#prooftheory — 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

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

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

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

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

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/

Readings shared July 12, 2025. https://jaalonso.github.io/vestigium/posts/2025/07/13-readings_shared_07-12-25 #ASP #ATP #CLP #CategoryTheory #CoqProver #Emacs #FunctionalProgramming #Haskell #ITP #IsabelleHOL #LLMs #LeanProver #Logic #LogicProgramming #Math #Prolog #ProofTheory #Prover9

#DifferentialPropositionalCalculus • 7
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In our #Model of #Propositions as #Mappings of a #UniverseOfDiscourse to a set of 2 values, in other words, #IndicatorFunctions of the form \(f:X\to\mathbb{B},\) #SingularPropositions are those singling out the #MinimalDistinctRegions of the universe, represented by single cells of the corresponding #VennDiagram.

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#ModelTheory #ProofTheory #Semiotics

Survey of Animated Logical Graphs
• https://inquiryintoinquiry.com/2023/03/28/survey-of-animated-logical-graphs-5/

This is a Survey of blog and wiki posts on Logical Graphs, encompassing several families of graph-theoretic structures originally developed by Charles S. Peirce as graphical formal languages or visual styles of syntax amenable to interpretation for logical applications.

#Peirce #Logic #LogicalGraphs #EntitativeGraphs #ExistentialGraphs
#Boole #BooleanAlgebra #BooleanFunctions #ModelTheory #ProofTheory
#SpencerBrown #LawsOfForm #PropositionalCalculus #LogicAsSemiotics

#LogicalGraphs • 14
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

The procedure just described is called “traversing” the tree and the string read off is called the “#TraversalString” of the tree. The reverse operation of going from the string to the tree is called “parsing” the string and the tree constructed is called the “#ParseGraph” of the string.

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

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

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

\(\text{proof hint : proof : proposition :: untyped term : typed term : type}\)

See my notes on #PropositionsAsTypes for more.
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Logic #Combinators #ProofTheory #TypeTheory
#CurryHowardIsomorphism #LambdaCalculus

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

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

\(\text{proof hint : proof : proposition :: untyped term : typed term : type}\)

See my notes on #PropositionsAsTypes for more.
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Logic #Combinators #ProofTheory #TypeTheory
#CurryHowardIsomorphism #LambdaCalculus

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

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

\(\text{proof hint : proof : proposition :: untyped term : typed term : type}\)

See my notes on #PropositionsAsTypes for more.
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Logic #Combinators #ProofTheory #TypeTheory
#CurryHowardIsomorphism #LambdaCalculus

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

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

\(\text{proof hint : proof : proposition :: untyped term : typed term : type}\)

See my notes on #PropositionsAsTypes for more.
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Logic #Combinators #ProofTheory #TypeTheory
#CurryHowardIsomorphism #LambdaCalculus

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

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

\(\text{proof hint : proof : proposition :: untyped term : typed term : type}\)

See my notes on #PropositionsAsTypes for more.
• https://oeis.org/wiki/Propositions_As_Types_Analogy

#Logic #Combinators #ProofTheory #TypeTheory
#CurryHowardIsomorphism #LambdaCalculus

This afternoon I had the pleasure of sneaking in to a session of Scottish Programming Languages and Verification Summer School, organised by @edwinb and colleagues in Computer Science at St Andrews.

@dorchard gave a neat talk on graded modalities. It’s neat to see substructural logics applied in the wild, and there was some logical insight, too, on the different behaviour of box-type and diamond-type modalities in a constructive setting.

#logic #modality #prooftheory

#LogicalGraphs • 12
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Once we make the connection between one of #Peirce's #AlphaGraphs and its character string expression it's not too big a leap to see how the character string codes up the structure of the topological #DualGraph in the space of #RootedTrees.

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 11
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Editing the composite picture of #AlphaGraphs and #DualGraphs in Figure 4 to bring out the dual graphs by themselves affords a view of the second #InitialEquation shown in Figure 5.

Figure 5
• https://oeis.org/w/images/4/46/Logical_Graph_Figure_5_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 3
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no

We begin on a low but expansive plateau of #FormalSystems #Peirce mapped out in his system of #AlphaGraphs \((\alpha),\) a platform so abstract in its mathematical forms as to support at least two interpretations for use in the conduct of logical reasoning. Along the way, we incorporate the later contributions of George #SpencerBrown, who revived and augmented Peirce's system in his book #LawsOfForm.

#Logic #GraphTheory #ModelTheory #ProofTheory

#DifferentialPropositionalCalculus • 7
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In our #Model of #Propositions as #Mappings of a #UniverseOfDiscourse to a set of 2 values, in other words, #IndicatorFunctions of the form \(f:X\to\mathbb{B},\) #SingularPropositions are those singling out the #MinimalDistinctRegions of the universe, represented by single cells of the corresponding #VennDiagram.

