The most trained and fittest officers from 21 to 28 years of age have been deputed to protect US President Joe Biden who is expected to arrive in Delhi on September 8. The team will also have helicopters apart from the planes, which Biden will use for travelling
#PersonalSecurity #Hi-TechArms #Four #LeggedBomb #US #GuardPrezBiden #G20
https://www.news18.com/india/personal-security-hi-tech-arms-four-legged-bomb-detectors-how-us-will-guard-prez-biden-at-g20-8565818.html

@mitch no idea what that is but also…. We will never forget #Four SeasonsTotalLandscaping

The Wiki article uses GF(2) and GF(4), with a nod towards Galois.
https://en.wikipedia.org/wiki/Finite_field#Field_with_four_elements

Here are the addition and multiplication tables:

\[ \begin{array}{c|cccc}
+ & 0 & 1 & \phi & \phi + 1 \\
\hline
0 & 0 & 1 & \phi & \phi + 1 \\
1 & 1 & 0 & \phi + 1 & \phi \\
\phi & \phi & \phi + 1 & 0 & 1 \\
\phi + 1 & \phi + 1 & \phi & 1 & 0 \\
\end{array} \]\[
\begin{array}{c|cccc}
\times & 0 & 1 & \phi & \phi + 1 \\
\hline
0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & \phi & \phi + 1 \\
\phi & 0 & \phi & \phi + 1 & 1 \\
\phi + 1 & 0 & \phi + 1 & 1 & \phi \\
\end{array} \]As in the Boolean case, we can use various polynomials to represent the various logical functions.

As a quick warmup, we'll do Belnap's "Useful Four Valued Logic" called #FOUR.

The first difference with \( \mathbb Z_2 \) is that there are two kinds of negation.

In this case, the four elements of the logic are called F, T, B, and N, for false, true, both, and neither. Both negations flip T and F, but differ in how they treat B and N. This is called the truth / knowledge distinction. Negating something true makes it false (truth dimension), but what is the negation of having too much information (B)? In one case you could say having no information (N), but in another sense the negation of Both should be Both, and this is what Belnap chose.
\[ \lnot a = a^2 + T \](the other negation is just \( a + T \).

\[\begin{array}{c|c}
a & \lnot a \\
\hline
F & T \\
T & F \\
B & B \\
N & N \\
\end{array}
\]

Now we can define AND. In the next post.

🧵

Actually the *first* cut is to notice that if we restrict attention to just 0 and 1, arithmetic in \( \mathbb F_4 \) is exactly the same as in \( \mathbb Z_2 \). In fact, we can recover binary #logic in about 12 different ways, depending on which elements we pick for \( \top \) and \( \bot \). But we'll skip that. The next cut is Dunn's 4-valued logic #FOUR. We'll get back to #RM3

I first came across this construction in (French):

P. V. GROSJEAN
The logic on the splitting field of paradoxes, Seminar of Philosophy and Mathematics, 1988, Issue 7

🇫🇷 COMMUNIQUÉ 🇫🇷

Les fortes chaleurs sont arrivées. Tout au long de l'année, il est conseillé de se placer dans un four à chaleur tournante allumé au minimum à 180°C au moins deux minutes par jour. De la sorte, le corps peut ainsi s'habituer aux températures estivales.

Ceci est un message du Ministère chargé de la Transition écologique et de la Cohésion des territoires.

#france #été #chaleur #canicule #four #chaud #gouvernement #écologie

Gears Tactics developer Splash Damage are switching to a four-day work week - https://www.rockpapershotgun.com/gears-tactics-developer-splash-damage-are-switching-to-a-four-day-work-week #Transformers:Reactivate #MultiplayerCompetitive #MultiplayerCooperative #Birdview/Isometric #ActionAdventure #XboxGameStudios #SinglePlayer #four-dayweek #SplashDamage #GearsTactics #Strategy #PC

J''ai envie de me faire plaisir et m'acheter un #four / #barbecue #solaire.

Ou même le faire si quelqu'un a une #tuto bricoleur avec 2 mains gauches.

Quelqu'un a des conseil sur le sujet ?

Paul fails to serve out the match in the 3rd set but eventually beats Raonic, 64 76(4) 67(4) 64. #four #Wimbledon

Lucky loser Michael Mmoh comes back from 1-4 in the 3rd-set tiebreak to beat Auger-Aliassime, 76(4) 67(4) 76(4) 64. #four #Wimbledon

(Krajinovic withdrew.)

mann, die scheibe habe ich auch bis zum erbrechen gehört
https://youtu.be/XIATjH1AxVc
#foreigner
#four
#urgent

2021 - #FOUR SEASONS - SABINE PIGALLE

#photography #ValerieBelin

https://www.sabinepigalle.fr/portfolio-item/2021-four-seasons/

Tropical Depression #Four in the central Atlantic Ocean earlier today. This system may become a tropical storm. #TD4 #weather #WX

Night-time satellite view of Tropical Depression #Four in the central Atlantic Ocean #TD4 #weather #WX

Tropical Depression #Four has been designated in the central Atlantic Ocean. #TD4

See the latest forecasts here: https://zoom.earth/storms/04l-2023/

2021 - #FOUR SEASONS - SABINE PIGALLE

#photography #ValerieBelin

https://www.sabinepigalle.fr/portfolio-item/2021-four-seasons/

#Valley with a River and a #Town with #Four Towers, #HerculesSegers, c. #1626-c.1627

#HerculesSegers #DutchArt #art

http://www.rijksmuseum.nl/en/collection/RP-P-OB-836

#pink #flowers #clover #shamrock #green #plant #four #leaf #naturephotography #bloom #photo #nature #photography #BloomScrolling

#Valley with a River and a #Town with #Four Towers, #HerculesSegers, c. #1626-c.1627

#HerculesSegers #DutchArt #art

http://www.rijksmuseum.nl/en/collection/RP-P-OB-837

Fucsovics loses the last 4 games of the 2nd set but eventually beats Wu Yibing, 64 46 64 in Stuttgart. #four #tennis

#Valley with a River and a #Town with #Four Towers, #HerculesSegers, c. #1626-c.1627

#HerculesSegers #DutchArt #art

http://www.rijksmuseum.nl/en/collection/RP-P-H-OB-835