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The work introduces the purpose and structure, then surveys existential graphs (Alpha, Beta) and theory of signs, including diagrams, icons, indices, symbols, types and tokens. It formalizes syntax and semantics, builds calculi, and proves soundness and completeness, followed by translations to propositional logic and first-order logic and further extensions.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mathematical-logic-with-diagrams-based-on-the-existential-graphs-of-peirce/657680/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mathematical-logic-with-diagrams-based-on-the-existential-graphs-of-peirce/657680.png","ImageObject",300,407,{"name":92,"@type":93},"Noah","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main goal of this treatise’s diagrammatic approach?","Question",{"text":112,"@type":113},"It constructs diagrams to illustrate the general course of thought so that any course of thought can be represented with exactitude.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which systems of existential graphs are discussed in the work?",{"text":117,"@type":113},"The treatise presents existential graphs in stages including Alpha, Beta, and Gamma, and later develops syntax and semantics for formal versions.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the document connect diagram systems to logical calculi and logic translation?",{"text":121,"@type":113},"It develops calculi and proves soundness and completeness, then provides translations to propositional logic and discusses first-order logic with syntactical translations and equivalence results.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657680,1793073590,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},8796095462418,"https://ap-avatar.wpscdn.com/avatar/80000253c1241d02b47?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778826106357471780","Mathematical Logic with Diagrams  \nBased on the Existential Graphs of Peirce  \nFrithjof Dau, TU Dresden, Germany  \n2  \nDisclaimer: This is (nearly) the 􀀌nal version of this treatise. There will be no more content added. It is only subject of a further proof-reading. For this reason, if you 􀀌nd any misspellings, gaps, 􀀍aws, etc., please contact me ([dau@dr-dau.net](dau@dr-dau.net)). Similarly, do not hesitate to contact me if you have any questions.  \nFrithjof Dau, January 23, 2008  \nCome on, my Reader, and let us construct a diagram to illustrate the general course of thought; I mean a system of diagrammatization by means of which any course of thought can be represented with exactitude.  \nPeirce, Prolegomena to an Apology For Pragmaticism, 1906  \nContents  \nStart  \n1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1  \n1. 1 The Purpose and the Structure of this Treatise   3  \n2 Short Introduction to Existential Graphs : : : : : : : : : : : : : : : : : : 7  \n2.1 Alpha .................................................. 8  \n2.2 Beta ................................................... 11  \n2.3 Gamma ................................................ 14  \n3 Theory of Signs : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 17  \n3.1 Diagrams ............................................... 18  \n3.2 Icons, Indices, Symbols ................................... 18  \n3.3 Types and Tokens, Signs and Replicas ..................... 23  \n4 The Role of Existential Graphs in Peirce's Philosophy : : : : : 25  \n4.1 Foundations of Knowledge and Reasoning .................. 26  \n4.2 Existential Graphs ....................................... 32  \n4.3 Conclusion ............................................. 37  \n5 Formalizing Diagrams : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 39  \n5.1 Problems with Existential Graphs Replicas ................. 40  \n5.2 The First Approach to Diagrams .......................... 45  \n5.3 Linear Representations of Logic ........................... 48  \n5.4 The Second Approach to Diagrams ........................ 52  \n6 Contents  \n6 Some Remarks to the Books of Zeman, Roberts, and Shin : 55  \nAlpha  \n7 Syntax for Alpha Graphs : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 61  \n8 Semantics and Calculus for Formal Alpha Graphs : : : : : : : : : 75  \n8.1 Semantics for Formal Alpha Graphs ....................... 75  \n8.2 Some Remarks to the Calculus ............................ 76  \n8.3 Calculus for Alpha Graphs ................................ 78  \n8.4 Some Simple Theorems ................................... 80  \n9 Soundness and Completeness : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 83  \n9.1 Soundness .............................................. 83  \n9.2 Completeness ........................................... 85  \n10 Translation to Propositional Logic : : : : : : : : : : : : : : : : : : : : : : : : : 89  \nBeta  \n11 Getting Closer to Syntax and Semantics of Beta : : : : : : : : : : : 95  \n11.1 Lines of Identities and Ligatures ........................... 96  \n11.2 Predicates .............................................. 106  \n11.3 Cuts ................................................... 109  \n11.4 Border Cases: LoIs Touching a Cut or Crossing on a Cut ..... 116  \n12 Syntax for Existential Graphs : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 121  \n12.1 Relational Graphs with Cuts .............................. 121  \n12.2 Existential Graph Instances ............................... 124  \n12.3 Further Notations for Existential Graph Instances ........... 132  \n12.4 Formal Existential Graphs ................................ 135  \n13 Semantics for Existential Graphs : : : : : : : : : : : : : : : : : : : : : : : : : : 139  \n13.1 Semantics for Existential Graph Instances .................. 139  \n13.2 Semantics for Existential Graphs .......................","cbCaidb7sXQOMYZH","https://ap.wps.com/l/cbCaidb7sXQOMYZH","pdf",4603163,343,"English","# Introduction\n## The Purpose and the Structure of this Treatise\n# Short Introduction to Existential Graphs\n## Alpha\n## Beta\n## Gamma\n# Theory of Signs\n## Diagrams\n## Icons, Indices, Symbols\n## Types and Tokens, Signs and Replicas\n# The Role of Existential Graphs in Peirce's Philosophy\n## Foundations of Knowledge and Reasoning\n## Existential Graphs\n## Conclusion\n# Formalizing Diagrams\n## Problems with Existential Graphs Replicas\n## Linear Representations of Logic\n## The Second Approach to Diagrams\n# Translation to Propositional Logic\n## Linear Representations of Logic","[{\"question\":\"What is the main goal of this treatise’s diagrammatic approach?\",\"answer\":\"It constructs diagrams to illustrate the general course of thought so that any course of thought can be represented with exactitude.\"},{\"question\":\"Which systems of existential graphs are discussed in the work?\",\"answer\":\"The treatise presents existential graphs in stages including Alpha, Beta, and Gamma, and later develops syntax and semantics for formal versions.\"},{\"question\":\"How does the document connect diagram systems to logical calculi and logic translation?\",\"answer\":\"It develops calculi and proves soundness and completeness, then provides translations to propositional logic and discusses first-order logic with syntactical translations and equivalence results.\"}]","Mathematical Logic with Diagrams - Based on the Existential Graphs of Peirce | PDF",1792986199,864]