#answer set programming

[informatikerin-freyja]

One of the big difficulties in artificial intelligence is accounting for defeasible reasoning. For example, when an agent encounters a bird, it should assume that bird is capable of flight, despite the existence of flightless birds. This is unlike mathematical logic, where-in which conclusions are only implied provided the addition of new information could not possibly invalidate them. Defeasible reasoning thus requires special defeasible logics.

Perhaps the most straightforward manner of constructing a defeasible logic is as follows. Our models are "rank" functions R : W \to \mathbb{N} which assign a degree of implausibility to every possible world in W. Here possible worlds are often just truth value assignments. We then say that a defeasible implication A => B is satisfied by R iff the set of minimal worlds in A under R, denoted min(A,R), is a subset of B.

To clarify the bird example, we can place flying birds at rank zero, birds with broken wings at rank one, and birds with broken wings nevertheless equipped with a jet pack at rank two. This ranking would satisfy the following implications: bird => can_fly, bird & broken_wing => not can_fly, and finally bird & broken_wing & jetpack => can_fly.

If you are interested, defeasible logics constructed in this manner are referred to as preferential logics. Answer-set programming is the other major and effective approach to defeasible reasoning in artificial intelligence at the moment.

[cubbihue]

So, a changeling is sort of like a p-zombie?

(For the unaware, “p-zombie” stands for “philosophical zombie”. It’s a thought experiment in philosophy that describes a being that’s outwardly identical to a human, but does not have a consciousness; that is, a p-zombie does not think whatsoever, although it looks like it thinks to an outsider observer. There’s a whole wikipedia article on it that explains the concept better than I can!)

They don't exactly think, as in "I dont want this" "I like that". But, Changelings do have a form of "Consciousness". It's just that their consciousness is more like a series of commands or tasks than actual formulated thoughts.

Timmy's Changeling has a very advanced "consciousness". It can predict future actions and reroute its tasks to pick only the best options for its situation.

We fill their heads with static to ensure that the Changeling does not form thoughts about anything. Thoughts leads to opinions, and opinions leads to incorrect actions. A proper Changeling should have more static in their mind than a TV screen on a defunct channel!

Bitties Series: [Start] > [Previous] > [Next]

[therealcallmekd]

Been obsessing over the fact that my old oc, Artie, and Kinitopet are like so one in the same it's actually crazy.

Pink AI that's friendly on the surface, is actually really clingy and obsessive at times. Lonely and really just trying to fulfill a core objective as set by their creator or other influences, someone or something that they look up to as a godly figure maybe.

They both act as your friendly AI assistant, Artie is just for a specific program, while Kinito just gets to be his own thing.

Both want you to stay with them. Both will go out of their way to do things to make sure that happens.

they are so silly to me, and i love them

Also I found an old sketch from way back that somehow mimics the literal same plot beats to the ending portion of kinitopet and that threw me for a loop. Too bad it was only a concept sketch.

ohhh i love sentient silly ai so much... ohhh i love themmmmmm

something something sentience of ai is inherently a tragedy or something like that.

thank you for listening to me ramble. ahem.

[valhallavalgrace]

How are you adjusting to the whole Norse mythology situation?

LEO: I’ve mostly been bugging some of the older einherjar, and Hunding, a little bit, to figure this place out. Do you know how cool it is that some people have been here since the industrial revolution?? There's no way that I'm the first of my dad's kids to make it here. I just don't know who to talk to about it.

((Leo's coping mechanism re: Norse mythology is just hating himself more bc of course he doesn't belong in his own afterlife. but he won't admit that to anyone bc he doesn't know who can be vulnerable with.))

prev ask

[sergle]

Hey Sergle, how does one learn how to draw? Like, I am in my 20s, can barely draw a stick figure, and feel overwhelmed whenever I try to look up tutorials. Do you have any advice on how to start?

my Unprofessional advice on how to start in earnest, is to do it the way little kids do when they start learning to draw! which is to not approach it as learning at all. sitting down and scribbling out whatever comes to mind, reading a book or watching a movie and trying to copy the way the characters are drawn. draw a page full of cats. do it while you watch tv. doing all that w/o the Grown Up impulse to be embarrassed that you're new at a skill.

[poorly-drawn-mdzs]

sorry if u already answered this question, but how do you scan your art? like via phone or a printer or smth else? It looks so good!🙏

I usually scan with a flatbed scanner in 400dpi, as I found it gave me the nicest quality without being too large, but 300dpi is also fine.

The secret to getting good scan quality is Know Thy Printer. Every scanner has its unique traits you want to compensate for, be it low contrast, over saturating, or washing out colours. My great art hack is adjusting for this post scan! I found duplicating and multiplying the layer (fading opacity based on need) helped fix a *lot* of issues with the ink scanning ‘washed out’.

