In the following example, the verb in the subordinate clause following "would know" is backshifted:
CIRCUS Manager:“All you have to do is look the lion in the eye and show him you're not afraid.”
Assistant: “Yes, but the lion would know I was just being deceitful.”
But, I also found the following sentences in English grammar text books:
It would seem there has been a mistake.
One would suppose the danger is over.
I should say that this book meets your requirements.
I should think it's going to rain soon.
What is the rule of tense backshift in a subordinate clause following a past form modal verb?
Best Answer
The first example you give is actually a past conditional construction. The "Yes, but" in the first example basically skips a conditional phrase, making it essentially a form of:
An alternative form, where there isn't any shifting, would be:
In this case, the verb "to be" isn't modified by the "would" directly per se, but the tense is changed to match the rest of the sentence.
Unfortunately, unlike some other languages, in English there often isn't any distinction between the subjunctive/conditional form of a verb and the past participle, so it can sometimes be tricky to tell which is being used in a given sentence.
As for the other examples:
The remaining ones are also unmodified, and as was mentioned in one of the comments, the "should" or "would" are basically particulate constructions - so you might occasionally hear them spoken colloquially, but they are really just there for emphasis and could just as well be left out (especially in the case of "I should think it's going to rain soon", which is synonymous with just "I think it's going to rain soon").
It should be noted, though, that the two involving "would" could also be used in a conditional sense - and if so, then the following verbs would also be modified similarly:
But generally speaking, "It would seem" and "I would think" are just common turns of phrase that don't take any modification - the "would" only serves as emphasis.