AbstractIt is introduced an immune dynamic n-valued Łukasiewicz logic $$ID{\L }_n$$
I
D
Ł
n
on the base of n-valued Łukasiewicz logic $${\L }_n$$
Ł
n
and corresponding to it immune dynamic $$MV_n$$
M
V
n
-algebra ($$IDL_n$$
I
D
L
n
-algebra), $$1< n < \omega $$
1
<
n
<
ω
, which are algebraic counterparts of the logic, that in turn represent two-sorted algebras $$(\mathcal {M}, \mathcal {R}, \Diamond )$$
(
M
,
R
,
◊
)
that combine the varieties of $$MV_n$$
M
V
n
-algebras $$\mathcal {M} = (M, \oplus , \odot , \sim , 0,1)$$
M
=
(
M
,
⊕
,
⊙
,
∼
,
0
,
1
)
and regular algebras $$\mathcal {R} = (R,\cup , ;, ^*)$$
R
=
(
R
,
∪
,
;
,
∗
)
into a single finitely axiomatized variety resembling R-module with “scalar” multiplication $$\Diamond $$
◊
. Kripke semantics is developed for immune dynamic Łukasiewicz logic $$ID{\L }_n$$
I
D
Ł
n
with application in immune system.
Augmented Lagrangian optimization under fixed-point arithmetic