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#ModelTheory #ProofTheory #Semiotics

#DifferentialPropositionalCalculus • 7
• https://inquiryintoinquiry.com/2020/03/05/differential-propositional-calculus-7/

In our #Model of #Propositions as #Mappings of a #UniverseOfDiscourse to a set of 2 values, in other words, #IndicatorFunctions of the form \(f:X\to\mathbb{B},\) #SingularPropositions are those singling out the #MinimalDistinctRegions of the universe, represented by single cells of the corresponding #VennDiagram.

#Logic #LogicalGraphs #DifferentialLogic
#PropositionalCalculus #BooleanFunctions
#ModelTheory #ProofTheory #Semiotics

Propositions As Types Analogy • 1

Re: R.J. Lipton • Mathematical Tricks

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.

See my working notes on the Propositions As Types Analogy for more information.

#Animata #CSPeirce #CombinatorCalculus #CombinatoryLogic #CurryHowardIsomorphism #GraphTheory #LambdaCalculus #Logic #LogicalGraphs #Mathematics #ProofTheory #PropositionsAsTypesAnalogy #TypeTheory

#ThemeOneProgram • #SurveyPage
• https://inquiryintoinquiry.com/2022/06/12/survey-of-theme-one-program-4/

A program I worked on all through the 80s aimed to develop #Algorithms and #DataStructures for integrating #EmpiricalLearning and #LogicalReasoning. I had earlier developed programs for #Learning #TwoLevelFormalLanguages and for #PropositionalLogic #ConstraintSatisfaction based on C.S. #Peirce's #LogicalGraphs. Getting those 2 faculties to work together meant integrating the ways of #Empiricism and #Rationalism.

#ThemeOneProgram #Learning #Reasoning
#Logic #LogicalGraphs #FormalLanguages
#Algorithm #DataStructure #GraphTheory
#Peirce #PragmaticSemioticInformation
#Empiricism #Rationalism #Pragmatism
#ModelTheory #ProofTheory #Semiotics
#ParallelDistributedProcessing #PDP
#Grossberg #McClelland #Rumelhart

#LogicalGraphs • 1
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no

A #LogicalGraph is a graph-theoretic structure in one of the systems of graphical syntax Charles Sanders #Peirce developed for #Logic.

In his papers on #QualitativeLogic, #EntitativeGraphs, and #ExistentialGraphs, Peirce developed several versions of a graphical formalism, or a graph-theoretic formal language, designed to be interpreted for logic.

#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

"A major function [of deductive #logic is in] assessing exactly what is involved in asserting some set of propositions. […] By omitting some premiss without which the deduction of some conclusion is not valid, it misrepresents the premiss from which this conclusion is obtained, and hence responsibility for the conclusion. To agree to accept partial responsibility as good enough here is like agreeing to say that somebody was responsible for the dinner when he peeled potatoes and the cook did the rest. The first statement cannot be accepted as an elliptical, but allowable, way of making the second statement. And similarly suppression [of some premiss] enables us to obtain as causally responsible a partially sufficient rather than a fully sufficient causal condition."

Valerie Plumwood in Australasian Journal of Logic, 2023: https://ojs.victoria.ac.nz/ajl/issue/view/894 v @rrrichardzach

#Plumwood #causality #correlations #economics #reason #ProofTheory #PhilSci #truth #science #ethics #ecofeminism #freedom

#LogicalGraphs • 17
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Editing the composite picture of #AlphaGraphs and #DualGraphs in Figure 8 to bring out the dual graphs by themselves affords a view of the first #InitialEquation shown in Figure 9.

Figure 9
• https://oeis.org/w/images/8/85/Logical_Graph_Figure_9_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 17
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Editing the composite picture of #AlphaGraphs and #DualGraphs in Figure 8 to bring out the dual graphs by themselves affords a view of the first #InitialEquation shown in Figure 9.

Figure 9
• https://oeis.org/w/images/8/85/Logical_Graph_Figure_9_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 17
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Editing the composite picture of #AlphaGraphs and #DualGraphs in Figure 8 to bring out the dual graphs by themselves affords a view of the first #InitialEquation shown in Figure 9.

Figure 9
• https://oeis.org/w/images/8/85/Logical_Graph_Figure_9_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 16
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Turning to the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}",\) Figure 8 shows the planar maps and their corresponding #DualGraphs superimposed.

Figure 8
• https://oeis.org/w/images/0/09/Logical_Graph_Figure_8_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 16
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Turning to the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}",\) Figure 8 shows the planar maps and their corresponding #DualGraphs superimposed.

Figure 8
• https://oeis.org/w/images/0/09/Logical_Graph_Figure_8_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory

#LogicalGraphs • 16
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality

#Duality • Logical and Topological

Turning to the #InitialEquation or #LogicalAxiom whose text expression is \(``\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}",\) Figure 8 shows the planar maps and their corresponding #DualGraphs superimposed.

Figure 8
• https://oeis.org/w/images/0/09/Logical_Graph_Figure_8_Visible_Frame.jpg

#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory