#proof-theory — Public Fediverse posts

My *next* talk in this spring/summer of research combines some longstanding interests of mine (Graham Priest’s Logic of Paradox) and more recent interests (natural deduction and the sequent calculus). I bet you didn’t think that you could creatively apply Gentzen’s thoroughly standard rules of natural deduction to give you a sound and complete calculus for Priest’s LP, but it turns out that you can.

https://consequently.org/presentation/2026/lp-subst-arche/

#prooftheory #NaturalDeduction #paradox #philosophy

My *next* talk in this spring/summer of research combines some longstanding interests of mine (Graham Priest’s Logic of Paradox) and more recent interests (natural deduction and the sequent calculus). I bet you didn’t think that you could creatively apply Gentzen’s thoroughly standard rules of natural deduction to give you a sound and complete calculus for Priest’s LP, but it turns out that you can.

https://consequently.org/presentation/2026/lp-subst-arche/

#prooftheory #NaturalDeduction #paradox #philosophy

My *next* talk in this spring/summer of research combines some longstanding interests of mine (Graham Priest’s Logic of Paradox) and more recent interests (natural deduction and the sequent calculus). I bet you didn’t think that you could creatively apply Gentzen’s thoroughly standard rules of natural deduction to give you a sound and complete calculus for Priest’s LP, but it turns out that you can.

https://consequently.org/presentation/2026/lp-subst-arche/

#prooftheory #NaturalDeduction #paradox #philosophy

My *next* talk in this spring/summer of research combines some longstanding interests of mine (Graham Priest’s Logic of Paradox) and more recent interests (natural deduction and the sequent calculus). I bet you didn’t think that you could creatively apply Gentzen’s thoroughly standard rules of natural deduction to give you a sound and complete calculus for Priest’s LP, but it turns out that you can.

https://consequently.org/presentation/2026/lp-subst-arche/

#prooftheory #NaturalDeduction #paradox #philosophy

My *next* talk in this spring/summer of research combines some longstanding interests of mine (Graham Priest’s Logic of Paradox) and more recent interests (natural deduction and the sequent calculus). I bet you didn’t think that you could creatively apply Gentzen’s thoroughly standard rules of natural deduction to give you a sound and complete calculus for Priest’s LP, but it turns out that you can.

https://consequently.org/presentation/2026/lp-subst-arche/

#prooftheory #NaturalDeduction #paradox #philosophy

It’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

#logic #prooftheory #rocqprover

It’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

#logic #prooftheory #rocqprover

It’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

#logic #prooftheory #rocqprover

It’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

#logic #prooftheory #rocqprover

It’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

#logic #prooftheory #rocqprover

I’m looking forward to spending time today with @ohad, @modaltype and other folks at the LFCS at Edinburgh, and getting to talk about some weird substructural modal logic.

https://consequently.org/presentation/2026/tlmh-edi/

#logic #prooftheory

I’m looking forward to spending time today with @ohad, @modaltype and other folks at the LFCS at Edinburgh, and getting to talk about some weird substructural modal logic.

https://consequently.org/presentation/2026/tlmh-edi/

#logic #prooftheory

I’m looking forward to spending time today with @ohad, @modaltype and other folks at the LFCS at Edinburgh, and getting to talk about some weird substructural modal logic.

https://consequently.org/presentation/2026/tlmh-edi/

#logic #prooftheory

I’m looking forward to spending time today with @ohad, @modaltype and other folks at the LFCS at Edinburgh, and getting to talk about some weird substructural modal logic.

https://consequently.org/presentation/2026/tlmh-edi/

#logic #prooftheory

I’m looking forward to spending time today with @ohad, @modaltype and other folks at the LFCS at Edinburgh, and getting to talk about some weird substructural modal logic.

https://consequently.org/presentation/2026/tlmh-edi/

#logic #prooftheory

Oh, look! In a few weeks time I’m going to be over in Edinburgh, giving a talk the LFCS. https://informatics.ed.ac.uk/lfcs/lfcs-seminar-tuesday-5th-may-greg-restall

If you’re in town on May 5 and like crazy proof theory, this could be fun. I’ll be talking about what happens when you take a hypersequent calculus for the modal logic S5, and *thoroughly* linearise it, removing all traces of contraction and weakening. The result is stranger than you might think. (Well, it was stranger than I first thought, anyway.) Along the journey we experience strange algebras, cut elimination and decidability arguments, and weird local/global perspective shifts. I learned a lot when thinking about this stuff, so hopefully the audience gets something out of it, too.