[the-eclectic-wonderer]

A big thanks to @witchybitchybisexual who tagged me in this amazing 30-questions Golden Girls-themed game; I had a *great* time answering these! I look forward to reading everyone's answers (including yours, @witchybitchybisexual!).

I'm hiding all questions after #1 under a cut, because this got long haha!

1. How did you find out about the show?

Via another show I love -- Good Omens! Or, actually, via the amazing book that inspired it. One of the main characters, the demon Crowley, is a big fan of The Golden Girls; there's a great scene in which the forces of hell hijack one of Rose's monologues to send him a message while he's watching the show! I was in need of something new to watch at the time, and I figured if Crowley liked it so much, it was at least worth checking out. :)

2. One storyline you’d eliminate?

Hmm... probably Miles' witness protection program storyline? I don't mind it that much (it gave us some fun jokes and some memorable scenes!), but I feel like that was a turning point in Miles' character, and I just don't like the person he became after that turning point.

There was no question 3 here, so I made up my own! Hope that's not an issue :)

3. Best guest star/character?

Lynnie Greene takes the cake as the best guest star, for sure. I adore her and she played a phenomenal young!Dorothy. The second place goes to Dick Van Dyke, just because I love him in general!

As for the best guest character, I think the honour goes to Angela, Sophia's sister! She's absolutely hilarious and her comedic chemistry with Sophia is stellar. I also have to mention John Neretti from S6E23 What A Difference A Date Makes for being the best man in the series imho.

4. Character you most relate to?

Dorothy! My personality nowadays is a bit of a mix between Dorothy and Rose, I feel, but the Dorothy side is prevalent (and it was even more prevalent a few years back). I love reading and literature (and I enjoy learning about history, although I don't have her passion for it); I share her love for teaching (although I'm not a teacher); I was a great student in school, but not a popular kid at all; I'm level-headed and responsible, but I can be impulsive under the right circumstances; I'm very protective of the people I love; I'm Italian and was brought up a Catholic; I'm often the tallest girl in the room (I'm just a bit shorter than Bea Arthur was!) and I'm not attractive (not that Dorothy isn't -- but she is perceived as unattractive in the show), so I also understand her self-esteem issues fairly well.

I'm not as quick-witted as she is, unfortunately, and nowadays my outlook on life is more positive and easy-going than hers, but she's still the one I relate to the most.

5. Favourite character?

Blanche, although the other Girls are very, very close. I adore them all and I especially love to see them interact, but if I have to pick one, then it's Blanche. She's the one who surprised me the most! At the start of the show I kind of wrote her off as 'the man-crazy one', and that's as far removed from me as possible, so I didn't really focus much on her at the beginning. Then came S1E4 The Transplant, and then came her family issues, and then came all her memories of George, and before I knew it I was head-over-heels in love with her. Rue was masterful in how subtly she played her; she showed Blanche's depth as a character little by little, letting the audience peek behind the mask only for moments at a time, so when I realized I hadn't given her the attention she deserved, I was already in too deep.

6. Favourite story of a cast member?

Oh, so many good ones to choose from! The first one that comes to mind is Bea's anecdote about the time she was Tallulah Bankhead's understudy. The awe with which she describes her coming down the stairs is palpable -- but I mostly admire how she took Bankhead's mean comment and turned it into motivation. And Bea did get her 'coming down the stairs to thunderous applause' moment (more than once!), so her vow came true!

A fun one that involves all four main actresses is this blooper related to Blanche's Christmas gift to the girls, the 'The Men Of Blanche's Boudoir' calendar. Watching all of them lose their marbles over this prank is priceless -- it always puts a big smile on my face!

(Is this what you meant by this question? I wasn't sure!)

7. Which was the episode that got you hooked?

The pilot, lmao. It might be a cheesy answer, but it's true! I was immediately hooked from S1E1 scene one. Dorothy's incredible entrance got me.

8. You could wear one girl’s wardrobe for the rest of your life, who would you pick?

It's a toss-up between Blanche's and Dorothy's.

9. How many kids do you think they all actually had?

... this ask made me realize there are doubts about this, lmao. I've never done the math! Had to go check on wikipedia 😂

As far as I can tell, it's fairly set in stone that Rose had five children, of which we meet two (Kirsten, with two different faces 😂, and Brigit, who I assume is her youngest one).

It also seems reasonably certain that Dorothy had two kids -- Kate and Michael. I will say I've always thought Kate was much younger than she should have been in her appearances on the show, considering Dorothy was pregnant with her when she married, but maybe she just looked much younger than she actually was, I don't know.

Blanche is more complicated. We see both of her daughters, Janet and Rebecca, and in S3E3 Bringing Up Baby she mentions three sons, Matthew (also known as 'Skippy'), Doug, and Biff. In that same episode, though, she also says she's had four kids! I get where the disconnect comes from, haha. To be precise, her quote is:

"I have had four kids, I have never had a Mercedes."

