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

作     者：Lanzinger, Matthias Sferrazza, Stefano Gottlob, Georg 

作者机构：Univ Oxford Oxford OX1 2JD England Tech Univ Wien Vienna Austria 

出 版 物：《THEORY AND PRACTICE OF LOGIC PROGRAMMING》 (Theory Pract. Logic Programm.)

年 卷 期：2022年第22卷第5期

页      面：678-692页

核心收录：

学科分类：08[工学] 0835[工学-软件工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Austrian Science Fund (FWF) [P30930] Royal Society [RP\R1\ 201074] Royal Society "RAISON DATA" project [RP\R1\ 201074] Austrian Science Fund (FWF) [P30930] Funding Source: Austrian Science Fund (FWF) 

主　　题：Datalog fuzzy logic programming logic programming Lukasiewicz logic uncertainty in AI Datalog(+/-) 

摘      要：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 MV-Datalog(+/-) as extensions of Datalog and Datalog(+/-), respectively, to the fuzzy semantics of infinite-valued Lukasiewicz logic 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 Datalog(+/-).