logic, theory

(ごうり) Rational, but... actually more like ‘reasonable’ or ‘moderate’. (i.e. get up at a reasonable hour or a reasonable compromise) You can use 合理 even if there is not math proof involved.
(りろん) Theory, as in scientific theory or “theory vs. practice”
(ろんり) Logic. Logical - 論理的な.   $$$
(りくつ) There’s no exact English equivalent... maybe “rational argument that makes sense” ??? (The last kanji 屈 literally means “make someone yield”). Theory – as in theory vs. practice. (Opposite of 実際.) 理屈で言 ほど実際にはやさしくない – be not so easy in practice as in theory. 理屈 is often used in the negative, to mean, “That doesn’t make any sense!” Or, “You can’t reason with him. He won’t listen to reason.” 理屈 is also used in the expression 屁理屈 a.k.a. bullshit reasoning.