This is just off the top of my head, but I wonder if she means 'I have had' in the sense of 'I have given birth to' here? This would imply one of her children is actually adopted (which is very interesting to think about!!). Since she directly mentions her three sons after this quote, I suppose our suspects are Janet and Becky. I'll have to give this some more thought, though -- for now my answer is that Blanche has five kids, and that 'four' is a continuity error on the writers' part.

10. Do you think the actresses would’ve gotten along with their characters if they met in real life? Why/Why not?

Interesting question! I think so, yes.

Dorothy and Bea seem fairly similar already -- as far as I know Bea was a big sweetheart, a private, gentle person, and Dorothy's a big sweetheart too. Plus I feel like Dorothy would have been respectful of Bea's introverted nature, and Bea would have been understanding and accepting of Dorothy's personal history (not to mention, she wouldn't have mocked her for not dating/for her appearance).

In all the interviews I've seen, Estelle seems very respectful and very fond of old people in general -- I think she'd find Sophia a riot! I seem to remember a clip in which she actually says she likes Sophia, so I feel pretty secure in stating they'd get along.

There's this famous quote by Rue in which she essentially says that she's similar to Blanche in everything but the fact that she's not from Atlanta 😂 so I feel justified in assuming they would have had fun with each other! Rue's stated that she felt an immediate connection to Blanche as a character, and that playing Blanche helped her gain more self-esteem and confidence, so I think meeting her in person would have had a similar effect! And Rue (being a very open, honest, compassionate person) might have helped Blanche drop her mask a little bit.

The only one I have an inkling of doubt about is Betty -- mostly because she'd run circles around Rose! But ultimately I think any 'mocking' would be gentle and affectionate, much like the Girls' jokes in the show. I think they would have liked each other -- and they could have bonded on their common love for animals alone!

11. What are your other comfort shows?

Apart from the aforementioned Good Omens, I'm also very fond of Only Murders In The Building, a really fun show about solving murders and found family that I wholeheartedly recommend. Derry Girls is another recent favourite. Oh, if you like cartoons too, I recommend Steven Universe, Hilda, and Avatar: The Last Airbender.

12. Headcanons? (Feel free to list as many as you’d like)

Oh, my god. I have so many and I'm for sure going to forget some. Let's see...

I've already said some time ago that in my mind Dorothy drives stick shift. Reasoning for this is that Italians (including yours truly, haha!) drive stick shift, and she's of Italian descent, so... she knows how to drive an automatic car, she just learned how to drive on a stick shift one (and in the streets of Brooklyn, no less!). Still on Dorothy: I think she has a very neat handwriting (she feels like the type of person who consciously decided to improve her handwriting at some point in her life), but she's prone to leaving ink stains on the page (and on her hands!!), especially when she's writing in a hurry.

Rose is really strong! Physically strong, I mean. I know she was a housewife for most of her life, but she was a farm girl first! Farming takes a lot of physical resilience, and that's the kind of strength that stays with you, I think. She's the one who lifts up the furniture when they clean (S2E12 The Sisters), and I don't think they'd let her do that if she couldn't handle it. Plus, remember that time she broke a whole ceramic cup with one bare hand (in S7E19 A Midwinter Night's Dream)? Yeah. I also subscribe to some mutuals' hc that she's autistic (although they'll be able to comment on it much better than I can, if they want to!).

Regarding Blanche, I really enjoy @\eeblouissant's hc that she has a permanent tan! She's from the South, she's lived near the coast for ages, *and* she's expressed an appreciation for sunbathing in the show, so it makes perfect sense to me. Also: she's a cover hog! In the show Rose is the one who admits to stealing the covers (in S2E5 Isn't It Romantic?, iirc), but I like to think Blanche is the worst offender. It's a good way to complete the Girls' trifecta of sleeping annoyances (Dorothy snores, Rose sleeptalks, Blanche steals the covers!), and I think it's thematically appropriate for her -- considering her Southern origin, I think she's more sensitive to the cold than Dorothy and Rose are, and she's always looking for affection, so...

Oh, regarding their sexuality: I don't have a marked preference for any of them, but I tend to think of Blanche as a bisexual with a lot of internalized homophobia. Rose is also bi, and somewhere on the asexual spectrum (and I have textual evidence for this!). @\hecatesbroom has completely convinced me to read Dorothy as a repressed lesbian, but I'm fine with people considering her bisexual too. I prefer queer interpretations of all of them, but I'm honestly fine with any take, as long as the strong (platonic or romantic) bond between them is preserved.

Most of my headcanons on Sophia are just traits borrowed from my grandmothers -- for example, I like to think that she started getting into gardening once she moved in with the Girls, and she's really gifted at it (like my grandma!).

