LobstersAbstract Machines for Logic Programs
https://chrisistyping.bearblog.dev/abstract-machines-for-logic-programs/
Greg RestallIt’s neat to see that an old (fiddly, complicated) decidability argument I wrote up in the 1990s is getting some attention. Here, Raj Goré and Anthony Peigné formalise (and generalise) my decidability argument for display formulations of some substructural logics. This is interesting work, worth looking into.
https://link.springer.com/article/10.1007/s11225-026-10239-8
A General Formalised Framework for Reasoning About Display Calculi - Studia Logica
We encode Belnap’s basic theory of display calculi in the proof assistant Coq/Rocq version 8.18.0 and formalise the proof that Belnap’s conditions C2–C8 imply the cut-elimination theorem. Our framework allows us to formally prove meta-theoretic results such as Hilbert-completeness and derivability of explicit rules, such as cut, but also others if required. What makes our formalisation powerful is that it works entirely with an abstraction that can be instantiated to many possible logics and display calculi, although we make no attempt to precisely characterise the logics that can be properly displayed in our formalisation. For this reason, our work can be seen as a formalisation of a display calculus framework and a cut-elimination theorem for a wide range of display calculi. As examples, we apply our work to classical propositional logic (CPL), tense logic (Kt), and non-commutative non-associative Lambek calculus to obtain complete display calculi as well as formally proved cut-elimination theorems, but we believe our formalisation to be also applicable to many others. We also encoded a proof of the decidability of CPL that relies only on the structure of proofs within an additive display calculus for CPL. To our knowledge, our work is the first formalisation of a decidability result in display calculus. Moreover, all of our formal proofs are constructive as they never require the addition of the law of excluded middle in Coq’s environment (which is constructive by default), which means we were also able to extract computer programs from our proof of cut-elimination able to convert CPL/Kt/Lambek derivation trees into cut-free ones. As formal proofs are known to be significantly longer to write than usual pen-and-paper proofs, our work led to the development of a multitude of files of Coq code comprising more than 15,000 lines.
José A. AlonsoA general formalised framework for reasoning about display calculi. ~ Rajeev Goré, Anthony Peigné. https://link.springer.com/article/10.1007/s11225-026-10239-8 #RocqProver #ITP #Logic
A General Formalised Framework for Reasoning About Display Calculi - Studia Logica
We encode Belnap’s basic theory of display calculi in the proof assistant Coq/Rocq version 8.18.0 and formalise the proof that Belnap’s conditions C2–C8 imply the cut-elimination theorem. Our framework allows us to formally prove meta-theoretic results such as Hilbert-completeness and derivability of explicit rules, such as cut, but also others if required. What makes our formalisation powerful is that it works entirely with an abstraction that can be instantiated to many possible logics and display calculi, although we make no attempt to precisely characterise the logics that can be properly displayed in our formalisation. For this reason, our work can be seen as a formalisation of a display calculus framework and a cut-elimination theorem for a wide range of display calculi. As examples, we apply our work to classical propositional logic (CPL), tense logic (Kt), and non-commutative non-associative Lambek calculus to obtain complete display calculi as well as formally proved cut-elimination theorems, but we believe our formalisation to be also applicable to many others. We also encoded a proof of the decidability of CPL that relies only on the structure of proofs within an additive display calculus for CPL. To our knowledge, our work is the first formalisation of a decidability result in display calculus. Moreover, all of our formal proofs are constructive as they never require the addition of the law of excluded middle in Coq’s environment (which is constructive by default), which means we were also able to extract computer programs from our proof of cut-elimination able to convert CPL/Kt/Lambek derivation trees into cut-free ones. As formal proofs are known to be significantly longer to write than usual pen-and-paper proofs, our work led to the development of a multitude of files of Coq code comprising more than 15,000 lines.
N-gated Hacker NewsCan #LLMs model real-world systems in TLA+? 🤔 Oh sure, because who wouldn't want a linguistically confused #AI applying #logic it doesn't truly comprehend to complex systems modeling? 🙄 Next up: teaching your cat to do your taxes! 🐱💼
https://www.sigops.org/2026/can-llms-model-real-world-systems-in-tla/ #TLA+ #complexsystems #catstaxes #HackerNews #ngated
https://www.sigops.org/2026/can-llms-model-real-world-systems-in-tla/ #TLA+ #complexsystems #catstaxes #HackerNews #ngated
Can LLMs model real-world systems in TLA+?
Editors’ note: AI has been actively pushing the frontier of applied formal methods for computing systems. In this article, the Specula team wrote about their experience of evaluating LLMs on modeling system code, the basic capability for agentic model checking, using TLA+, a specification language f
AnsonGeometry is logic and logic is the battlefield of adulthood.
-- Col. Lyle C. Rumford
#Columbo #television #mystery #PatrickMcGoohan #ByDawnsEarlyLight #geometry #logic
Jon AwbreyLanguage Learning And Logical Modeling —
Wrote my first “Language Learning Module”, strictly speaking, a two‑level formal language learner, back in the 80s and it pretty much told me what every conceivable upscale of that ilk would be like. But it did not cross the threshold of logical reasoning, so I used Peirce's logical graphs for that. Et sic deinceps …
#Peirce #Logic #Mathematics #Semiotics #LogicalGraphs
#LanguageLearningAlgorithm #LogicalModelingAlgorithm
spaceotter
ACP SectionFrom 11:00 to 12:00 on Thursday, May 28, the PLSL reading group will discuss "Proofs as Processes" by Samson Abramsky, as well as the first two sections of "Propositions as sessions" by Philip Wadler.
https://plsl.acp.sdu.dk/posts/2025-05-28-proofs-as-processes-propositions-as-sessions/
#PLSL #curryHoward #propositionsAsTypes #concurrency #logic #lambdaCalculus #piCalculus #programmingLanguages #functionalProgramming
Alexander J. SteinIt’s such a common response that psychologists have a name for the cognitive dissonance that occurs when people feel their love for animals clashes with their love of eating them, and the justifications that follow: The “meat paradox”.
#Meat #Logic #Ethics #Politics #Psychology #AnimalRights
Magnus IdodePeople say “two heads are better than one” 🤔
So I decided to prove mathematically how two heads can equal one 😂
Let:
1 person = 1 head
If two people agree on everything and think exactly the same way:
1 head + 1 head = 1 effective thinking pattern 🧠
Therefore:
2 heads = 1 head 😭📐
Conclusion:
Two heads are only better when both actually think differently 😄