nasin pi toki tu wan

nasin pi toki tu wan (toki Inli: syllogism, toki weka Elena: συλλογισμός, syllogismos, 'toki pini; toki pi pali lon') li toki pi tan lon kepeken pali pi lon kiwen tawa toki pini tan toki lon tu.

sama ni: jan sona e toki "jan ali li ken moli" (toki open suli) e toki "jan Sokate li jan" (toki open lili) la, jan li ken sona e ni: jan Sokate li ken moli. nasin li sitelen e linja tu wan ni:

jan ali li ken moli la;
jan Sokete li jan la;
tan ni la, jan Sokate li ken moli.

tenpo weka la, nasin tu li lon: nasin toki pi jan Alitotele en nasin toki pi nasin Sotowa

kule

nasin pi toki tu wan li jo e toki tu wan ni: toki open tu en toki pini. kule noke pi nasin toki li ni: nasin toki kule en nasin toki pilin en nasin toki tu

kule lili pi nasin toki kule

nasin toki kule li jo e sijelo ni (I - toki insa, L - toki lawa, P - toki pali):

toki open suli: I ale li P.

toki open lili: L ale li I.

toki pini: S ale li P.

toki open en toki pini li ken jo e sijelo ni: A anu E anu I anu O (o lukin e lipu anpa).

nimi	toki lawa	toki mute	toki linja	toki pali	kule	sama
A	L	ali	li	P	pona ale	jan ali li ken moli.
E	L	li lon ala	li	P	weka ale	jan li lon ala li ale pona
I	L	li lon	li	P	pona lon	jan li lon li jo sijelo pona.
O	L	li lon	li	P ala	weka lon	jan li lon li ike ala.

lon lipu Prior Analytics la, jan Alitotele li pali e sitelen A, B, C (sitelen Elena Alupa, Wita, Kanma).

lipu anpa ni li jo e sijelo e sitelen lili e sama pi nasin lon.

sijelo	sitelen lili	nasin lon
A ali li B	AaB	$\forall x.A(x)\rightarrow B(x)$ anu $\neg \exists x.A(x)\land \neg B(x)$
A li lon ala li B	AeB	$\neg \exists x.A(x)\land B(x)$ anu $\forall x.A(x)\rightarrow \neg B(x)$
A li lon li B	AiB	$\exists x.A(x)\land B(x)$
A li lon li B ala	AoB	$\exists x.A(x)\land \neg B(x)$

sijelo toki pi toki pini li L-P la, sijelo toki 4 li ni:

	sijelo #1	sijelo #2	sijelo #3	sijelo #4
toki open suli	I-P	P-I	I-P	P-I
toki open lili	L-I	L-I	I-L	I-L

sijelo lon pi nasin toki kule li ni:

sijelo #1	sijelo #2	sijelo #3	sijelo #4
Papala	Kesale	Tasisi	Kaleme
Kelale	Kamete	Sisami	Simati
Taliwi	Pesino	Pelison	Pesison
Pelijo	Paloko	Pokato	Kalemo
Papali	Kesalo	Pelaton	Pesapo
Kelalo	Kameto	Talasi	Pamali

sama ni:

sijelo Papala (AAA-1)

   jan ale li ken moli. (IaP)

   jan Elina ali li jan. (LaI)

∴ jan Elina ali li ken moli. (LaP)

sijelo Kelale (EAE-1)

sama: sijelo Kesale (EAE-2)

   akesi li lon ala li jo e linja sijelo. (IeP)

   akesi linja ali li akesi. (LaI)

∴ akesi linja li lon ala li jo e linja sijelo. (LeP)

sijelo Taliwi (AII-1)

sama: Tasisi (AII-3)

   kijetesantakalu ali li jo e linja sijelo. (IaP)

   soweli li lon li kijetesantakalu. (LiI)

∴ soweli li lon li jo e linja sijelo. (LaP)

sijelo Pelijo (EIO-1)

sama: sijelo Pesino (EIO-2), sijelo Pelison (EIO-3), sijelo Pesison (EIO-4)

   pali li lon ala li musi. (IeP)

   lukin sitelen li lon li pali. (LiI)

∴ lukin sitelen li lon li musi ala. (LoP)

sijelo Paloko (AOO-2)

   soweli lili li lon li soweli tomo ala. (IoP)

   soweli lili ali li soweli. (IoL)

∴ soweli li lon li soweli tomo ala. (LoP)