Deep and shallow embeddings of numerous logic formalisms in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous provision of deep and shallow embeddings of various degrees (maximal/minimal) in classical higher-order logic. This enables flexible, interactive and automated theorem proving and counterexample finding at meta and object level, as well as automated faithfulness proofs between these logic embeddings. The method is beneficial for logic education, research and application and is illustrated here initially using simple propositional modal logic. However, the approach is conceptual in nature and not limited to this simple logic context. For example, it also supports quantifiers. To illustrate this, this paper additionally introduces deep and shallow embeddings of quantified Boolean formulas, and, maintaining a high degree of proof automation, faithfulness between these embeddings is proved using respective lemmata, including a substitution lemma. This work demonstrates how mathematical proof assistant systems can facilitate the exploration and rapid prototyping of formal logics. This is relevant not only for formalisation of mathematical knowledge, but also for the mechanisation of legal and normative reasoning and the encoding of foundational metaphysical theories, for example.

The presented material significantly extents the work covered in the following two papers: Christoph Benzmüller: Faithful Logic Embeddings in HOL - Deep and Shallow. CADE 2025 : 280-301. Doi: 10.1007/978-3-031-99984-0_16 (Preprint: arXiv:2502.19311) Christoph Benzmüller: Faithful Logic Embeddings in HOL - Deep and Shallow (Isabelle/HOL dataset). Arch. Formal Proofs 2025 (2025). https://www.isa-afp.org/entries/FaithfulPMLinHOL.html

=== Online talk ===

Join Zoom Meeting https://cam-ac-uk.zoom.us/j/89856091954?pwd=Bba77QB2KuTideTlH6PjAmbXLO8HbY.1

Meeting ID: 898 5609 1954 Passcode: ITPtalk

Speaker: Christoph Benzmüller (Otto-Friedrich-Universität Bamberg and Freie Universität Berlin)
Thursday 12 March 2026, 17:00-18:00
Venue: Online; live-streamed at MR14 Centre for Mathematical Sciences.
Series: Formalisation of mathematics with interactive theorem provers ; organiser: Jonas Bayer.

Add to your calendar or Include in your list

https://talks.cam.ac.uk/talk/index/242896

snopes_feed

Posted by Emery Winter

https://www.snopes.com/fact-check/kansas-transgender-drivers-licenses/

The legislation was written so that trans people's licenses are revoked immediately without a grace period to swap to new licenses.

https://www.snopes.com/fact-check/kansas-transgender-drivers-licenses/

notalwaysright_feed

Posted by Not Always Right

https://notalwaysright.com/400232-2/400232/

https://notalwaysright.com/?p=400232

Read

(My brother is trying to get me and our parents to clean the house by suggesting things to throw away. He sets his sights on five candles we keep in the kitchen) Brother: “How about those candles? What sentimental value could they have?” Me: “It’s not sentimental, they’re for when the power goes out.” Brother: […]

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https://notalwaysright.com/400232-2/400232/

https://notalwaysright.com/?p=400232

irregularcomic_feed

https://www.irregularwebcomic.net/3054.html

Irregular Webcomic! #3054

https://www.irregularwebcomic.net/3054.html

notalwaysright_feed

Posted by Not Always Right

https://notalwaysright.com/dictators-dictate-not-discuss/407161/

https://notalwaysright.com/?p=407161

Read Dictators Dictate, Not Discuss

Owner: "Good. See this order? It's special. This guy is the CEO of a big company; he'll just send a sandwich list and nothing more. Just take the order and send it to the kitchen, and no talking whatsoever."

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https://notalwaysright.com/dictators-dictate-not-discuss/407161/

https://notalwaysright.com/?p=407161

notalwaysright_feed

Posted by Not Always Right

https://notalwaysright.com/400231-2/400231/

https://notalwaysright.com/?p=400231

Read

A privacy and security training I have to take contained a reminder not to hold a employee door open for people who are not wearing credentials. I was reminded of an company wide email I received 30 years ago. It said just that: “Do not under any circumstances allow anyone in who is not wearing […]

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https://notalwaysright.com/400231-2/400231/

https://notalwaysright.com/?p=400231

icanhascheezburger_feed

Posted by Laurent Shinar

https://cheezburger.com/44384773/22-vintage-photos-of-cats-being-cute-through-the-ages

While it is known that our relationship with cats began many hundreds of years ago. Photographic proof of that budding relationship has been hard to come by, which is why we are delighted to share these vintage pics of cats being cute.

From the days of the ancient Egyptians, to the medieval times, to ancient Rome, cats have a well documented story in our hooman history books. Sometimes revered as gods themselves, other times contributing to their pawrents being put on trial for witchcraft, their history alongside hoomanity is convoluted and care-filled. But it is true that even with all that has been written about that relationship, there has been little to no visual confirmation that cats have been close to us for all this time.