#logic #prooftheory

Oh, look! In a few weeks time I’m going to be over in Edinburgh, giving a talk the LFCS. https://informatics.ed.ac.uk/lfcs/lfcs-seminar-tuesday-5th-may-greg-restall

If you’re in town on May 5 and like crazy proof theory, this could be fun. I’ll be talking about what happens when you take a hypersequent calculus for the modal logic S5, and *thoroughly* linearise it, removing all traces of contraction and weakening. The result is stranger than you might think. (Well, it was stranger than I first thought, anyway.) Along the journey we experience strange algebras, cut elimination and decidability arguments, and weird local/global perspective shifts. I learned a lot when thinking about this stuff, so hopefully the audience gets something out of it, too.

#logic #prooftheory

Oh, look! In a few weeks time I’m going to be over in Edinburgh, giving a talk the LFCS. https://informatics.ed.ac.uk/lfcs/lfcs-seminar-tuesday-5th-may-greg-restall

If you’re in town on May 5 and like crazy proof theory, this could be fun. I’ll be talking about what happens when you take a hypersequent calculus for the modal logic S5, and *thoroughly* linearise it, removing all traces of contraction and weakening. The result is stranger than you might think. (Well, it was stranger than I first thought, anyway.) Along the journey we experience strange algebras, cut elimination and decidability arguments, and weird local/global perspective shifts. I learned a lot when thinking about this stuff, so hopefully the audience gets something out of it, too.

#logic #prooftheory

Oh, look! In a few weeks time I’m going to be over in Edinburgh, giving a talk the LFCS. https://informatics.ed.ac.uk/lfcs/lfcs-seminar-tuesday-5th-may-greg-restall

If you’re in town on May 5 and like crazy proof theory, this could be fun. I’ll be talking about what happens when you take a hypersequent calculus for the modal logic S5, and *thoroughly* linearise it, removing all traces of contraction and weakening. The result is stranger than you might think. (Well, it was stranger than I first thought, anyway.) Along the journey we experience strange algebras, cut elimination and decidability arguments, and weird local/global perspective shifts. I learned a lot when thinking about this stuff, so hopefully the audience gets something out of it, too.

#logic #prooftheory

Oh, look! In a few weeks time I’m going to be over in Edinburgh, giving a talk the LFCS. https://informatics.ed.ac.uk/lfcs/lfcs-seminar-tuesday-5th-may-greg-restall

If you’re in town on May 5 and like crazy proof theory, this could be fun. I’ll be talking about what happens when you take a hypersequent calculus for the modal logic S5, and *thoroughly* linearise it, removing all traces of contraction and weakening. The result is stranger than you might think. (Well, it was stranger than I first thought, anyway.) Along the journey we experience strange algebras, cut elimination and decidability arguments, and weird local/global perspective shifts. I learned a lot when thinking about this stuff, so hopefully the audience gets something out of it, too.

#logic #prooftheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

Propositions As Types Analogy • 1
• https://inquiryintoinquiry.com/2013/01/29/propositions-as-types-analogy-1/

One of my favorite mathematical tricks — it almost seems too tricky to be true — is the Propositions As Types Analogy. And I see hints the 2‑part analogy can be extended to a 3‑part analogy, as follows.

