Greg Restall · @consequently
917 followers · 81 posts · Server hcommons.socialAfter a short summer break exploring Scotland, it’s time to slowly get back into the saddle, giving a few talks, and preparing for the new academic year’s teaching.
First up, a short visit to Bochum for a PhD exam, and an impromptu talk on non-classical models for the identity predicate.
https://consequently.org/presentation/2023/exploring-three-valued-models-for-identity/
#logic #modeltheory #prooftheory #philosophicallogic
Artem Chernikov · @archernikov
537 followers · 62 posts · Server mathstodon.xyzA workshop and a conference on #ModelTheory in Wroclaw, Poland this Fall!
Model Theory Workshop: 15 - 18 September 2023
https://math.uni.wroc.pl/~pkowa/registrationw23.html
Model Theory Conference: 19 - 23 September 2023
https://math.uni.wroc.pl/~pkowa/registrationc23.html
Artem Chernikov · @archernikov
537 followers · 61 posts · Server mathstodon.xyz
#ModelTheory Conference in Seoul, in commemoration of Byunghan Kim’s 60th birthday.
Aug. 28-30, 2023
The registration deadline is June 15, 2023.
This conference is ASL-sponsored, so students (who are ASL members) are eligible for ASL travel support. Partial travel expenses can also be provided to those who present a poster.
https://sites.google.com/yonsei.ac.kr/modeltheoryseoul2023/home?authuser=0
Artem Chernikov · @archernikov
526 followers · 60 posts · Server mathstodon.xyzThe video of my yesterday's talk at the #IAS on some uses of #ModelTheory in #Erdős #Geometry is now online. (Please ignore the nonsense that I've said instead of the definition of modularity!)
#geometry #erdos #modeltheory #ias
Artem Chernikov · @archernikov
508 followers · 56 posts · Server mathstodon.xyz
Jon Awbrey · @Inquiry
129 followers · 624 posts · Server mathstodon.xyz
#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
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #Peirce #logic #initialequation #dualgraphs #alphagraphs #duality #LogicalGraphs
Artem Chernikov · @archernikov
466 followers · 51 posts · Server mathstodon.xyz
Slides from my talk at the #ModelTheory Conference in celebration of Ludomir Newelski's 60th birthday in Będlewo, Poland. It's about recent work with Kyle Gannon on convolution semigroups of measures in NIP groups, which turn out to be particularly structured!
https://www.math.ucla.edu/~chernikov/slides/Newelski2022.pdf
Jon Awbrey · @Inquiry
109 followers · 499 posts · Server mathstodon.xyz
#LogicalGraphs • 16
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality
#Duality • Logical and Topological
Turning now to the #InitialEquation or #LogicalAxiom whose text expression is \(\texttt{(}~\texttt{)(}~\texttt{)}=\texttt{(}~\texttt{)}\), Figure 8 shows the planar maps and their #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
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #Peirce #logic #dualgraphs #logicalaxiom #initialequation #duality #LogicalGraphs
Jon Awbrey · @Inquiry
97 followers · 425 posts · Server mathstodon.xyz#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
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #Peirce #logic #traversalstring #duality #LogicalGraphs
Jon Awbrey · @Inquiry
96 followers · 414 posts · Server mathstodon.xyz#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
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #logic #rootedtrees #dualgraph #alphagraphs #Peirce #duality #LogicalGraphs
Jon Awbrey · @Inquiry
96 followers · 408 posts · Server mathstodon.xyz
#LogicalGraphs • 11
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Duality
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
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #Peirce #logic #initialequation #dualgraphs #alphagraphs #LogicalGraphs
Jon Awbrey · @Inquiry
94 followers · 376 posts · Server mathstodon.xyz
#LogicalGraphs • 6
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Progenesis
In Lieu of a Beginning —
Consider the #FormalEquations indicated in Figures 1 and 2.
Figure 1
• https://oeis.org/w/images/8/81/Logical_Graph_Figure_1_Visible_Frame.jpg
Figure 2
• https://oeis.org/w/images/6/66/Logical_Graph_Figure_2_Visible_Frame.jpg
For the time being these two forms of transformation may be referred to as axioms or initial equations.
#Logic #Peirce #SpencerBrown #LawsOfForm
#PropositionalCalculus #BooleanFunctions
#GraphTheory #ModelTheory #ProofTheory
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #lawsofform #spencerbrown #Peirce #logic #formalequations #LogicalGraphs
Jon Awbrey · @Inquiry
94 followers · 375 posts · Server mathstodon.xyz#LogicalGraphs • 5
• https://oeis.org/w/index.php?title=Logical_Graphs&stable=0&redirect=no#Abstract_POV
#AbstractPointOfView (cont.)
