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richard zach skip to content richard zach menu cv teaching research contact featured rzach an introduction to proof theory normalization cut elimination and consistency proofs paolo mancosu sergio galvan and richard zach an introduction to proof theory normalization cut elimination and consistency proofs oxford oxford university press 2021 doi 10 1093 oso 9780192895936 001 0001 published in the uk on august 17 2021 available in hardcover and paperback an introduction to proof theory provides an accessible introduction to the theory of proofs with details worked out continue reading an introduction to proof theory normalization cut elimination and consistency proofs 2025 03 24 2025 03 26 rzach accessible open textbooks in math heavy disciplines the challenge the authoring platform of choice in many math heavy disciplines is latex it produces typeset documents of excellent quality and handles formulas and mathematical diagrams extremely well practically every researcher or instructor in mathematics physics and computer science is adept at using it and it has a wide user base outside these core disciplines continue reading accessible open textbooks in math heavy disciplines 2024 07 03 2024 07 03 rzach multseq 2 0 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 2024 03 24 2026 05 11 rzach w w tait 1929 2024 the 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 2023 07 27 2023 08 10 rzach converting latex to html technical notes i 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 assume that your latex code is basically continue reading converting latex to html technical notes 2023 07 27 2023 07 27 openlogic forall x now in html for extra accessibility i m happy to report that forall x calgary is now available in an html version for reading online read the full post at the open logic project 2023 02 18 2023 02 18 rzach sheffer stroke before sheffer edward stamm it 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 2022 12 15 2022 12 15 rzach introduction à la théorie de la démonstration élimination des coupures normalisation et preuves de cohérence mancosu 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 2022 07 27 2022 11 05 rzach an epimorphism between fine and ferguson s matrices for angell s ac zach 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 2022 01 10 2022 11 05 rzach epsilon theorems in intermediate logics baaz 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 2022 01 03 2022 01 11 rzach the genealogy of elkind 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 2021 12 21 2022 01 28 rzach cut free completeness for modular hypersequent calculi for modal logics k t and d 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 2021 09 01 2022 01 28 rzach cut elimination and normalization for generalized single and multi conclusion sequent and natural deduction calculi zach richard 2021 cut elimination and normalization for generalized single and multi conclusion sequent and natural deduction calculi the review of symbolic logic 14 3 645 86 doi 10 1017 s1755020320000015 any set of truth functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives such a sequent calculus gives rise to a continue reading cut elimination and normalization for generalized single and multi conclusion sequent and natural deduction calculi 2021 07 29 2021 07 29 rzach new details on why tarski was reluctant to leave poland before wwii paolo mancosu has a new paper out in the journal of humanistic mathematics this article makes available some early letters chronicling the relationship between the biologist joseph h woodger and the logician alfred tarski using twenty five unpublished letters from tarski to woodger preserved in the woodger papers at university college london i reconstruct their relationship continue reading new details on why tarski was reluctant to leave poland before wwii 2021 07 10 2021 07 29 rzach updates to olp for fall 2021 edition of sets logic computation in preparation for the fall 2021 edition of sets logic computation the material in the open logic project has seen 2021 06 23 2021 06 29 rzach famous logicians and their inconsistent theories a couple of days ago daniel litt linked to patrick brosnan s computer verified proof of the inconsistency of peano arithmetic the proof is correct i just put it in quotes because it relies on a quirk of the proof verification system used metamath which requires you to explicitly prohibit certain variable substitutions the axiom of pa continue reading famous logicians and their inconsistent theories 2021 06 20 2021 06 20 rzach forall x calgary goes international and other updates icymi forall x calgary has been translated into german and portuguese forall x dortmund by simon wimmer is the german 2021 06 11 2022 12 07 rzach learning outcomes and grade specifications in a formal logic course zach richard 2021 learning outcomes and grade specifications in a formal logic course poster presentation presented at the mastery grading university conference 2021 online june 11 https drive google com file d 1q6rayxfrz2k79ntahomreq9idagnbvln view formal logic is a staple of undergraduate philosophy departments courses are typically run as straight lectures with problem sets and exams i will describe a design for such continue reading learning outcomes and grade specifications in a formal logic course 2021 05 03 2021 05 18 rzach multlog 1 13 released multlog is a prolog program that converts a specification of a finite valued logic propositional or first order into optimal inference rules for a number of related analytic proof systems many sided sequent calculus signed tableaux many sided natural deduction and clause translation calculi for signed resolution the specification of the logic can be produced by a simple tcl tk continue reading multlog 1 13 released 2020 12 18 2020 12 18 rzach teaching logic online report well my intro to formal logic logic i course is in the can i think it was a success i could not have done it without graham leach krouse s carnap system and my excellent team husna farooqui sarah hatcher hannah o riain and dvij raval a while back i wrote about the plan to implement specification based continue reading teaching logic online report posts navigation older posts search for recent posts accessible open textbooks in math heavy disciplines multseq 2 0 w w tait 1929 2024 converting latex to html technical notes forall x now in html for extra accessibility recent comments accessible open textbooks in math heavy disciplines open education talks on accessible open textbooks in math heavy disciplines jeroen wouters on accessible open textbooks in math heavy disciplines deyan ginev on accessible open textbooks in math heavy disciplines norbert preining on accessible open textbooks in math heavy disciplines 数学重的学科中的开放式教材可获得 偏执的码农 on accessible open textbooks in math heavy disciplines archives march 2025 july 2024 march 2024 july 2023 february 2023 december 2022 july 2022 january 2022 december 2021 september 2021 august 2021 july 2021 june 2021 may 2021 december 2020 september 2020 august 2020 june 2020 may 2020 march 2020 january 2020 november 2019 september 2019 august 2019 february 2019 january 2019 november 2018 october 2018 september 2018 july 2018 june 2018 may 2018 april 2018 march 2018 february 2018 november 2017 october 2017 september 2017 august 2017 june 2017 may 2017 april 2017 february 2017 january 2017 december 2016 november 2016 september 2016 august 2016 july 2016 may 2016 april 2016 march 2016 february 2016 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