MV-Datalog+/-: Effective Rule-based Reasoning with Uncertain Observations (Extended Abstract)

Lanzinger, Matthias; Sferrazza, Stefano; Gottlob, Georg

doi:10.24963/ijcai.2023/718

Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence 2023

DOI: 10.24963/ijcai.2023/718

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MV-Datalog+/-: Effective Rule-based Reasoning with Uncertain Observations (Extended Abstract)

Matthias Lanzinger

Stefano Sferrazza

Georg Gottlob

Abstract: Modern data processing applications often combine information from a variety of complex sources. Oftentimes, some of these sources, like Machine-Learning systems or crowd-sourced data, are not strictly binary but associated with some degree of confidence in the observation. Ideally, reasoning over such data should take this additional information into account as much as possible. To this end, we propose extensions of Datalog and Datalog+/- to the semantics of Lukasiewicz logic Ł, one of the most common fuzzy l… Show more

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“…Preliminary ideas for t-Datalog (i.e., without existential quantification) were previously presented as an extended abstract[31].…”

mentioning

confidence: 99%

MV-Datalog+-: Effective Rule-based Reasoning with Uncertain Observations

Lanzinger¹,

Sferrazza²,

Gottlob³

2022

Theory and Practice of Logic Programming

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Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like machine-learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation. We propose MV-Datalog and $\mathrm{MV-Datalog}^\pm$ as extensions of Datalog and $\mathrm{Datalog}^\pm$ , respectively, to the fuzzy semantics of infinite-valued Łukasiewicz logic $\mathbf{L}$ as languages for effectively reasoning in scenarios where such uncertain observations occur. We show that the semantics of MV-Datalog exhibits similar model theoretic properties as Datalog. In particular, we show that (fuzzy) entailment can be decided via minimal fuzzy models. We show that when they exist, such minimal fuzzy models are unique and can be characterised in terms of a linear optimisation problem over the output of a fixed-point procedure. On the basis of this characterisation, we propose similar many-valued semantics for rules with existential quantification in the head, extending $\mathrm{Datalog}^\pm$ .

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“…Preliminary ideas for t-Datalog (i.e., without existential quantification) were previously presented as an extended abstract[31].…”

mentioning

confidence: 99%

MV-Datalog+-: Effective Rule-based Reasoning with Uncertain Observations

Lanzinger¹,

Sferrazza²,

Gottlob³

2022

Theory and Practice of Logic Programming

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Logical Rule-Based Knowledge Graph Reasoning: A Comprehensive Survey

Zeng,

Cheng,

2023

Mathematics

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With its powerful expressive capability and intuitive presentation, the knowledge graph has emerged as one of the primary forms of knowledge representation and management. However, the presence of biases in our cognitive and construction processes often leads to varying degrees of incompleteness and errors within knowledge graphs. To address this, reasoning becomes essential for supplementing and rectifying these shortcomings. Logical rule-based knowledge graph reasoning methods excel at performing inference by uncovering underlying logical rules, showcasing remarkable generalization ability and interpretability. Moreover, the flexibility of logical rules allows for seamless integration with diverse neural network models, thereby offering promising prospects for research and application. Despite the growing number of logical rule-based knowledge graph reasoning methods, a systematic classification and analysis of these approaches is lacking. In this review, we delve into the relevant research on logical rule-based knowledge graph reasoning, classifying them into four categories: methods based on inductive logic programming (ILP), methods that unify probabilistic graphical models and logical rules, methods that unify embedding techniques and logical rules, and methods that jointly use neural networks (NNs) and logical rules. We introduce and analyze the core concepts and key techniques, as well as the advantages and disadvantages associated with these methods, while also providing a comparative evaluation of their performance. Furthermore, we summarize the main problems and challenges, and offer insights into potential directions for future research.

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MV-Datalog+/-: Effective Rule-based Reasoning with Uncertain Observations (Extended Abstract)

Cited by 2 publications

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MV-Datalog+-: Effective Rule-based Reasoning with Uncertain Observations

MV-Datalog+-: Effective Rule-based Reasoning with Uncertain Observations

Logical Rule-Based Knowledge Graph Reasoning: A Comprehensive Survey

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