Proof Hint ∶ Proof ∶ Proposition
∷
Untyped Term ∶ Typed Term ∶ Type

or

Proof Hint ∶ Untyped Term
∷
Proof ∶ Typed Term
∷
Proposition ∶ Type

See my working notes on the Propositions As Types Analogy —
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Mathematics #CategoryTheory #ProofTheory #TypeTheory
#Logic #Analogy #Isomorphism #PropositionalCalculus
#CombinatorCalculus #CombinatoryLogic #LambdaCalculus
#Peirce #LogicalGraphs #GraphTheory #RelationTheory

I was recently reading Turing's essay "Intelligent Machinery" (<https://archive.org/details/turing1948>, <https://doi.org/10.1093/oso/9780198250791.003.0016>), and Turing says something very interesting:

"Recently the theorem of Gödel and related results (Gödel, Church, Turing) have shown that if one tries to use machines for such purposes as determining the truth or falsity of mathematical theorems *and one is not willing to tolerate an occasional wrong result*, then any given machine will in some cases be unable to give an answer at all."

the emphasis is mine. I didn't know about that clause, "and one is not willing to tolerate an occasional wrong result". Can any mathematician or logician here tell me where I can find more technical details about this and what it's meant by Turing? Thank you!

#mathematics #logic #prooftheory

I was recently reading Turing's essay "Intelligent Machinery" (<https://archive.org/details/turing1948>, <https://doi.org/10.1093/oso/9780198250791.003.0016>), and Turing says something very interesting:

"Recently the theorem of Gödel and related results (Gödel, Church, Turing) have shown that if one tries to use machines for such purposes as determining the truth or falsity of mathematical theorems *and one is not willing to tolerate an occasional wrong result*, then any given machine will in some cases be unable to give an answer at all."

the emphasis is mine. I didn't know about that clause, "and one is not willing to tolerate an occasional wrong result". Can any mathematician or logician here tell me where I can find more technical details about this and what it's meant by Turing? Thank you!

#mathematics #logic #prooftheory

I was recently reading Turing's essay "Intelligent Machinery" (<https://archive.org/details/turing1948>, <https://doi.org/10.1093/oso/9780198250791.003.0016>), and Turing says something very interesting:

"Recently the theorem of Gödel and related results (Gödel, Church, Turing) have shown that if one tries to use machines for such purposes as determining the truth or falsity of mathematical theorems *and one is not willing to tolerate an occasional wrong result*, then any given machine will in some cases be unable to give an answer at all."

the emphasis is mine. I didn't know about that clause, "and one is not willing to tolerate an occasional wrong result". Can any mathematician or logician here tell me where I can find more technical details about this and what it's meant by Turing? Thank you!

#mathematics #logic #prooftheory

I was recently reading Turing's essay "Intelligent Machinery" (<https://archive.org/details/turing1948>, <https://doi.org/10.1093/oso/9780198250791.003.0016>), and Turing says something very interesting:

"Recently the theorem of Gödel and related results (Gödel, Church, Turing) have shown that if one tries to use machines for such purposes as determining the truth or falsity of mathematical theorems *and one is not willing to tolerate an occasional wrong result*, then any given machine will in some cases be unable to give an answer at all."

the emphasis is mine. I didn't know about that clause, "and one is not willing to tolerate an occasional wrong result". Can any mathematician or logician here tell me where I can find more technical details about this and what it's meant by Turing? Thank you!

#mathematics #logic #prooftheory

I was recently reading Turing's essay "Intelligent Machinery" (<https://archive.org/details/turing1948>, <https://doi.org/10.1093/oso/9780198250791.003.0016>), and Turing says something very interesting:

"Recently the theorem of Gödel and related results (Gödel, Church, Turing) have shown that if one tries to use machines for such purposes as determining the truth or falsity of mathematical theorems *and one is not willing to tolerate an occasional wrong result*, then any given machine will in some cases be unable to give an answer at all."

the emphasis is mine. I didn't know about that clause, "and one is not willing to tolerate an occasional wrong result". Can any mathematician or logician here tell me where I can find more technical details about this and what it's meant by Turing? Thank you!

#mathematics #logic #prooftheory

Hi everyone — I’m Carlos Tomas Grahm, an independent mathematician with a background in continuum mechanics and mathematical logic.

I started in modeling under an NSF-funded Texas A&M grant, developing what’s still the most accurate carotid-artery model in the literature.

