The concept is similar but not identical to Randolph Clarke‘s idea of a “narrow incompatibilist.” A narrow incompatibilist is an incompatibilist on free will and a compatibilist on moral responsibility. Confusingly, this can include those who believe in free will and those who deny free will. Semicompatibilists assert only their belief in moral responsibility. They are agnostic on free will and argue that moral responsibility exists whether determinism or indeterminism is “true.”
A broad incompatibilist sees determinism as incompatible with both free will and moral responsibility. Broad incompatibilists thus include (very confusingly) both those who accept and those who deny free will and moral responsibility. Those who deny one or both are variously called “hard incompatibilists,” “illusionists,” or “impossibilists.”
Here is a taxonomy of determinist and compatibilist positions showing where semicompatibilism fits.
Many of these philosophers reduce free will to the “control condition” for moral responsibility. This is to make freedom dependent on moral responsibility, which we call an ethical fallacy.
As Fischer says:
Some philosophers do not distinguish between freedom and moral responsibility. Put a bit more carefully, they tend to begin with the notion of moral responsibility, and “work back” to a notion of freedom; this notion of freedom is not given independent content (separate from the analysis of moral responsibility). For such philosophers, “freedom” refers to whatever conditions are involved in choosing or acting in such a way as to be morally responsible.
Free will is of course a prerequisite for responsibility. Questions about free will are scientific questions about the physical nature of minds. The question of moral responsibility is a moral and ethical question, not a question for physical science. We must separate the problem of free will from the issue of moral responsibility.
Fischer has written three books on moral responsibility and compiled what is the largest anthology of articles on free will, determinism, and moral responsibility – his four-volume, 46-contributor, 72-entry, 1300+ pages, Free Will, a reference work in the Routledge Critical Concepts in Philosophy series.
Although it is titled “Free Will,” the material is mostly about moral responsibility.
Fischer and his students and colleagues created two important blogs on Free Will and Moral Responsibility:
The Information Philosopher Blog 
Bernard Bars refers to the theatre of consciousness. This is a metaphor that I have used before where a heckling audience member surfaces like Dennett’s homunculi and William James’s aggregation. Innate moral sentiments are fundamentally attributed to Peter Strawson and his fellow compatibilists. John Martin Fischer’s Critical Concepts are more than just flickers of freedom. Thanks Bob for this research.
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48:40 Bob says, “… how is it that John Martin Fischer can defend that which we are going to call free?”. Bob is referring to an aspect of moral responsibility that exists as a cultural phenomenon. I agree that we can reason the unreasonable as a reflection of the free and conscious agent (actor) we can collectively refer to as humanity. How this reason surfaces is something best left to science and evolution.
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