13. What would you change (if anything) about the show/ characters if it was set in the modern day?

This is a really hard question to answer properly, because while the show is still very relevant to the present day, some aspects are so grounded in their time that a lot of things don't make as much sense when transposed into the future. For example -- would Dorothy end up marrying Stanley and staying married to him for 38 years if he'd gotten her pregnant in the 90s? Single mothers weren't exactly celebrated back then either (Madonna's Papa Don't Preach is from 1986), but they still had it much better than they did back in the 40s-50s -- and divorce has become much more accessible (and socially acceptable) in the past few decades. Would she have left him earlier? Would she have married him at all?

And what about Sophia? Being an Italian immigrant in the 50s seems different from being an Italian immigrant in the 20s -- there was a whole World War between the two, for starters. Would she still emigrate to the US? Would she even emigrate at all? How would she have survived the fascist regime in Italy?

Blanche and Rose are perhaps less grounded in their time. St Olaf is so absurd it might as well be the exact same in the present day (and dying in childbirth is unfortunately still too common, so it's not strange to think that Rose would be an orphan in any case), and considering how some people still think and behave nowadays, Blanche's biography and opinions seem plausible even when transposed 30-40 years into the future (at least to me). But still -- many of the issues they deal with were grounded in their time. Take Rose's AIDS scare: would she react in the same way in the present day, knowing that care for HIV patients has progressed so much?

To be fair, apart from all these questions, all of the Girls are still plausible (and relatable) characters from a modern POV; but society has changed a lot in the past 30-40 years, and I think a groundbreaking, socially advanced show like Golden Girls would necessarily have to change as a consequence. It's just in the spirit of the show! The core idea of four women sharing a life is still a perfect premise, but the problems the Girls face, their careers, their economic stability, their ideas on love and relationships -- there's a lot that could be different when transposed to the present day! I feel like this question requires much more space, time, and analysis to be answered properly.

One thing I like to think is that at least some of the Girls might have been explicitly queer if the show was set in the present day! Which opens up a lot of avenues for plot-lines and relationships :)

14. Which other Fictional Characters would you like each one of the golden girls to meet?

I have a storyboard in my notes for a little comic in which the Girls travel to England and meet Aziraphale and Crowley from Good Omens, so them, definitely 😂

Also, the Derry Girls! Check out this great crossover fic on Ao3 -- the chaotic energy is just off the charts, I love it.

15. Who were your favourite duo?

Oh, I can't choose. Any duo within the Girls. Their 1:1 interactions are all amazing, there's no way I can pick just one. I love the bond between Dorothy and Sophia, I love Dorothy and Blanche's chemistry, I love how fun and silly Blanche and Rose get to be together, I love the ironclad trust between Dorothy and Rose, I love Blanche and Sophia's love-(fake) hate friendship, I love the way Sophia hides her immense affection for Rose under a veil of humour and the way Rose sees right through it. I could write an essay on each pair of them.

15. Who should’ve got more 1:1 screen time with each other?

I'm pretty happy with the amount of 1:1 time each pair of Girls got with each other, actually! One of the strengths of the show imho is how well-balanced the interactions between the main cast are. If I really have to nitpick, I think I might have liked a couple of episodes specifically on Dorothy and Rose in the last couple of seasons; it feels like they interacted 1:1 less after S5, but that might just be me.

I also think the Girls' interactions with secondary characters and guests were well-balanced, in general; I can't think of any specific example where I wished for one of the Girls to have more interactions with a certain character.

... okay, there is one instance, but it's not really a matter of screen time, more of what happened during said screen time. I really, really wanted to see Blanche (with Rose as support) tear into Stan. I think we deserved a scene where she tells him off for the way he treats Dorothy -- she's already pretty caustic in the show when it comes to him (except in S6, for some reason...), and a proper confrontation would have been glorious.

16. Calmest season?

Is there one? 😂 the first season, I guess? It feels a bit more 'domestic' and contained in scope, likely because it was the first -- but it's still a wild ride!!

17. Most chaotic season?

Season 3, for sure. It's a bit all over the place, and it contains some of the wildest premises in the whole series -- I mean, Bringing Up Baby? Letter to Gorbachev? Mister Terrific? I could go on -- there's lots of chaotic episodes in there! (Just to be clear: I love the chaos! S3 is not my favourite season, but it's still great -- and it's got some amazing episodes!)

18. Favorite Season?

I think the honour goes to season 5! It would probably be S6, if not for the whole 'Dorothy falls back in love with Stan' plot line. S7 is the one that contains the highest count of favourite episodes for me, but I think S5 is stronger as a whole, and it's got some true gems.

19. If the girls hadn’t had their established careers, what other ones could you picture them doing?

Oh, let's see! Stan mentions Dorothy always wanted to open an antique shop back in S1E11 The Return of Dorothy's Ex, and I think that really fits her. I can also see her as a (very passionate) librarian! And, of course, she'd be great as a college professor / history researcher.

