  We introduce Neuro-Symbolic Continual Learning, where a model has to solve a
sequence of neuro-symbolic tasks, that is, it has to map sub-symbolic inputs to
high-level concepts and compute predictions by reasoning consistently with
prior knowledge. Our key observation is that neuro-symbolic tasks, although
different, often share concepts whose semantics remains stable over time.
Traditional approaches fall short: existing continual strategies ignore
knowledge altogether, while stock neuro-symbolic architectures suffer from
catastrophic forgetting. We show that leveraging prior knowledge by combining
neuro-symbolic architectures with continual strategies does help avoid
catastrophic forgetting, but also that doing so can yield models affected by
reasoning shortcuts. These undermine the semantics of the acquired concepts,
even when detailed prior knowledge is provided upfront and inference is exact,
and in turn continual performance. To overcome these issues, we introduce COOL,
a COncept-level cOntinual Learning strategy tailored for neuro-symbolic
continual problems that acquires high-quality concepts and remembers them over
time. Our experiments on three novel benchmarks highlights how COOL attains
sustained high performance on neuro-symbolic continual learning tasks in which
other strategies fail.
