[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-657390-105":59,"doc-detail-657390-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","a-new-algorithmic-decision-for-categorical-syllogisms-via-carrolls-diagrams","A New Algorithmic Decision for Categorical Syllogisms via Carroll's Diagrams","","A calculus system SLCD (Syllogistic Logic with Carroll Diagrams) is developed to represent fundamental Aristotelian categorical propositions and to analyze syllogistic inference using the deletion of the middle term. The formalism supports synchronically bilateral and trilateral diagrammatic representations and is provided with a naive algorithmic procedure. An effective method is presented to decide whether a syllogistic reasoning is valid or not within SLCD.",{"@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/a-new-algorithmic-decision-for-categorical-syllogisms-via-carrolls-diagrams/657390/",{"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/a-new-algorithmic-decision-for-categorical-syllogisms-via-carrolls-diagrams/657390.png","ImageObject",300,407,{"name":92,"@type":93},"supergirl","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the SLCD system used for?","Question",{"text":112,"@type":113},"SLCD (Syllogistic Logic with Carroll Diagrams) provides a formal approach to logical reasoning using Carroll-style diagrams to represent Aristotelian categorical propositions and syllogistic inference.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does SLCD determine whether a syllogistic reasoning is valid?",{"text":117,"@type":113},"The paper presents an effective algorithm that decides validity by using the SLCD calculus system and its diagram-based representations.",{"name":119,"@type":110,"acceptedAnswer":120},"What inference criterion does the work focus on?",{"text":121,"@type":113},"The approach is shown to be closed under syllogistic inference based on deletion of the middle term.","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},657390,1792978549,{"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":8,"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":129,"read_time":144},962088121634,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","arXiv : 1802 .04 127v4 [ cs .AI] 28 Jan 2021  \nA New Algorithmic Decision for Categorical Syllogisms via Carroll's Diagrams  \nNecla Kircali Gursoya , Ibrahim Senturkb , Tahsin Onerb,􀀃 , Arif Gursoyb  \na Tire Kutsan Vocational School, Ege University, Izmir, 35900, Turkey b Department of Mathematics, Ege University, Izmir, 35100, Turkey  \nAbstract  \nIn this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and show that they are closed under the syllogistic criterion of inference which is the deletion of middle term. Therefore, it is implemented to let the formalism comprise synchronically bilateral and trilateral diagrammatical appearance and a naive algorithmic nature. And also, there is no need speci􀀌c knowledge or exclusive ability to understand as well as to use it. Consequently, we give an e􀀋ective algorithm used to determine whether a syllogistic reasoning valid or not by using SLCD.  \nKeywords: categorical syllogism, validity, algorithm  \n2010 MSC: 68Q60, 03B70, 68T27  \n1. Introduction  \nThe 􀀌rst idea on syllogisms was produced in the 􀀌eld of proper thinking by the Greek philosopher Aristotle. His idea mainly said that in his Prior Analytics:\\syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. I mean by the last  \n􀀃 Corresponding author  \nEmail addresses: [necla.kircali.gursoy@ege.edu.tr](necla.kircali.gursoy@ege.edu.tr) (Necla Kircali Gursoy), [ibrahim.senturk@ege.edu.tr](ibrahim.senturk@ege.edu.tr) (Ibrahim Senturk), [tahsin.oner@ege.edu.tr](tahsin.oner@ege.edu.tr) (Tahsin Oner), [arif.gursoy@ege.edu.tr](arif.gursoy@ege.edu.tr) (Arif Gursoy)  \nPreprint submitted to Journal of LATEX Templates January 29, 2021  \nphrase that they produce the consequence, and by this, that no further term is required from without in order to make the consequence necessary\"[1] .  \nA syllogism is a formal logical pattern to obtain a conclusion from the set of premises. A categorical syllogism can be de􀀌ned as a logical consequence which made up three categorical propositions. It consists of three propositions which are said to be statements or sentences called major premise, minor premise and conclusion, respectively. Each of them has a quanti􀀌ed relationship between two objects. The position of objects in premises generate a classi􀀌cation called as syllogistic 􀀌gures. So, there are 4 di􀀋erent types 􀀌gures. And, the combination of quanti􀀌ers ordering deduces 64 di􀀋erent combinations in each 􀀌gure. Therefore, a categorical syllogistic system consists of 256 syllogistic moods, 15 of which are unconditionally and 9 of them are conditionally; in total 24 of them are valid. Those syllogisms in the conditional group are also said to be strengthened, or valid under existential import, which is an explicit assumption of existence of some S, M or P. Then we add a rule to SLCD: Some X is X when X exists and consequently, we obtain the formal system SLCD y .  \nThroughout the centuries, categorical syllogistic system was a paramount part of logic. Innovations in the scope of mathematical logic in the 19th and the beginning of 20th centuries, the situation is changed. However, when J. Lukasiewicz introduced syllogistic as an axiomatic system built on classical propositional calculus [2], the situation became reversed once again. Thereby, categorical syllogistic system plays an important role in the mainstream of contemporary formal logic. Furthermore, Lukasiewicz axiomatization on syllogisms is still open and new ideas rise from time to time. In recent years, the using of syllogisms is studied extensively and investigated under di􀀋erent treatments such as computer science [3, 4]; engineering [5, 6]; arti􀀌cial intelligence [7], [8]; etc. And also, computer science oriented logicians began to t","cbCaics3tA8A6Jkj","https://ap.wps.com/l/cbCaics3tA8A6Jkj","pdf",434506,21,"English","# Introduction\n## Preliminaries","[{\"question\":\"What is the SLCD system used for?\",\"answer\":\"SLCD (Syllogistic Logic with Carroll Diagrams) provides a formal approach to logical reasoning using Carroll-style diagrams to represent Aristotelian categorical propositions and syllogistic inference.\"},{\"question\":\"How does SLCD determine whether a syllogistic reasoning is valid?\",\"answer\":\"The paper presents an effective algorithm that decides validity by using the SLCD calculus system and its diagram-based representations.\"},{\"question\":\"What inference criterion does the work focus on?\",\"answer\":\"The approach is shown to be closed under syllogistic inference based on deletion of the middle term.\"}]","A New Algorithmic Decision for Categorical Syllogisms via Carroll's Diagrams | PDF",53]