Software systems for modelling and executing rules.
Standards: BPMN, DMN, SBVR
Sometimes framed as a subdiscipline of Business Process Management (BPM), "the discipline in which people use various methods to discover, model, analyze, measure, improve, optimize, and automate business processes." [Wikipedia]
Web-based tooling for BPMN, DMN, CMMN, and Forms | bpmn.io
Oracle Intelligent Advisor
IBM Operational Decision Manager
Drools: Open source, Rete-based, JSR94-compliant. Red Hat enterprise version is called JBoss. Friends with jBPM, if you also need a workflow engine
Camunda: FOSS BPM. Good DMN support
Bonita: FOSS BPM
OpenL Tablets: Open source, Java, uses Excel for decision tables
OpenRules
Jess: Rete-based, basis of JSR94 reference implementation. Seems… dead?