of the polynomial hierarchy
Automated Reasoning
This volume, LNAI 13385, constitutes the refereed proceedings of the 11th International Joint Conference on Automated Reasoning, IJCAR 2022, held in Haifa, Israel, in August 2022. The 32 full research papers and 9 short papers presented together with two invited talks were carefully reviewed and selected from 85 submissions. The papers focus on the following topics: Satisfiability, SMT Solving,Arithmetic; Calculi and Orderings; Knowledge Representation and Jutsification; Choices, Invariance, Substitutions and Formalization; Modal Logics; Proofs System and Proofs Search; Evolution, Termination and Decision Prolems. This is an open access book
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