NOTE: I will describe references used in the U.S. It is possible that relations are described differently in other countries and especially in languages other than English.Many people think that a "half first cousin" is someone who shares one grandparent with you but not both of them. For instance, my great-grandfather was married twice. He had several children by his first wife. The wife then died in childbirth and great-grandfather later remarried and had more children by his second wife. I am descended from great-grandfather and his first wife. I recently met a man who is descended from great-grandfather and his second wife. Some people would think that this other man and I are half-second cousins. "Half" apparently refers to a mistaken belief that we only share half the relationship because of our different great-grandmothers.
In fact, we are second cousins. Period.
In the United States, the standard reference for defining family relationships is Black's Law Dictionary. It is primarily a legal reference and is used by courts, lawyers, genealogical organizations, and many others.
Black's Law Dictionary defines first cousins as:
"The children of one's aunt or uncle."
Note that it says "aunt OR uncle," not both. All that is required is to share one aunt or one uncle, not both.Black's Law Dictionary defines second cousins as:
"Persons who are related to each other by descending from the same great-grandfather or great-grandmother."
Note that it says "the same great-grandfather OR great-grandmother," it does not say BOTH great-grandparents. Second cousins need to share only one great-grandparent. If they do share both great-grandparents, the relationship doesn't change; they are still second cousins.
Source citation: you can see an image of the appropriate page from Black's Law Dictionary at http://blacks.worldfreemansociety.org/2/C/c0293.jpgCanon law (religious law, usually referring to the Catholic church but other religions also have rules that may be referred to as Canon law) agrees with Black's legal definitions. I am including a Canon law relationship chart that is a bit complex to read but, with a little study, quickly shows all such relationships. (Double-click on the chart to see a larger image.)
To read the chart, start with the Common Progenitor at the top of the chart, abbreviated as CP. Note that all that is required is one progenitor, not two. Go down the left side of the chart to find the first person in question (son/daughter, grandson/daughter, great-grandson/daughter, etc.), then go down the right side of the chart to find the second person in question. Next, find where the two individuals intersect. The relationship might say "2 cous" for second cousin or perhaps "2 cous 1 r" for second cousin once removed.
Sadly, even some genealogy software perpetuates this myth concerning half-cousins. I have seen programs that automatically calculate family relationships and provide an answer of "half-cousins" or "half second cousins" or something similar. However, the standard references used in genealogy all disagree. To be blunt, such programs are wrong.
What's in your database?