Minimal bases of temporal attribute implications

We deal with dependencies in object-attribute data which is recorded at separate points in time. The data is formalized by finitely many tables encoding the relationship between objects and attributes and each table can be seen as single formal context observed at separate point in time. Given such data, we are interested in concise ways of characterizing all if-then dependencies between attributes that hold in the data and are preserved in all time points. In order to formalize the dependencies, we use particular if-then rules called attribute implications annotated by time points which can be seen as particular formulas of linear temporal logic. We introduce non-redundant bases of dependencies from data as non-redundant sets entailing exactly all dependencies that hold in the data. In addition, we investigate minimality of bases as stronger form of non-redundancy. For given data, we present description of minimal bases using the notion of pseudo-intents generalized in the temporal setting. The present paper is a continuation of our previous paper on entailment of attribute implications annotated by time points.