But that ends today, as we invite you to dive into this collection of cute cats featured in vintage photos from various points in the last 100 years. So if you ever found yourself wondering whether cat pawrents dressed their feline fur babies in cute costumes 70 years ago, you have come to the right place.

https://cheezburger.com/44384773/22-vintage-photos-of-cats-being-cute-through-the-ages

icanhascheezburger_feed

Posted by Ayala Sorotsky

https://cheezburger.com/44527365/funny-feline-fiesta-35-cat-memes-to-enjoy-right-meow

Welcome to the ultimate cat pawrty!

The guest list is set, the catnip is officially uncorked, and the zoomies are scheduled for approximately 3:00 AM. When you live with a cat, every day is essentially a surprise feline fiesta where you aren't quite sure if you're the guest of honor or just the designated snack dispenser. These whiskery celebrations are all about vibing with the peak party animal energy that only a cat can provide, from the impurressive mid-air pounces to the accidental face-plants into the water bowl.

There's no better time than right meow to ditch your human responsibilities and join the floofy festivities. Whether your resident cat is currently wearing a discarded taco wrapper as a festive hat or attempting a fast-paced salsa dance across your kitchen counters, their commitment to the fiesta is legendary. It's a colorful, chaotic world of purrs and puns where the only rule is to keep the treats flowing and the belly rubs (briefly) allowed. Let's get this pawrty purring!

https://cheezburger.com/44527365/funny-feline-fiesta-35-cat-memes-to-enjoy-right-meow

icanhascheezburger_feed

Posted by Mariel Ruvinsky

https://cheezburger.com/44523525/20-fabulous-felines-with-unique-and-rare-fur-patterns-and-markings

No matter how many cats you have seen, there are always more out there that will amaze you with their uniqueness.

Here at ICHC, we like to say that every single cat is unique. Because it is true. Especially to that cat's owner. We say that as people who own the simplest cats - simple in every way. They are still special. There is always something. Maybe at first glance, someone else wouldn't see it. But you know. Some of the simplest cats have a folded ear or two. Maybe these cats have an extra toe bean. Maybe they have a single paw that is a different color or a stripe on their tail that seems like it shouldn't be there. There is always something to make them unique.

With all that said, we have to admit that some cats instantly look different and unique - without having to so much as squint. There are always cats with unique fur patterns - things that are rare and unexpected. And the beautiful thing about the internet - and our jobs as people writing for ICHC - is that we can put together a list of these special kitties for all of you guys to view and enjoy.

https://cheezburger.com/44523525/20-fabulous-felines-with-unique-and-rare-fur-patterns-and-markings

oursin

Happy birthday,

sister_luck!

notalwaysright_feed

Posted by Not Always Right

https://notalwaysright.com/400230-2/400230/

https://notalwaysright.com/?p=400230

Read

I used to have a credit card with the slogan, don’t leave home without it. I was finally able to make the last payment to zero out my account. After work I sit down at my computer and make that final payment and go on my merry way. Payments for this account need to be […]

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https://notalwaysright.com/400230-2/400230/

https://notalwaysright.com/?p=400230

nanila posting in

awesomeers

It's challenge time!

Comment with Just One Thing you've accomplished in the last 24 hours or so. It doesn't have to be a hard thing, or even a thing that you think is particularly awesome. Just a thing that you did.

Feel free to share more than one thing if you're feeling particularly accomplished! Extra credit: find someone in the comments and give them props for what they achieved!

Nothing is too big, too small, too strange or too cryptic. And in case you'd rather do this in private, anonymous comments are screened. I will only unscreen if you ask me to.

Go!

notalwaysright_feed

Posted by Not Always Right

https://notalwaysright.com/dial-tone-deaf/407157/

https://notalwaysright.com/?p=407157

Read Dial Tone Deaf

Caller: "What time do you open?"
Me: "I don't?"
Caller: "What. Time. Does. The. Store. Open?"
Me: "...I think you have the wrong number. You've called my cell phone."

Read Dial Tone Deaf

https://notalwaysright.com/dial-tone-deaf/407157/

https://notalwaysright.com/?p=407157

girlgenius_main_feed

http://www.girlgeniusonline.com/comic.php?date=20260304

The Girl Genius comic for Wednesday, March 04, 2026 has been posted.

http://www.girlgeniusonline.com/comic.php?date=20260304

kiya

Set

Miscellanea:

The polar stars
With fixed purpose;

Thunderbolt iron
To open the power
(Great of strength)
to speak;

Confusion;
Discord;
Overcoming that which would
Annihilate;

The sinister and redheaded;
The foreign.

And
Problematic
Men—
Angry drunks,
Queer,
And the ball-less.

Collected.

ysabetwordsmith

Good news includes all the things which make us happy or otherwise feel good. It can be personal or public. We never know when something wonderful will happen, and when it does, most people want to share it with someone. It's disappointing when nobody is there to appreciate it. Happily, blogging allows us to share our joys and pat each other on the back.

What good news have you had recently? Are you anticipating any more? Have you found a cute picture or a video that makes you smile? Is there anything your online friends could do to make your life a little happier?