These rules had been in use long before Hillel analyzed them and wrote them down. He simply explicated them for use when expounding the Law of the Torah.
Hillel's rules of logic for interpreting the Torah are:
Kal vachomer (Light and heavy) That which applies in a less important case will apply in a more important case, and vice versa.
2. Gezeirah shavah (Equivalence of expresions) An analogy can be made between two separate texts on the basis of a similar phrase, word, or root.
3. Binyan av When a principle is found in several passages, A consideration found in one passage applies all of them.
4. Kelal ufrat (The general and the particular) A general principle may be restricted by a more detailed description of it in another verse.
5. Sh'enei ketuvim
(Standard from two passages) Two laws may be related together to form a principle, which then can be used to interpret other laws.
6. Ke yotzei bo mimakom acher (Like that in another place) An explanation of a word in one text can be clarified by use of same word in an unrelated text.
7. Davar halameid mi'inyano (Definition from context) The total context, not just the isolated statement, must be considered for an accurate interpretation.