Uncertain Reasoning in Justification Logic
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Uncertain Reasoning in Justification Logic

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Uncertain Reasoning in Justification LogicThis thesis studies the combination of two well known formal systems for knowledge representation: probabilistic logic and justification logic. Our aim is to design a formal framework that allows the analysis of epistemic situations with incomplete information. In order to achieve this we introduce two probabilistic justification logics, which are defined by adding probability operators to the minimal justification logic J. We prove soundness and

This thesis studies the combination of two well known formal systems for knowledge representation: probabilistic logic and justification logic. Our aim is to design
a formal framework that allows the analysis of epistemic situations with incomplete information. In order to achieve this we introduce two probabilistic justification logics, which are defined by adding probability operators to the minimal justification logic J. We prove soundness and completeness theorems for our logics and establish decidability procedures. Both our logics rely on an infinitary rule so that strong completeness can be achieved. One of the most interesting mathematical
results for our logics is the fact that adding only one iteration of the probability
operator to the justification logic J does not increase the computational complexity
of the logic.

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SKU: 71975213954

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Fort Morgan, US
★★★★★ 5
Good for night sessions
Size: Medium, Pattern Name: Pack of 1
Picked this up for evening fetch sessions and it’s been a win. It charges up fast, couple minutes under a lamp or in sunlight and it’s good to go, and the glow is genuinely bright, not the sad dim purple some of these put out. Makes it way easier to find in the yard at dusk, and the dog can actually track it. It’s a little on the softer side compared to a regular tennis ball, but durable enough to hold up to my big dog, who is not gentle with toys. Still kicking after plenty of chomping and slobber. Fits a standard Chuckit! launcher perfectly, which is the whole point. Pros: • Glows brightly and clearly in the dark • Charges fast from any light source • Holds up well even with a big, enthusiastic chewer • Fits standard ball-throwing sticks • Great for evening or early-morning fetch Cons: • A bit softer than a regular tennis ball — a determined power-chewer could probably destroy it eventually • Glow fades after a while, so you’ll need to recharge it during long sessions • Only glows if it’s been charged, which is obvious but easy to forget Tips: • Charge it under a bright light or in the sun for a few minutes before heading out • A flashlight works in a pinch if you forgot to charge it • Keep it out of permanent fetch duty — rotate with a regular ball so it lasts longer • Not a chew toy, even though it’s tempting to leave it with the dog Five stars. If you’ve got a dog and a yard, this makes evening fetch actually doable.
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Reviewed in the United States on May 24, 2026
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VOKLST
Port Orchard, US
★★★★★ 5
Westies Fav
Size: Small, Pattern Name: Pack of 1
Best Westie ball ever, my dog loves this ball. Exactly her size! 3" tennis balls are too big & she rips the fur off. this silicone-ish ball has no fur & is 2&1/2 " We have 2" balls from her electronic ball laucher, but she still loves this glow in the dark best!
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Reviewed in the United States on May 4, 2026
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Book Junkie
Pawtucket, US
★★★★★ 5
Best dog ball in the world!
Size: Large, Pattern Name: Pack of 1, Size: Large, Pattern Name: Pack of 1
My dog is singularly obsessed with playing ball. He would drop a steak to chase a ball. (He'd return to the steak, but not without the retrieved ball. He's not an idiot.) He makes dangerous leaps, crashes into trees, and runs fast enough to catch thrown balls before they even hit the ground. Since he doesn't care about his own wellbeing, it's my job to protect him as much as I can. And a lot of balls are hard enough to cause him pain or dental damage when he mistimes a catch. Enter the ChuckIt Glow Ball! The minute Cowboy got his first Glow Ball, he no longer had any interest in the dozens of tennis balls scattered around the house and yard. If I took the Glow Ball away and instead threw a tennis ball, Cowboy would run to retrieve the ball, then return without it and begin looking all over the house for the Glow Ball. The Glow Ball is tough enough to survive Cowboy's big, sharp chompers, yet it's soft enough to do no harm when it hits him in the face. The glow feature is a huge bonus, too. Cowboy gets distracted by chipmunks and squirrels when we're playing, so he sometimes can't remember where he dropped the ball to pursue the interloper. If the ball was exposed to enough light before it was misplaced, it will be easy to find once the sun goes down. (Otherwise, Cowboy always finds it eventually.) When I'm feeling nocturnal, I'll put the ball under a light for a few minutes to activate the electrons, then treat my boy to a middle-of-the-night game of fetch. I was so happy to see these on sale, I bought a lifetime supply for my pantry. The size guide seems accurate. ChuckIt recommended the large size for a dog of Cowboy's weight and that size is perfect. Highly recommended product.
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Reviewed in the United States on October 14, 2024
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Daisy W.
New York, US
★★★★★ 5
Indestructible Doodle ball!
Size: Large (Pack of 1), Color: Multi
If your dog chews threw every tennis ball and toy, chuckit rubber fetch balls are the only one! Our dog LOVES it, he digs it out and has to have several so that there are a few outside and a couple inside because he chews them when he's bored inside and chases them outside! You dog will love it. It's a great value, especially if you watch for sales. It's our go to fog toy!!
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Reviewed in the United States on May 2, 2026
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beck
Lowell, US
★★★★★ 5
Dogs Favorite Ball
Size: Large (Pack of 1), Color: Multi
Great fetch ball! Super durable rubber that holds up way better than a regular tennis ball and has an awesome bounce. Easy for dogs to spot and perfect for endless games of fetch. Doesn’t get soggy or fall apart — definitely a must-have for active dogs!
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Reviewed in the United States on April 29, 2026

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