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

TL;DR

This paper introduces MV-Datalog+-, an extension of Datalog for effective reasoning with uncertain, fuzzy observations using Lukasiewicz logic, maintaining desirable model-theoretic properties and enabling rule-based reasoning in uncertain scenarios.

Contribution

It extends Datalog and Datalog+- with fuzzy semantics based on Lukasiewicz logic, providing a framework for reasoning with uncertain observations and rules with existential quantification.

Findings

Fuzzy entailment can be decided via minimal fuzzy models.

Minimal fuzzy models are unique when they exist.

Models can be characterized by linear optimization over fixed-point outputs.

Abstract

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 (when they exist) 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+-. This paper is under consideration for acceptance in TPLP.