These days I’m exploring how the structure of definitions shapes proofs — from ordered vs. non-ordered reasoning to broader questions in complexity theory.

I’m here to share occasional notes (and probably too many thoughts) on proof structure, modeling, and the weirdly human process of finding rigor.

Looking forward to meeting others who love the math side of things — whether it’s theory, teaching, or applied modeling.

#Mathematics #Logic #Modeling #Complexity #ProofTheory #Mathstodon

Hi everyone — I’m Carlos Tomas Grahm, an independent mathematician with a background in continuum mechanics and mathematical logic.

I started in modeling under an NSF-funded Texas A&M grant, developing what’s still the most accurate carotid-artery model in the literature.

These days I’m exploring how the structure of definitions shapes proofs — from ordered vs. non-ordered reasoning to broader questions in complexity theory.

I’m here to share occasional notes (and probably too many thoughts) on proof structure, modeling, and the weirdly human process of finding rigor.

Looking forward to meeting others who love the math side of things — whether it’s theory, teaching, or applied modeling.

#Mathematics #Logic #Modeling #Complexity #ProofTheory #Mathstodon

Hi everyone — I’m Carlos Tomas Grahm, an independent mathematician with a background in continuum mechanics and mathematical logic.

I started in modeling under an NSF-funded Texas A&M grant, developing what’s still the most accurate carotid-artery model in the literature.

These days I’m exploring how the structure of definitions shapes proofs — from ordered vs. non-ordered reasoning to broader questions in complexity theory.

I’m here to share occasional notes (and probably too many thoughts) on proof structure, modeling, and the weirdly human process of finding rigor.

Looking forward to meeting others who love the math side of things — whether it’s theory, teaching, or applied modeling.

#Mathematics #Logic #Modeling #Complexity #ProofTheory #Mathstodon

Hi everyone — I’m Carlos Tomas Grahm, an independent mathematician with a background in continuum mechanics and mathematical logic.

I started in modeling under an NSF-funded Texas A&M grant, developing what’s still the most accurate carotid-artery model in the literature.

These days I’m exploring how the structure of definitions shapes proofs — from ordered vs. non-ordered reasoning to broader questions in complexity theory.

I’m here to share occasional notes (and probably too many thoughts) on proof structure, modeling, and the weirdly human process of finding rigor.

Looking forward to meeting others who love the math side of things — whether it’s theory, teaching, or applied modeling.

#Mathematics #Logic #Modeling #Complexity #ProofTheory #Mathstodon

Hi everyone — I’m Carlos Tomas Grahm, an independent mathematician with a background in continuum mechanics and mathematical logic.

I started in modeling under an NSF-funded Texas A&M grant, developing what’s still the most accurate carotid-artery model in the literature.

These days I’m exploring how the structure of definitions shapes proofs — from ordered vs. non-ordered reasoning to broader questions in complexity theory.

I’m here to share occasional notes (and probably too many thoughts) on proof structure, modeling, and the weirdly human process of finding rigor.

Looking forward to meeting others who love the math side of things — whether it’s theory, teaching, or applied modeling.

#Mathematics #Logic #Modeling #Complexity #ProofTheory #Mathstodon

Tomorrow, I get to give the last of my three talks on inferentialism. It’s time to buckle up your λs, and join in the search for some unicorns…

https://consequently.org/presentation/2025/whl-a/

#prooftheory #semantics #linguistics

Tomorrow, I get to give the last of my three talks on inferentialism. It’s time to buckle up your λs, and join in the search for some unicorns…

https://consequently.org/presentation/2025/whl-a/

#prooftheory #semantics #linguistics

Tomorrow, I get to give the last of my three talks on inferentialism. It’s time to buckle up your λs, and join in the search for some unicorns…

https://consequently.org/presentation/2025/whl-a/

#prooftheory #semantics #linguistics

Tomorrow, I get to give the last of my three talks on inferentialism. It’s time to buckle up your λs, and join in the search for some unicorns…

https://consequently.org/presentation/2025/whl-a/

#prooftheory #semantics #linguistics

My very first package on CRAN! <https://cran.r-project.org/package=Pinference>
I hope it may be of use especially to teachers of the basics of probability and of symbolic logic and proof theory.