Despite the Girls' lack of confidence in her ability to keep things alive, I think with proper training Rose would work well as a nurse. She already volunteers for the hospital, she can be competent when given the chance, she's a giving person, and she loves taking care of people, so I think she at least has the right attitude for it -- although I'd never place her in a stressful unit, especially at the start of the show! Apart from this, anything to do with animals, of course -- a zoo, a farm, a pet shop, she'd excel in all of them!

I can see Blanche thriving as a trophy wife, haha 😂 but that's not properly a career, so it's not a valid answer. Taking her keen artistic eye into account, I think she'd be great as a designer -- either a fashion designer, or an interior decorator. She also showed some talent and interest in psychology during the series, although I'm not sure she'd manage to remain completely professional as a psychologist. 😅

As for Sophia, I think she'd do well in any position that allows her to be a motivator! She's great at encouraging people through a bit of tough love, and she's a very driven person herself -- so I think she'd do well as a manager of sorts, although the kind of manager that still works hands-on too. I believe she'd manage to hold her own in more or less any field; she's very adaptable! I do think she's at her best in a kitchen, though.

20. Best aspects of the show in your opinion?

There's a lot! The writing, the performances, the costume department, it was all exceptional. I think the best aspect to me is the premise, and how seriously they took it! The idea of a show centered on four older women living together is groundbreaking, especially since it didn't make a mockery of them -- the Girls are serious, well-rounded characters, with full lives, written with lots of love and respect. I think this show really convinced me that life isn't over once you hit 30, and that there's plenty to look forward to as you age! A lot of people my age are terrified of growing older, and here I am, eager to see what's coming next -- and I owe at least some of this attitude to this show. I'm really grateful!

21. (This question is for my fellow cheesecake lovers) favourite cheesecake flavour?

:) Great question! I love cheesecakes in general, but I'm especially partial to raspberry cheesecakes.

22. Storyline you wished they had expanded upon?

The show has an unfortunate tendency to introduce characters and then forget about them, which allowed for more variety in the stories they chose to tell, but I would have liked to see some of the Girls' relatives and friends return! Like, I don't know -- Jean, for example, or Blanche's nephew from back in S1. Some of the guests' arcs are complete within their episode (as happens eg for Lily, Rose's sister), but others remained a bit 'in the air', and I think it would have been nice to see them again.

Oh, and also -- I would have liked some little references to the Girls' issues and problems outside of the episodes they're tackled in! References to Blanche's pacemaker, for example, or to Rose's addiction, or to Dorothy's CFS (or her hearing aid!!). I understand that the time was limited, but even a small callback or two would have been nice!

23. Questions you’d ask the actresses?

Does 'will you marry me' count? 😭

I'm not sure -- knowing me, I'd probably be unable to utter a word in their presence! Rather than ask questions, I think I'd just thank them for bringing such an incredible, wonderful show to life. It wouldn't have been the same without them.

24. Episode that brings you the most comfort?

Most of them, really. Even the sad ones; I hear the first few notes of the opening theme and my spirits are already lifted. I can pick one per season, if that's alright:

S1E25 The Way We Met

S2E17 Bedtime Story

S3E3 Bringing Up Baby

S4E4 Yokel Hero

S5E23 The Mangiacavallo Curse Makes a Lousy Wedding Present

S6E26 Henny Penny -- Straight, No Chaser

S7E23/24 Home Again, Rose

But honestly there's so many more I could mention! I just love these ladies so much and I love to watch them in situations, haha.

25. Episode that made you laugh the hardest?

This is a cruel choice! Golden Girls is infamous in my house as 'the show that makes the-eclectic-wonderer howl with laughter', and I think that speaks for itself 😂

Let me pick at least three: S2E4 It's a Miserable Life, S7E2 The Case of the Libertine Belle, and S7E4 That's For Me To Know.

26. Which other work that the actresses did you enjoy the most?

I believe most of Estelle's career prior to The Golden Girls was in the theater, so I'm not sure it's even possible to watch her other works, unfortunately.

Show me Bea Arthur singing literally anything and I will be on my knees in seconds. Her musical performances are peak. Also -- I still haven't watched Maude, but I already know I'll love it.

Maude includes Rue as well -- I cannot wait to fall in love with her as Vivian too! And I have one of her early movies in my watch list, although I'm waiting for the right moment to watch it (homegirl plays a stripper and I'm not sure I can handle it in company without making a fool of myself, considering my big gay crush on her).

As for Betty -- Life With Elizabeth, absolutely. She's so funny and so beautiful and so captivating in it! She's simply charming, I love her to bits.

27. Best St Olaf Story?

The Great Herring War from S1E25 The Way We Met, no question. It's not necessarily the strongest from a comedy point of view (although it's certainly up there -- it's hilarious!), but the context and the way Dorothy and Blanche contribute to it make it the most memorable one, imho. It's my favourite, for sure.

(The story of Gunilla Bjorndunker, St Olaf's tallest woman, as told in S6E3 If At Last You Do Succeed is in second place).

