
## Source Code: Openhyperpowerset.Java

1 /∗
2 ∗ Op enhyp e rpowe rset . j av a : p a r t o f pa ckag e R e f e r e eTo o lb ox ; **Im p l em e nt at ion** 3 ∗ **o f open h yp e rp ow e r s e t .**
4 **∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗**
5 ∗ Copyr ight ( c ) 2010 FrÃc dÃc **ric D am b r e v i l l e**
6 ∗
7 ∗ Author : FrÃc dÃc **ric D am b r e v i l l e <h t tp : / / em a i l . f r e d e r i c d a m b r e v i l l e . com>**
8 ∗ 9 ∗ **Th is f i l e i s p a r t o f R e f e r e eTo o lb ox .**
10 ∗
11 ∗ **R e f e r e eTo o lb ox i s f r e e s o f t w a r e : you can r e d i s t r i b u t e i t and/ o r mod i fy** 12 ∗ **i t und e r th e t e rms o f th e GNU G e n e r a l P u b l i c L i c e n s e a s p u b l i sh e d by** 13 ∗ **th e Fr e e S o f twa r e Foundat ion , e i t h e r v e r s i o n 3 o f th e L i c e n se , o r**
14 ∗ **( a t your o p t i o n ) any l a t e r v e r s i o n .**
15 ∗ 16 ∗ R e f e r e eTo o lb ox i s d i s t r i b u t e d i n th e hope th a t i t w i l l be u s e **f u l ,**
17 ∗ but WITHOUT ANY WARRANTY; w i th ou t ev en th e im p l i e d warranty o f 18 ∗ **MERCHANTABILITY o r FITNESS FOR A PARTICULAR PURPOSE. S e e the**
19 ∗ **GNU G e n e r a l P u b l i c L i c e n s e f o r more d e t a i l s .** 20 ∗
21 ∗ **You sh ou ld have r e c e i v e d a copy o f th e GNU G e n e r a l P u b l i c L i c en s e**
22 ∗ **a l on g w ith R e f e r e eTo o lb ox . I f not , s e e <h t tp : / /www . gnu . o rg / l i c e n s e s />.** 23 **∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗∗**
24 ∗/
25 26 **pa ckag e** RefereeToolbox ;
27 28 /∗∗
29 ∗ Im p l em e nt at ion o f an open h yp e rp ow e r s e t s t r u c t u r e . An open **h yp e rp ow e r s e t i s an** 30 ∗ h yp e rp ow e r s e t d e f i n e d on th e b a s i s o f a f r e e b o o l e an a l g e b r a **: i t i s g e n e r a t e d**
31 ∗ from th e atom i c p r o p o s i t i o n s o f th e f r e e b o o l e an a l g e b r a but **w i th ou t th e u s e o f** 32 ∗ **th e complement o p e r a t o r o f th e f r e e b o o l e an a l g e b r a .**
33 ∗ **<BR><BR>** 34 ∗ **The open h yp e rp ow e r s e t i m p l i e s an open wor ld h y p o t h e s i s , tha t i s :**
35 ∗**<BR><BR>**
36 ∗ **<i> <b>OR</b><sub>0 =< i < s i z eFram e </sub> atom i c ( i ) != one</ i>** 37 ∗ **<BR><BR>**
38 ∗ **A lthough g e n e r a t e d w i th ou t th e complement o f th e f r e e Boo l ean a l g e b r a , th e open**
39 ∗ **h yp e rp ow e r s e t a c t u a l l y has p r op e r complement and cocomp lement o p e r a t o r s .**
40 ∗ The complement and cocomp lement a r e d i s t i n c t o p e r a t o r s f o r **th e open** ←֓
h yp e rp ow e r s e t .

41 ∗
42 ∗ @author <A h r e f =" h t tp : / / em a i l . f r e d e r i c d a m b r e v i l l e . com">FrÃc dÃc ric ←֓
D am b r e v i l l e</A>
43 ∗ 44 ∗
45 ∗
46 ∗ **<BR><BR><t a b l e b o rd e r = '1 ' c e l l P a d d i n g ='4'>< t r><td>**
47 ∗ <f o n t c o l o r ="\#008000" s t y l e =" f on t−**f am i l y : g e o r g i a ">**
48 ∗ Copyr ight ( c ) 2010 FrÃc dÃc **ric D am b r e v i l l e<BR>**
49 ∗ **<BR>** 50 ∗ **R e f e r e eTo o lb ox i s f r e e s o f t w a r e : you can r e d i s t r i b u t e i t and/ o r mod i fy**
51 ∗ **i t und e r th e t e rms o f th e GNU G e n e r a l P u b l i c L i c e n s e a s p u b l i sh e d by**
52 ∗ **th e Fr e e S o f twa r e Foundat ion , e i t h e r v e r s i o n 3 o f th e L i c e n se , o r** 53 ∗ **( a t your o p t i o n ) any l a t e r v e r s i o n .<BR>** 54 ∗ **<BR>**
55 ∗ R e f e r e eTo o lb ox i s d i s t r i b u t e d i n th e hope th a t i t w i l l be u s e **f u l ,**
56 ∗ but WITHOUT ANY WARRANTY; w i th ou t ev en th e im p l i e d warranty o f 57 ∗ **MERCHANTABILITY o r FITNESS FOR A PARTICULAR PURPOSE. S e e the**
58 ∗ **GNU G e n e r a l P u b l i c L i c e n s e f o r more d e t a i l s .<BR>** 59 ∗ **<BR>**
60 ∗ **You sh ou ld have r e c e i v e d a copy o f th e GNU G e n e r a l P u b l i c L i c en s e** 61 ∗ **a l on g w ith R e f e r e eTo o lb ox . I f not , s e e**
62 ∗ **<a h r e f = ' h t tp : / /www . gnu . o r g / l i c e n s e s / '> h t tp : / /www . gnu . o r g / l i c e n s e s /</a>.**
63 ∗ **</f on t ></t a b l e><BR>** 64 ∗
65 ∗/
66 **p u b l i c c l a s s** Openhyperpowerset<L **e x t e nd s** Openhyperpowerset<L>> **e x t e nd s** Freeboolean ←֓
<L> {
67 **p r o t e c t e d** L theZero = **n u l l** ;
68 **p r o t e c t e d** L theOne = **n u l l** ;
69