If I'm trying to decide what person he is in a sentence, I am making a
inference.
What kind of inference?

Explanation:

analogy :

an inference that if things agree in some respects they probably agree in others

corollary :

(logic) an inference that follows directly from the proof of another proposition

derivation :

a line of reasoning that shows how a conclusion follows logically from accepted propositions

deduction, entailment, implication :

something that is inferred (deduced or entailed or implied)

extrapolation :

an inference about the future (or about some hypothetical situation) based on known facts and observations

presumption :

(law) an inference of the truth of a fact from other facts proved or admitted or judicially noticed

abstract thought, logical thinking, reasoning :

thinking that is coherent and logical

well stockyards mean a large yard containing pens and sheds, typically adjacent to a slaughterhouse, in which livestock is kept and sorted. and i'm assuming that by party you   mean a large group of people which does make sense because chicago is a very crowded place much like new york. stockyards tend to take up a lot of room due to needing the area for pens to keep animals in and the fact that stockyards are usually right by slaughterhouse where they process and distribute the product. so its much like a zoo but with some dead animal products close by.

b. our party quickly made its way into the cave / but we failed to find our host [the cyclops] himself inside.