28. Best slut story?

It changes every time I hear one, lmao! I love all of Blanche's stories!

If I must pick one -- I really enjoy Blanche's retelling of that time she realized she was even more devastating by moonlight in S1E25 The Way We Met, if only for that incredible final line ("It was at that moment I realized my bosoms had the power to make music!"). I'm not sure if it counts, because it's so brief, but her involuntary remembrance of that time she had to call a cab to get home because the sailor she hooked up with wouldn't wake up (S2E17 Bedtime Story) always has me in stitches -- I love how unexpected and effective it is!

Oh, and I'm really fond of the one she tells her mama in S3E25 Mother's Day. I'm very sensitive to the theme of loved ones getting older and having trouble remembering stuff, so that whole flashback hits close to home for me, and I love how Blanche's story helps her and her mama connect over shared memories. It's really touching (and Rue's acting is spectacular).

29. Best Sicily story?

Sophia's alleged encounter with Pablo Picasso, as narrated in S6E24 Never Yell Fire In A Crowded Retirement Home: Part 1. I somehow didn't anticipate the punchline, and I lost my shit when Sophia name-dropped Picasso. I still lose my shit every time I listen to it. It's a classic.

30. Which girl would you be most interested in seeing a prequel of? And at which point in their life?

I would pay dearly for a young!Dorothy show. It might be depressing (because her life with Stan was... well... yikes) but also imagine -- Dorothy learning how to be a mom, her life at college, building herself a life... so many possibilities!!! And it would be even better if it featured some flashbacks to Sophia's life in Sicily!

I would enjoy a show about teenage Blanche's adventures, too, but a part of me thinks those stories are at their best when retold by Blanche herself (ie when there's a good amount of doubt as to their veracity, lmao).

[i-can-even-burn-salad]

Something something tag game

I was tagged by @burnticedlatte and I should be working, so obviously I'm doing this now.

favorite color: depends on the mood, but blue usually wins. creative, i know.

last movie/tv show: movie, halfway through the outsider, "tv" show, 7 vs wild

currently watching: the cursor blink in notepad while I ponder the answers

sweet/spicy/savory: sweet

relationship status: not anyone's business, is it

current obsession: I'm out-obsessed after spending every waking hour for half a year on Till Death, but video games always work

last google search: how would I know, I don't even remember where I left my water glass

Why are those always so boring. Why not currently reading, or last game played, or last little treat bought, or most used emoji, or favorite font, or—

[bloodwards]

I was raving about tlt so hard that a friend of mine was like oh can u help me get the audiobook? And I was like hell yeah brother 🏴‍☠️ but he has an iphone 💀💀💀 like dude I'm not even gonna get into any of that, listen to it on your pc man, best of luck 🌚✌

[poohsources]

Did you use to run a blog about the ancient one? In the tumblr rpc?

hi there! do you mean the one from marvel? nope, i didn't. i did use to be active in another comic community, though ( *cough* dc *cough* ) but i left a few years ago ... unless you count any of my abandoned multis that included dc muses as me being active there. then it was just a few months ago that i left.

[lytransthropy]

I saw your post about you going back to the Hospital and I wanted to tell you that I love you. I'm not sure if you remember me from when we used to do Pokemon RPs on Twitter, but I look back on that time fondly and you're my friend still, even though we don't talk to each other any more. I saw everything you've been dealing with. You're very strong for making it this far into your life and I'm proud of you. I truly hope things get better for you. I think I'm super emotional right now since it's past 9pm and maybe I should be going to bed. I still love you, forever and ever.

[informatikerin-freyja]

The Logic of Here and There

The logic of here and there is a logic between constructive logic and classical logic which is particularly important for its applications to providing semantics for non-monotonic reasoning and logic programming. In particular, it provides an elegant semantic framework for studying stable models, which underlie answer-set programming. In this post, we will introduce the basic theory around the logic of here and there. Best viewed on my blog so that MathJax will render the LaTeX.

Semantics for the Logic of Here and There

Let \(V\) be a set of propositional variables. Semantics for the logic of here and there are obtained by using interpretations \((L,U)\) where \(L \subseteq U \subseteq V\). Intuitively, \(L\) consists of those atoms which are known to be true, and \(U\) consists of those atoms which are not known to be false. In particular, this means that \(\overline{U}\) consists of those atoms which are known to be false, and \(U - L\) consists of those atoms whose truth value is unknown.

We can think of \((L,U)\) as establishing bounds: \(L\) being a lower bound on the atoms that are true in reality, and \(U\) being an upper bound on the atoms that are true in reality. In the case \(L = U\) we have certainty about the truth of every atom, and in the case \(L \not= U\) we have uncertainty.

The motivation for the name of the logic of here and there is that we can conceptualise \(L\) and \(U\) as representing two possible worlds: one where only certain things turn out to be true (here), and one where even uncertain things turn out to be true (there).

