The early Buddhist texts are full of four-way analyses along the lines of "Either-or, Neither-nor, Both-and, Not both-and or Neither-nor"
Mahavira of Jains proposed seven kinds:
Affirmation:
syād-asti—in some ways, it is,
Denial:
syān-nāsti—in some ways, it is not,
Joint but successive affirmation and denial:
syād-asti-nāsti—in some ways, it is, and it is not,
Joint and simultaneous affirmation and denial:
syād-asti-avaktavyaḥ—in some ways, it is, and it is indescribable,
Joint and simultaneous affirmation and denial:
syān-nāsti-avaktavyaḥ—in some ways, it is not, and it is indescribable,
Joint and simultaneous affirmation and denial:
syād-asti-nāsti-avaktavyaḥ—in some ways, it is, it is not, and it is indescribable,
Joint and simultaneous affirmation and denial:
syād-avaktavyaḥ—in some ways, it is indescribable.
Hinduism too used these techniques and developed a separate philosophy for it - Nyāya.
https://en.wikipedia.org/wiki/Nyaya
"Nyāya, literally meaning "justice", "rules", "method" or "judgment", is one of the six orthodox (astika) schools of Hinduism. This school's most significant contributions to Indian philosophy was systematic development of the theory of logic, methodology, and its treatises on epistemology."