A conditional execution system and scheduler. Pretty much a self-hosted IFTTT. So far it doesn't have a lot of modules but that'll probably change at some point. Already following.
Rhasspy (pronounced RAH-SPEE) is an offline, multilingual voice assistant toolkit inspired by Jasper that works well with Home Assistant, Hass.io, and Node-RED. Designed so that you don't have to use any not-self-hosted software under the hood, from speech recognition to TTS. Emits JSON events. Vocabulary can be expanded with the automated assistance feature. Will run on something as simple as a RasPi but doesn't treat x86(-64) like a second-class citizen. Commands/intents are specified in a fairly easy templating language.
Stanford has open sourced a self-hosted, personal assistant system. Designed with privacy in mind. Speech recognition, analysis, task execution. They want to make so that it's easy and highly useful for everyone to integrate into their stuff. Can monitor things and filter for certain things. Aims for composability. Services (skills) are also open source and crowdsourced.
Github: https://github.com/stanford-oval
Another F/OSS personal assistant. Skill-based. Speech recognition and synthesis. Uses node.js and Python.
Jarvis is an ultra-light and multilingual voice assistant. Designed for home automation, it can run on energy efficient systems (eg Raspberry Pi). Very easy to use, it leaves you the choice of recognition engine and speech synthesis and installs them for you. It is extremely customizable, including via the addition of plugins. French and English.
FOSS AI personal assistant software. Implements actions/useful features, skills and API connectors. Can answer questions and ask for context for better answers (interesting!) Has a dedicated android app as well as a web interface. Written in Java, but nobody's perfect.