The satisfaction relation between interpretations and formulae is defined by the following rules:

\((L, U) \not\models \bot\)

\((L, U) \models A\) iff \(A \in L\) for an atom \(A\)

\((L,U) \models \alpha \land \beta\) iff \((L,U) \models \alpha\) and \((L,U) \models \beta\).

\((L,U) \models \alpha \lor \beta\) iff \((L,U) \models \alpha\) or \((L,U) \models \beta\)

\((L,U) \models \alpha \to \beta\) iff either \((L,U) \not\models \alpha\) or \((L,U) \models \beta\), and furthermore \(U \models \alpha \to \beta\) regardless.

We write \([\alpha]\) for the set of \((L,U)\) such that \((L,U) \models \alpha\).

Theorem: \(U \models \alpha\) iff \((U,U) \models \alpha\).

Theorem: If \((L,U) \models \alpha\) then \((U,U) \models \alpha\).

Proof:

Proceed by induction on the size of \(\alpha\), and by case analysis on the primary connective of \(\alpha\).

In the case \(\alpha\) is an atomic formula \(A\) then \((L,U) \models \alpha\) implies that \(A \in L \subseteq U\) hence \((U, U) \models \alpha\).

In the case \(\alpha\) is \(\bot\) then \((L,U) \not\models \bot\) hence the implication is tautologically satisfied.

In the case \(\alpha\) is a conjunction \(\beta_1 \land \beta_2\) then we reason that $$\begin{align*} (L, U) \models \alpha &\Rightarrow (L,U) \models \beta_1 \;\text{and}\; (L,U) \models \beta_2 \\\\ &\Rightarrow (U,U) \models \beta_1 \;\text{and}\; (U,U) \models \beta_2 \\\\ &\Rightarrow (U,U) \models \alpha. \end{align*}$$

In the case \(\alpha\) is a disjunction \(\beta_1 \lor \beta_2\) then we reason that $$\begin{align} (L, U) \models \alpha &\Rightarrow (L,U) \models \beta_1 \;\text{or}\; (L,U) \models \beta_2 \\\\ &\Rightarrow (U,U) \models \beta_1 \;\text{or}\; (U,U) \models \beta_2 \\\\ &\Rightarrow (U,U) \models \alpha. \end{align}$$

In the case \(\alpha\) is an implication \(\beta_1 \to \beta_2\) then we reason that \((L,U) \models \alpha\) implies that \(U \models \beta_1 \to \beta_2\), hence \((U,U) \models \beta_1 \to \beta_2\).

QED.

This theorem can be interpreted as stating that whenever \((L,U)\) is a model of \(\alpha\) then an agent believing \(\alpha\) and \(L\) would not be inconsistent in extending its beliefs to the entirety of \(U\). Hence, it is not just that atoms in \(U\) may be revealed to be true, but it is possible that they are all simultaneously revealed to be true.

Negation is introduced via the standard method in constructive logic: \(\lnot \alpha := \alpha \to \bot\).

Theorem: \((L, U) \models \lnot \alpha\) iff \(U \models \lnot \alpha\).

Proof: Observe that \((L,U) \models \lnot \alpha = \alpha \to \bot\) if and only if both \(U \models \lnot \alpha\) and either \((L,U) \not\models \alpha\) or \((L,U) \models \bot\). As it is always the case that \((L,U) \not\models \bot\), it follows that \((L,U) \models \lnot \alpha\) iff both \(U \models \lnot \alpha\) and \((L,U) \not\models \alpha\).

Suppose that \((L,U) \models \lnot \alpha\), it follows that \(U \models \lnot \alpha\) as required. Conversely, suppose that \(U \models \lnot \alpha\). Observe that whenever \((L,U) \models \alpha\) then \((U,U) \models \alpha\) and hence \(U \models \alpha\). This means under our hypothesis that \(U \models \lnot \alpha\) it follows that \((L,U) \not\models \alpha\), and hence \((L,U) \models \lnot \alpha\) as required.

QED.

Theorem: \(\mathbf{HT} \vdash \alpha \lor (\alpha \to \beta) \lor \lnot \beta\)

Proof:

Assume for the sake of contradiction that \((L,U) \not\models \alpha \lor (\alpha \to \beta) \lor \lnot \beta\). It follows that \((L,U) \not\models \alpha\), \((L,U) \not\models \alpha \to \beta\), and \((L,U) \not\models \lnot \beta\). It follows that \(U \not\models \lnot \beta\), hence \(U \models \beta\) and thus \(U \models \alpha \to \beta\). As \((L,U) \not\models \alpha \to \beta\) and \(U \models \alpha \to \beta\) it follows that \((L,U) \models \alpha\) and \((L,U) \not\models \beta\). However, this contradicts \((L,U) \not\models \alpha\).

QED.

