Nāyaṁ

adjective noun “leading”; usually m: way (fig.), method, plan, manner; inference; sense, meaning (in grammar); behaviour, conduct AN.ii.193 = Cnd.151 (˚hetu through inference); Ne.2 (method), Ne.4 (id.), Ne.7, Ne.113; Mil.316 (nayena = nayahetu); Kp-a.74; Vv-a.112 (sense, context, sentence) Pv-a.1 (ways or conduct), Pv-a.117 (meaning), Pv-a.126 (id.), Pv-a.136, Pv-a.280
■ nayaṃ neti to draw a conclusion, apply an inference, judge, behave SN.ii.58 = Vb.329; Ja.iv.241 (anayaṃ nayati dummedho: draws a wrong conclusion) Pv-a.227 (+ anumināti)
■ With -ādi˚; N. has the function of continuing or completing the context “and similarly,” e.g. ˚ādinaya-pavatta dealing with this & the following Vv-a.2;… ti ādinā nayena thus & similarly, & so forth Ja.i.81; Pv-a.30
■ Instr. nayena (-˚) as adv. in the way of, as, according(ly): āgata according to what has been shown or said in… Ja.i.59; Vv-a.3; Pv-a.280; purima˚ as before Ja.i.59 Ja.iv.140; vutta˚ as said (above) (cp. vutta-niyāmena Pv-a.13, Pv-a.29, Pv-a.36, Pv-a.71, Pv-a.92 etc
■ sunaya a sound judgment Ja.iv.241; dunnaya a wrong principle, method or judgment, or as adj.: wrongly inferred, hard to be understood, unintelligible AN.iii.178 = Ne.21; Ja.iv.241.

from nayati, to lead, see neti

1. method, truth, system, later = logic: ˚gantha book on logic Dāvs iii.41.
2. fitness right manner, propriety, right conduct, often applied to the “right path” (ariyamagga = ariyañāya Vin.i.10) DN.iii.120; SN.v.19, SN.v.141, SN.v.167 sq., SN.v.185; AN.ii.95 AN.iv.426; AN.v.194; Dhp.i.249;
   ■ ariya ñ. SN.ii.68; SN.v.387; the causal law SN.v.388; = kalyāṇa-kusala-dhammatā AN.ii.36; used in apposition with dhamma and kusala DN.ii.151; MN.ii.181, MN.ii.197; is replaced herein by sacca SN.i.240; = Nibbāna at Vism.219, Vism.524;
   ■ ñ- paṭipanna walking in the right path SN.v.343; AN.ii.56; AN.iii.212, AN.iii.286 AN.v.183. -Nu

Sk. nyāya = ni + i