The Talmud uses many types of logical arguments.
A Chazakah (Hebrew: חזקה) usually refers to the default assumption; i.e. what is assumed until there is evidence to the contrary. For example, if one is known to have owned property, it is assumed that he still owns it until proven otherwise. However, with movable items, the Chazakah lies with whoever currently has the item in his possession, not with the one who had previously owned it.
This principle also applies to non-monetary cases, such as that food known to be kosher maintains its status until there is evidence to the contrary. Also, one who engages in acts done only by Kohanim (priests) is assumed to be a kohen himself, until proven otherwise. (See status quo Kohen.)
A law is de'oraita (Hebrew: דאורייתא) if it is derived from the Torah; if a law is derabanan (Hebrew: דרבנן) it is mandated by the rabbinical sages. The concepts of de-'oraita (Aramaic: דאורייתא) and de-rabbanan (Aramaic: דרבנן) are used extensively in discussion of Jewish law and are of concern for modern observance of Judaism.
The former refers to halachic requirements that rabbinic literature understands to be Biblically mandated, while the latter refers to halachic requirements that are rabbinically mandated. In Aramaic, de-'oraita means "from the Torah" and de-rabbanan means from our Rabbis.