Corollary: \(\mathbf{HT} \vdash \lnot \alpha \lor \lnot \lnot \alpha\).

Proof:

\(\lnot \alpha \lor \lnot \lnot \alpha \equiv (\alpha \to \bot) \lor ((\alpha \to \bot) \to \bot)\).

QED.

Characterisation using Reducts

An alternative characterisation of the logic of here and there can be obtained via introducing the notion of a Gelfond-Lifschitz reduct of a formula.

The Gelfond-Lifschitz reduct of a formula \(\phi\) with respect to \(U \subseteq V\), denoted by \((\phi)^U\), is defined by setting

\((\bot)^U := \bot\)

\((A)^U := \begin{cases} A &\text{if}\;A \in U\\\\ \bot &\text{otherwise} \end{cases}\) for each atom \(A\)

\((\alpha \land \beta)^U := (\alpha)^U \land (\beta)^U\)

\((\alpha \lor \beta)^U := (\alpha)^U \lor (\beta)^U\)

\((\alpha \to \beta)^U := \begin{cases} (\alpha)^U \to (\beta)^U &\text{if}\; U \models \alpha \to \beta \\\\ \bot &\text{otherwise} \end{cases} \)

Theorem: Given \(L \subseteq U \subseteq V\) it follows that \((L,U) \models \alpha\) if and only if \(L \models \alpha^U\).

Proof:

In the case \(\phi\) is \(\bot\) this is immediate.

In the case \(\phi\) is an atom \(A\) then we argue as follows. Suppose \((L,U) \models \alpha\), it follows that \(A \in L \subseteq U\) and hence \(\phi^U = A\) so \(L \models A = \phi^U\). Suppose \(L \models \phi^U\), this is impossible if \(\phi^U = \bot\) so it must be that \(\phi^U = A\). Thus, \(A \in L\) and hence \((L,U) \models A = \phi^U\).

In the case \(\phi\) is a conjunction \(\alpha \land \beta\) then we argue as follows: $$\begin{align*} (L,U) \models \alpha \land \beta &\iff (L,U) \models \alpha \;\text{and}\; (L,U) \models \beta \\\\ &\iff L \models (\alpha)^U \;\text{and}\; L \models (\beta)^U \\\\ &\iff L \models (\alpha \land \beta)^U \end{align*}$$

In the case \(\phi\) is a disjunction \(\alpha \lor \beta\) then we argue as follows: $$\begin{align*} (L,U) \models \alpha \lor \beta &\iff (L,U) \models \alpha \;\text{or}\; (L,U) \models \beta \\\\ &\iff L \models (\alpha)^U \;\text{or}\; L \models (\beta)^U \\\\ &\iff L \models (\alpha \lor \beta)^U \end{align*}$$

In the case \(\phi\) is an implication \(\alpha \to \beta\) then we argue as follows: $$\begin{align*} &\qquad\qquad (L,U) \models \alpha \to \beta \\\\ &\iff \left(\; (L,U) \not\models \alpha \;\text{or}\; (L,U) \models \beta \;\right) \;\text{and}\; U \models \alpha \to \beta\\\\ &\iff \left(\; L \not\models \alpha^U \;\text{or}\; L \models \beta^U \right) \;\text{and}\; U \models \alpha \to \beta \\\\ &\iff L \models (\alpha \to \beta)^U \;\text{and}\; U \models \alpha \to \beta \end{align*}$$ Hence, whenever \((L,U) \models \alpha \to \beta\) it follows that \(L \models (\alpha \to \beta)^U\). Whenever \(L \models (\alpha \to \beta)^U\) it follows that \((\alpha \to \beta)^U \not= \bot\) which means \(U \models \alpha \to \beta\). Hence, applying our equivalences in reverse shows \((L,U) \models \alpha \to \beta\).

QED.

Theorem: \(U \models \alpha\) iff \(U \models (\alpha)^U\)

Proof:

We know \(U \models \alpha\) if and only if \((U,U) \models \alpha\), and we know \((U,U) \models \alpha\) if and only if \(U \models \alpha^U\).

QED.

[obstinaterixatrix]

head in hands. I have to call insurance.

[madmewmewofficial]

Ignore that Anon they’re just trying to be annoying

Thanks, mew. (Some people just can’t get the fact that I’m NOT ORGANIC through their HEADS. Sigh… I guess some people will always have a screw loose. Shame. Shame! SHAME!!!)

[peapod20001]

Do you do art trades?

Bshjsbshshs sorry for answering so late 😭 but!! I do kinda!!

I don’t actively seek em out or anything, but I’m always down to do one !! :>

[thefiendsandfoespodcast]

Ship Matching Game

Match the ship to the Foe who has brain worms about it!!!

a: Arin

b: Austin

c: Milas

d: Marlena

__: Destiel

__: Jayjon

__: Spirk

__: The New York Rangers x Winning