Hidden Markov Models, or HMMs, are a family of probabilistic models used for describing and analyzing sequential phenomena such as written and spoken text, biological sequences and sensor data from monitoring of hospital patients and industrial plants. An inherent characteristic of all HMM subspecies is their control by some sort of probabilistic, finite state machine, but which may differ in the detailed structure and specific sorts of conditional probabilities. In the literature, however, the different HMM subspecies tend to be described as separate kingdoms with their entrails and inference methods defined from scratch in each particular case. Here we suggest a unified characterization using a generic, probabilistic-logic framework and generic inference methods, which also promote experiments with new hybrids and mutations. This may even involve context dependencies that traditionally are considered beyond reach of HMMs.