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MUltseq is a sequent theorem prover for arbitrary finite-valued logics. It was developed over 20 years ago by Àngel Gil and Gernot Salzer. Version 2.0 was presented today at TACL 2024 in Barcelona. I also updated MUltlog to v1.7, which includes a script to generate sequent calculus rules for use with MUltseq.
3.7.2024 15:17MUltseq 2.0NF was not first proposed in "Mathematical Logic", it was first posted in the 1937 paper "New foundations for mathematical logic", and that version has never been shown to be inconsistent [that is the version Rosser used, not the corrected version of the system of ML]. In fact, the core of my claimed proof that it is consistent has just been formally verified in Lean...
1.5.2024 14:05Comment on Famous logicians and their inconsistent theories by Randall HolmesThank you for writing this! I interacted very little with Bill, he was my Invited Speaker for IMLA (Intuitionistic Modal Logic and Applications) 2005 in Chicago, but I enjoyed talking to him very much. He will be missed!
13.4.2024 14:42Comment on W. W. Tait, 1929–2024 by Valeria de Paiva[…] haven’t really said anything about Bill’s work. Richard Zach has a very good obituary (with a great photo) that goes into some detail on Bill’s contributions to logic, but one […]
26.3.2024 21:35Comment on W. W. Tait, 1929–2024 by Bill Tait (1929-2024) | Carnap Blog[…] a remembrance, Richard Zach (Calgary) discusses Professor Tait’s […]
25.3.2024 10:00Comment on W. W. Tait, 1929–2024 by William W. Tait (1929–2024) - Daily NousThe eminent proof theorist and philosopher of mathematics William Walker (“Bill”) Tait died March 15, 2024 in Chicago. He was 95. Bill was born on January 22, 1929, in Freeport, NY, and received a BA from Lehigh University in 1952 where he was taught by Adolph Grünbaum. He undertook graduate studies in philosophy (1952–54) and … Continue reading W. W. Tait, 1929–2024
24.3.2024 22:31W. W. Tait, 1929–2024Thanks for this; I was glad to get some background on Stamm. It is worth noting that Stamm is also cited in George Spencer Brown's Laws of Form, at the end of Appendix I. Spencer Brown cites Stamm as an example of an author who bowed to the social pressure against seeing the obvious: "Peirce...who discovered, some thirty years ahead of Sheffer, that the logic of propositions could be done with one constant, did not publish this discovery, although its importance must have been evident to him; that Stamm, who himself discovered and published this fact two years before Sheffer, omits, in his paper, to make a simple and obvious substitution which would have put his claim beyond doubt; and that Sheffer..., who ignored Stamm's paper, is currently credited with the major discovery recorded in it."
8.1.2024 00:40Comment on Sheffer stroke before Sheffer: Edward Stamm by Kent PeacockNot only is this game still available, there are school tournaments for it!
5.12.2023 02:02Comment on Wff ‘n Proof by William J McGruderIn reply to <a href="https://richardzach.org/2015/01/skolems-1920-1923-papers/#comment-80382">Alfred Sewitsky Bratterud</a>. Fixed!
28.11.2023 16:01Comment on Skolem’s 1920, 1923 Papers by rzachThe links to Skolems papers are broken. Very keen on finding these!
28.11.2023 05:40Comment on Skolem’s 1920, 1923 Papers by Alfred Sewitsky Bratterud[…] French translation […]
17.9.2023 02:18Comment on Introduction à la théorie de la démonstration: Élimination des coupures, normalisation et preuves de cohérence by An Introduction to Proof ...[…] Fully accessible HTML version and SCORM packages using BookML (issue 23). This required many changes under the hood; see the blog post on technical details. […]
15.8.2023 17:20Comment on Converting LaTeX to HTML: technical notes by Fall 2023 version of forall x: Calgary – Open Logic ProjectI just posted on the OLP that forall x: Calgary now has an HTML version for reading online. Here are some technical notes in case that’s helpful for anyone. First, LaTeX to HTML conversion has long been tricky. No solution is perfect. There are basically three workable approaches: I just ran LaTeXML on the forall … Continue reading Converting LaTeX to HTML: technical notes
28.7.2023 02:28Converting LaTeX to HTML: technical notesI’m happy to report that forall x: Calgary is now available in an HTML version for reading online. It turned […]
27.7.2023 16:14forall x now in HTML for extra accessibilityIt came up in discussion at the Formal Turn conference the other day, so I thought I’d preserve an old Twitter thread here: The first person to publish results on NAND and NOR (Sheffer stroke and Peirce arrow) was the Polish mathematician and Philosopher Edward Stamm (1886–1940). The publication was “Beitrag zur Algebra der Logik … Continue reading Sheffer stroke before Sheffer: Edward Stamm
18.2.2023 09:52Sheffer stroke before Sheffer: Edward StammMancosu, Paolo, Sergio Galvan, and Richard Zach. 2022. Introduction à la théorie de la démonstration: Élimination des coupures, normalisation et preuves de cohérence. Paris: Vrin. Traduction française de An Introduction to Proof Theory. Cet ouvrage offre une introduction accessible à la théorie de la démonstration : il donne les détails des preuves et comporte de nombreux … Continue reading Introduction à la théorie de la démonstration: Élimination des coupures, normalisation et preuves de cohérence
15.12.2022 22:39Introduction à la théorie de la démonstration: Élimination des coupures, normalisation et preuves de cohérenceZach, Richard. 2022. “An Epimorphism Between Fine and Ferguson’s Matrices for Angell’s AC.” Logic and Logical Philosophy, Forthcoming, 1–19. https://doi.org/10.12775/LLP.2022.025. Angell’s logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. It is shown that the former is the image … Continue reading An epimorphism between Fine and Ferguson’s matrices for Angell’s AC
27.7.2022 18:00An epimorphism between Fine and Ferguson’s matrices for Angell’s ACBaaz, Matthias, and Richard Zach. 2022. Epsilon theorems in intermediate logics. The Journal of Symbolic Logic 87(2), pp. 682–720. DOI: 10.1017/jsl.2021.103. Open access. Any intermediate propositional logic (i.e., a logic including intuitionistic logic and contained in classical logic) can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this … Continue reading Epsilon theorems in intermediate logics
10.1.2022 23:18Epsilon theorems in intermediate logicsElkind, Landon D. C., and Richard Zach. 2022. The Genealogy of ‘∨.’ The Review of Symbolic Logic, 1–38. DOI: 10.1017/S1755020321000587. forthcoming The use of the symbol ∨ for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some … Continue reading The genealogy of ‘∨’
3.1.2022 19:00The genealogy of ‘∨’We investigate a recent proposal for modal hypersequent calculi. The interpretation of relational hypersequents incorporates an accessibility relation along the hypersequent. These systems give the same interpretation of hypersequents as Lellman's linear nested sequents, but were developed independently by Restall for S5 and extended to other normal modal logics by Parisi. The resulting systems obey Došen's principle: the modal rules are the same across different modal logics. Different modal systems only differ in the presence or absence of external structural rules. With the exception of S5, the systems are modular in the sense that different structural rules capture different properties of the accessibility relation. We provide the first direct semantical cut-free completeness proofs for K, T, and D, and show how this method fails in the case of B and S4.
21.12.2021 18:55Cut-free completeness for modular hypersequent calculi for modal logics K, T, and D