However we saw unit resolution for a propositional inference rule in the previous lecture:
(A? B, ¬B) /A
Thus we can take this a little further to propositional binary resolution:
A ? B, ¬ B ? C / A? C
There would be in Binary resolution gets its name from the fact that each sentence is a disjunction of exactly two literals. Thus we say here the two opposing literals B and ¬B are resolved - and they are removed where the disjunctions are merged.
Now in the binary resolution rule can be seen to be sound it means that if both A and C were false then at least one of the sentences at the top line would be false. Hence as this is an inference rule then we are supposing that the top line is true. So thus we can't have both A and C being false, that means either A or C must be true. After that we can infer the bottom line.