Uncountable thanks to all R people here who kindly helped with all my problems along the way. 🙏

#rstats #probability #logic #prooftheory

My very first package on CRAN! <https://cran.r-project.org/package=Pinference>
I hope it may be of use especially to teachers of the basics of probability and of symbolic logic and proof theory.

Uncountable thanks to all R people here who kindly helped with all my problems along the way. 🙏

#rstats #probability #logic #prooftheory

My very first package on CRAN! <https://cran.r-project.org/package=Pinference>
I hope it may be of use especially to teachers of the basics of probability and of symbolic logic and proof theory.

Uncountable thanks to all R people here who kindly helped with all my problems along the way. 🙏

#rstats #probability #logic #prooftheory

My very first package on CRAN! <https://cran.r-project.org/package=Pinference>
I hope it may be of use especially to teachers of the basics of probability and of symbolic logic and proof theory.

Uncountable thanks to all R people here who kindly helped with all my problems along the way. 🙏

#rstats #probability #logic #prooftheory

My very first package on CRAN! <https://cran.r-project.org/package=Pinference>
I hope it may be of use especially to teachers of the basics of probability and of symbolic logic and proof theory.

Uncountable thanks to all R people here who kindly helped with all my problems along the way. 🙏

#rstats #probability #logic #prooftheory

Coming up this afternoon, I’m giving the talk “Inferentialism for Everyone” for the local Arché Metaphysics and Logic crew here in St Andrews.

This talk attempts to distill material I’ve been thinking about for the last decade or so down to a concentrated but accessible form. I look forward to discovering how successful the distillation efforts are…

https://consequently.org/presentation/2025/whl-a/

#logic #prooftheory #inferentialism #semantics

Coming up this afternoon, I’m giving the talk “Inferentialism for Everyone” for the local Arché Metaphysics and Logic crew here in St Andrews.

This talk attempts to distill material I’ve been thinking about for the last decade or so down to a concentrated but accessible form. I look forward to discovering how successful the distillation efforts are…

https://consequently.org/presentation/2025/whl-a/

#logic #prooftheory #inferentialism #semantics

Coming up this afternoon, I’m giving the talk “Inferentialism for Everyone” for the local Arché Metaphysics and Logic crew here in St Andrews.

This talk attempts to distill material I’ve been thinking about for the last decade or so down to a concentrated but accessible form. I look forward to discovering how successful the distillation efforts are…

https://consequently.org/presentation/2025/whl-a/

#logic #prooftheory #inferentialism #semantics

Coming up this afternoon, I’m giving the talk “Inferentialism for Everyone” for the local Arché Metaphysics and Logic crew here in St Andrews.

This talk attempts to distill material I’ve been thinking about for the last decade or so down to a concentrated but accessible form. I look forward to discovering how successful the distillation efforts are…

https://consequently.org/presentation/2025/whl-a/

#logic #prooftheory #inferentialism #semantics

I've followed these odd reductions back to the original source, 'Ideas and Results in Proof Theory' by Prawitz (1971); see attached image. These rules are introduced alongside the more usual ones, but not really discussed later as far as I can tell, except implicitly in a section when he notes that not everyone would accept rules beyond beta reduction as capturing the notion of 'the same proof'. He asserts uniqueness of normalisation, which these rules clearly break. Despite this being a quite heavily cited paper (~1000 cites), no one seems to have explicitly noted there is anything odd here until a paper by Dyckhoff in 2014, as best as I can tell! #logic #proofTheory

I've followed these odd reductions back to the original source, 'Ideas and Results in Proof Theory' by Prawitz (1971); see attached image. These rules are introduced alongside the more usual ones, but not really discussed later as far as I can tell, except implicitly in a section when he notes that not everyone would accept rules beyond beta reduction as capturing the notion of 'the same proof'. He asserts uniqueness of normalisation, which these rules clearly break. Despite this being a quite heavily cited paper (~1000 cites), no one seems to have explicitly noted there is anything odd here until a paper by Dyckhoff in 2014, as best as I can tell! #logic #proofTheory

