List of Talmudic principles
The Talmud uses many types of logical arguments.
Chazakah
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.)
De'oraita
A law is de'oraita (Hebrew: דאורייתא) if it is derived from the Torah. See also Derabanan (below).
Derabanan
A law is derabanan (Hebrew: דרבנן) if it is mandated by the Rabbinical sages. See also De'oraita (above).
Kal Vachomer (A fortiori)
A Kal Vachomer (Hebrew: קל וחומר, literally "lenient and strict") derives one law from another through the following logic: If a case that is generally strict has a particular leniency, a case that is generally lenient will certainly have that leniency. The argument can also work in reverse, and also in areas where lenient or strict might not be precisely applicable.
Migo
A Migo (Hebrew: מיגו, literally "out of" or "since") is an argument for a defendant that he ought to be believed regarding a certain claim, since he could have made a different claim which would definitely have been believed. For example, if someone admits to having borrowed money, and claims to have paid it back, he is believed because he could have claimed that he never borrowed the money in the first place. (This is assuming that there is no other evidence for the loan.) This argument does not work in several cases, such as to claim money from another (as opposed to defending one's own money), or to argue from a claim involving one item to another.