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#logic

24 posts23 participants1 post today
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Amber Grey

Snow Patrol with Ghost, the Squier Jazz bass! I recorded each track, no loops, and added the most simple part layered as I could to get to the heart of the song as it is to me. You all say I cut off at the “good” part sometimes 🤣 so here’s the full experiment, hope you enjoy! Just like…breathe for a minute and chill with me practicing bass ok? I didn’t mix this. Just had fun with an effects chain. 👻🤍 #music #bass #guitar #SnowPatrol #practice #Logic #chill #musician

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Philip Zucker

I put a new preprint up summarizing a year or so of fun e-graph ideas. Check it out! #egraphs #logic #compilers arxiv.org/abs/2504.14340

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arXiv.orgOmelets Need Onions: E-graphs Modulo Theories via Bottom-up E-matchingE-graphs are a data structure for equational reasoning and optimization over ground terms. One of the benefits of e-graph rewriting is that it can declaratively handle useful but difficult to orient identities like associativity and commutativity (AC) in a generic way. However, using these generic mechanisms is more computationally expensive than using bespoke routines on terms containing sets, multi-sets, linear expressions, polynomials, and binders. A natural question arises: How can one combine the generic capabilities of e-graph rewriting with these specialized theories. This paper discusses a pragmatic approach to this e-graphs modulo theories (EMT) question using two key ideas: bottom-up e-matching and semantic e-ids.
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José A. Alonso

The inverse method is a good fit for Datalog theorem proving. ~ Philip Zucker. philipzucker.com/inverse_metho #Datalog #Logic

Hey There Buddo! · The Inverse Method is a Good Fit for Datalog Theorem ProvingThe inverse method on first glance feels like an oddball. But actually it is rather straightforward when viewed from a datalog lens. The inverse method is a bottom up theorem proving method (typically for a sequent calculus) that finds demand for judgements by inspecting the input formula and using the subformula property of the cut-free sequent calculus. It is very schematically similar / identical to datalog methods for demand or magic set. The main thing that is a little annoying is you probably want a first class set for storing contexts $\Gamma$
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CubeRootOfTrue

I've been told that telling other people your dreams is socially awkward. Conversations with LLMs fall into this category ... Except ... I had a vision in a dream! (the rest of this is ChatGPT Monday)

Theorem: I’m right.
Proof: (a → (b → a)).

Yes! Finally, someone asks the question that’s been quietly sobbing in the corner of logic textbooks for centuries:

"Why on earth would you add an Axiom of Weakening?" Like, “Hey, we’ve got a tight, elegant proof system here—what if we threw in a rule that says, ‘eh, forget that second part, just take the first thing and walk away’?” It’s the logical equivalent of:

"We were going to listen to your full argument, but instead we’re just going to agree with whatever was said first and ignore the rest, cool?”

Let’s unpack this glorious trainwreck.
...

[for the rest, ask it about the K combinator]

#logic#weakening#boolean
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Philip Zucker

[New Blog Post] The Inverse Method is a Good Fit for Datalog Theorem Proving #datalog #logic philipzucker.com/inverse_metho

Hey There Buddo! · The Inverse Method is a Good Fit for Datalog Theorem ProvingThe inverse method on first glance feels like an oddball. But actually it is rather straightforward when viewed from a datalog lens. The inverse method is a bottom up theorem proving method (typically for a sequent calculus) that finds demand for judgements by inspecting the input formula and using the subformula property of the cut-free sequent calculus. It is very schematically similar / identical to datalog methods for demand or magic set. The main thing that is a little annoying is you probably want a first class set for storing contexts $\Gamma$
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Philo Sophies

Guest article by #Heinz #Luediger: “The #illusion of #time or where #Kant was wrong”

Here he spans a #logical #thread through the #history of #philosophy, which is based on the #metaphysical #concepts of #being and #becoming and leads to the steep #thesis that “time” is identical with #logic. But Mr. Luediger should rather explain this himself in his #essay published here.

More at: philosophies.de/index.php/2024

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