I've followed these odd reductions back to the original source, 'Ideas and Results in Proof Theory' by Prawitz (1971); see attached image. These rules are introduced alongside the more usual ones, but not really discussed later as far as I can tell, except implicitly in a section when he notes that not everyone would accept rules beyond beta reduction as capturing the notion of 'the same proof'. He asserts uniqueness of normalisation, which these rules clearly break. Despite this being a quite heavily cited paper (~1000 cites), no one seems to have explicitly noted there is anything odd here until a paper by Dyckhoff in 2014, as best as I can tell! #logic #proofTheory

I've followed these odd reductions back to the original source, 'Ideas and Results in Proof Theory' by Prawitz (1971); see attached image. These rules are introduced alongside the more usual ones, but not really discussed later as far as I can tell, except implicitly in a section when he notes that not everyone would accept rules beyond beta reduction as capturing the notion of 'the same proof'. He asserts uniqueness of normalisation, which these rules clearly break. Despite this being a quite heavily cited paper (~1000 cites), no one seems to have explicitly noted there is anything odd here until a paper by Dyckhoff in 2014, as best as I can tell! #logic #proofTheory

I've followed these odd reductions back to the original source, 'Ideas and Results in Proof Theory' by Prawitz (1971); see attached image. These rules are introduced alongside the more usual ones, but not really discussed later as far as I can tell, except implicitly in a section when he notes that not everyone would accept rules beyond beta reduction as capturing the notion of 'the same proof'. He asserts uniqueness of normalisation, which these rules clearly break. Despite this being a quite heavily cited paper (~1000 cites), no one seems to have explicitly noted there is anything odd here until a paper by Dyckhoff in 2014, as best as I can tell! #logic #proofTheory

In this week's #blog I write briefly about a 2001 paper on designing lambda calculi for intuitionistic modal logic. https://blogs.fediscience.org/the-updated-scholar/2025/08/15/discussing-extended-curry-howard-correspondence-for-a-basic-constructive-modal-logic/ #logic #modalLogic #proofTheory #typeTheory

In this week's #blog I write briefly about a 2001 paper on designing lambda calculi for intuitionistic modal logic. https://blogs.fediscience.org/the-updated-scholar/2025/08/15/discussing-extended-curry-howard-correspondence-for-a-basic-constructive-modal-logic/ #logic #modalLogic #proofTheory #typeTheory

In this week's #blog I write briefly about a 2001 paper on designing lambda calculi for intuitionistic modal logic. https://blogs.fediscience.org/the-updated-scholar/2025/08/15/discussing-extended-curry-howard-correspondence-for-a-basic-constructive-modal-logic/ #logic #modalLogic #proofTheory #typeTheory

In this week's #blog I write briefly about a 2001 paper on designing lambda calculi for intuitionistic modal logic. https://blogs.fediscience.org/the-updated-scholar/2025/08/15/discussing-extended-curry-howard-correspondence-for-a-basic-constructive-modal-logic/ #logic #modalLogic #proofTheory #typeTheory

In this week's #blog I write briefly about a 2001 paper on designing lambda calculi for intuitionistic modal logic. https://blogs.fediscience.org/the-updated-scholar/2025/08/15/discussing-extended-curry-howard-correspondence-for-a-basic-constructive-modal-logic/ #logic #modalLogic #proofTheory #typeTheory

I am going to make an attempt to #blog a bit again, reading and writing about papers and books, old and new, that are cited by recent work in my area. This week, we look at a #proofTheory #logic textbook. https://blogs.fediscience.org/the-updated-scholar/2025/08/08/discussing-basic-proof-theory/

I am going to make an attempt to #blog a bit again, reading and writing about papers and books, old and new, that are cited by recent work in my area. This week, we look at a #proofTheory #logic textbook. https://blogs.fediscience.org/the-updated-scholar/2025/08/08/discussing-basic-proof-theory/