In particular, though we may note in passing such historical details as the circumstance that Charles Sanders #Peirce used a #StreamerCross symbol where George #SpencerBrown used a #CarpentersSquare marker, the theme of principal interest at the abstract level of form is neutral with regard to variations of that order.
#Logic #PropositionalCalculus #BooleanFunctions
#LawsOfForm #GraphTheory #ModelTheory #ProofTheory
#ProofTheory #modeltheory #graphtheory #lawsofform #BooleanFunctions #PropositionalCalculus #logic #carpenterssquare #spencerbrown #streamercross #Peirce #abstractpointofview #LogicalGraphs
Jon Awbrey · @Inquiry
90 followers · 359 posts · Server mathstodon.xyz#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.
#ProofTheory #modeltheory #graphtheory #logic #lawsofform #spencerbrown #alphagraphs #Peirce #formalsystems #LogicalGraphs
Jon Awbrey · @Inquiry
89 followers · 338 posts · Server mathstodon.xyz#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
#ProofTheory #modeltheory #graphtheory #BooleanFunctions #PropositionalCalculus #ExistentialGraphs #EntitativeGraphs #QualitativeLogic #logic #Peirce #logicalgraph #LogicalGraphs
Jon Awbrey · @Inquiry
81 followers · 259 posts · Server mathstodon.xyz
#ThemeOneProgram • #JetsAndSharks 1.3
• https://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-1/
The manner of representation may be illustrated by transcribing a well-known example from the #ParallelDistributedProcessing literature (#McClelland and #Rumelhart 1988) and working through a couple of the associated exercises as translated into #LogicalGraphs.
#Logic #Peirce #Semiotics #Semiosis
#Grossberg #CompetitionCooperation
#GraphTheory #ModelTheory #ProofTheory
#LogicalCacti #MinimalNegationOperators
#MinimalNegationOperators #logicalcacti #ProofTheory #modeltheory #graphtheory #competitioncooperation #grossberg #Semiosis #semiotics #Peirce #logic #LogicalGraphs #Rumelhart #McClelland #paralleldistributedprocessing #JetsAndSharks #ThemeOneProgram
Jon Awbrey · @Inquiry
81 followers · 258 posts · Server mathstodon.xyz#ThemeOneProgram • #JetsAndSharks 1.2
• https://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-1/
One way to do this is to interpret the blank or #UnmarkedState as the #RestingState of a #NeuralPool, the bound or #MarkedState as its #ActivatedState, and to represent a mutually inhibitory pool of #Neurons \(a,b,c\) by the proposition \(\texttt{(}a\texttt{,}b\texttt{,}c\texttt{)}.\)
#Logic #LogicalGraphs #Peirce
#Grossberg #McClelland #Rumelhart
#GraphTheory #ModelTheory #ProofTheory
#LogicalCacti #MinimalNegationOperators
#MinimalNegationOperators #logicalcacti #ProofTheory #modeltheory #graphtheory #Rumelhart #McClelland #grossberg #Peirce #LogicalGraphs #logic #neurons #activatedstate #markedstate #neuralpool #restingstate #unmarkedstate #JetsAndSharks #ThemeOneProgram
Jon Awbrey · @Inquiry
80 followers · 256 posts · Server mathstodon.xyz#ThemeOneProgram • #JetsAndSharks 1.1
• https://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-1/
Example 5. Jets and Sharks
The #PropositionalCalculus based on #MinimalNegationOperators can be interpreted in a way resembling the logic of #ActivationStates and #CompetitionConstraints in one class of #NeuralNetwork models.
#Logic #LogicalGraphs
#Peirce #Semiotics #Semiosis
#Grossberg #McClelland #Rumelhart
#ParallelDistributedProcessing #PDP
#GraphTheory #ModelTheory #ProofTheory
#ProofTheory #modeltheory #graphtheory #pdp #paralleldistributedprocessing #Rumelhart #McClelland #grossberg #Semiosis #semiotics #Peirce #LogicalGraphs #logic #neuralnetwork #competitionconstraints #activationstates #MinimalNegationOperators #PropositionalCalculus #JetsAndSharks #ThemeOneProgram
Artem Chernikov · @archernikov
261 followers · 43 posts · Server mathstodon.xyzIntro to Mathematical Logic: from the basic first-order #logic, through #Gödel's Completeness, to the fundamentals of #ModelTheory! All in 28 videos from a course I've taught at #UCLA:
https://youtube.com/playlist?list=PL54Pt_mZzBqibWHgesgEICeQHnwHom8xz
#ucla #modeltheory #godel #logic
Kameryn Williams · @kameryn
1 followers · 1 posts · Server mathstodon.xyz#Introduction I am a logician and mathematician, currently employed in Texas. Joining this server to talk with my friends about #logic, #SetTheory, #ModelTheory, and maybe even #ComputabilityTheory :)
#ComputabilityTheory #modeltheory #settheory #logic #introduction