We provide a categorical semantics for bounded Petri nets, both in the collective- and individual-token philosophy. In both cases, we describe the process of bounding a net internally, by just constructing new categories of executions of a net using comonads, and externally, using lax-monoidal-lax functors. Our external semantics is non-local, meaning that tokens are endowed with properties that say something about the global state of the net. We then prove, in both cases, that the internal and external constructions are equivalent, by using machinery built on top of the Grothendieck construction. The individual-token case is harder, as it requires a more explicit reliance on abstract methods.
{"title":"A Categorical Semantics for Bounded Petri Nets","authors":"F. Genovese, Fosco Loregiàn, D. Palombi","doi":"10.4204/EPTCS.372.5","DOIUrl":"https://doi.org/10.4204/EPTCS.372.5","url":null,"abstract":"We provide a categorical semantics for bounded Petri nets, both in the collective- and individual-token philosophy. In both cases, we describe the process of bounding a net internally, by just constructing new categories of executions of a net using comonads, and externally, using lax-monoidal-lax functors. Our external semantics is non-local, meaning that tokens are endowed with properties that say something about the global state of the net. We then prove, in both cases, that the internal and external constructions are equivalent, by using machinery built on top of the Grothendieck construction. The individual-token case is harder, as it requires a more explicit reliance on abstract methods.","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"1 1","pages":"59-71"},"PeriodicalIF":0.0,"publicationDate":"2021-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83091372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prevention of Pollution","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-7","DOIUrl":"https://doi.org/10.4324/9781003122647-7","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"111 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74681933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"British Ships","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-2","DOIUrl":"https://doi.org/10.4324/9781003122647-2","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91336419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Registration","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-3","DOIUrl":"https://doi.org/10.4324/9781003122647-3","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86273585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fishing Vessels","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-6","DOIUrl":"https://doi.org/10.4324/9781003122647-6","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"7 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91423583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-28DOI: 10.1017/cbo9781107297043.013
N. Phillips, Nicholas Craig, D. Steel
{"title":"Lighthouses","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.1017/cbo9781107297043.013","DOIUrl":"https://doi.org/10.1017/cbo9781107297043.013","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"96 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87697386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Safety","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-5","DOIUrl":"https://doi.org/10.4324/9781003122647-5","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83182526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Masters and Seamen","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-4","DOIUrl":"https://doi.org/10.4324/9781003122647-4","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88454125","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-28DOI: 10.4324/9781003122647-15
N. Phillips, Nicholas Craig, D. Steel
{"title":"Schedules","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-15","DOIUrl":"https://doi.org/10.4324/9781003122647-15","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"200 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82116340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-28DOI: 10.4324/9781003122647-13
N. Phillips, Nicholas Craig, D. Steel
{"title":"Legal Proceedings","authors":"N. Phillips, Nicholas Craig, D. Steel","doi":"10.4324/9781003122647-13","DOIUrl":"https://doi.org/10.4324/9781003122647-13","url":null,"abstract":"","PeriodicalId":11810,"journal":{"name":"essentia law Merchant Shipping Act 1995","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87286491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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