Pub Date : 2021-08-01DOI: 10.1215/00294527-2021-0026
S. Uckelman
{"title":"What Problem Did Ladd-Franklin (Think She) Solve(d)?","authors":"S. Uckelman","doi":"10.1215/00294527-2021-0026","DOIUrl":"https://doi.org/10.1215/00294527-2021-0026","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"38 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74637627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-08-01DOI: 10.1215/00294527-2021-0022
D. Szmuc, T. M. Ferguson
In this article we revisit a number of disputes regarding significance logics—i.e., inferential frameworks capable of handling meaningless, although grammatical, sentences—that took place in a series of articles most of which appeared in the Australasian Journal of Philosophy between 1966 and 1978. These debates concern (i) the way in which logical consequence ought to be approached in the context of a significance logic, and (ii) the way in which the logical vocabulary has to be modified (either by restricting some notions, or by adding some vocabulary) to keep as much of Classical Logic as possible. Our aim is to show that the divisions arising from these disputes can be dissolved in the context of a novel and intuitive proposal that we put forward.
{"title":"Meaningless Divisions","authors":"D. Szmuc, T. M. Ferguson","doi":"10.1215/00294527-2021-0022","DOIUrl":"https://doi.org/10.1215/00294527-2021-0022","url":null,"abstract":"In this article we revisit a number of disputes regarding significance logics—i.e., inferential frameworks capable of handling meaningless, although grammatical, sentences—that took place in a series of articles most of which appeared in the Australasian Journal of Philosophy between 1966 and 1978. These debates concern (i) the way in which logical consequence ought to be approached in the context of a significance logic, and (ii) the way in which the logical vocabulary has to be modified (either by restricting some notions, or by adding some vocabulary) to keep as much of Classical Logic as possible. Our aim is to show that the divisions arising from these disputes can be dissolved in the context of a novel and intuitive proposal that we put forward.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"45 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73563688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-21DOI: 10.1215/00294527-2022-0026
Peter Sinclair
Motivated by the Ax-Kochen/Ershov principle, a large number of questions about henselian valued fields have been shown to reduce to analogous questions about the value group and residue field. In this paper, we investigate the burden of henselian valued fields in the three-sorted Denef-Pas language. If $T$ is a theory of henselian valued fields admitting relative quantifier elimination (in any characteristic), we show that the burden of $T$ is equal to the sum of the burdens of its value group and residue field. As a consequence, $T$ is NTP${}_2$ if and only if its residue field and value group are; the same is true for the statements"$T$ is strong"and"$T$ has finite burden."
{"title":"Burden of Henselian Valued Fields in the Denef–Pas Language","authors":"Peter Sinclair","doi":"10.1215/00294527-2022-0026","DOIUrl":"https://doi.org/10.1215/00294527-2022-0026","url":null,"abstract":"Motivated by the Ax-Kochen/Ershov principle, a large number of questions about henselian valued fields have been shown to reduce to analogous questions about the value group and residue field. In this paper, we investigate the burden of henselian valued fields in the three-sorted Denef-Pas language. If $T$ is a theory of henselian valued fields admitting relative quantifier elimination (in any characteristic), we show that the burden of $T$ is equal to the sum of the burdens of its value group and residue field. As a consequence, $T$ is NTP${}_2$ if and only if its residue field and value group are; the same is true for the statements\"$T$ is strong\"and\"$T$ has finite burden.\"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42213891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-01DOI: 10.1215/00294527-2021-0011
I. V. D. Giessen, Rosalie Iemhoff
{"title":"Sequent Calculi for Intuitionistic Gödel-Löb Logic","authors":"I. V. D. Giessen, Rosalie Iemhoff","doi":"10.1215/00294527-2021-0011","DOIUrl":"https://doi.org/10.1215/00294527-2021-0011","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"473 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76521433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-01DOI: 10.1215/00294527-2021-0016
S. Guerrini, A. Masini
{"title":"Proof Nets for Classical Logic","authors":"S. Guerrini, A. Masini","doi":"10.1215/00294527-2021-0016","DOIUrl":"https://doi.org/10.1215/00294527-2021-0016","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"26 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73986034","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-01DOI: 10.1215/00294527-2021-0014
D. Gilbert, G. Venturi
{"title":"Reflexive-Insensitive Logics, the Boxdot Translation, and the Modal Logic of Generic Absoluteness","authors":"D. Gilbert, G. Venturi","doi":"10.1215/00294527-2021-0014","DOIUrl":"https://doi.org/10.1215/00294527-2021-0014","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84467435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-01DOI: 10.1215/00294527-2021-0012
Andreas Fjellstad, Jan-Fredrik Olsen
In this note, we show that the first-order logic IKω is sound with regard to the models obtained from continuum-valued Łukasiewicz-models for first-order languages by treating the quantifiers as infinitary strong disjunction/conjunction rather than infinitary weak disjunction/conjunction. Moreover, we show that these models cannot be used to provide a new consistency proof for the theory of truth IKTω obtained by expanding IKω with transparent truth, because the models are inconsistent with transparent truth. Finally, we show that whether or not this inconsistency can be reproduced in the sequent calculus for IKTω depends on how vacuous quantification is treated.
{"title":"IKTω and Łukasiewicz-Models","authors":"Andreas Fjellstad, Jan-Fredrik Olsen","doi":"10.1215/00294527-2021-0012","DOIUrl":"https://doi.org/10.1215/00294527-2021-0012","url":null,"abstract":"In this note, we show that the first-order logic IKω is sound with regard to the models obtained from continuum-valued Łukasiewicz-models for first-order languages by treating the quantifiers as infinitary strong disjunction/conjunction rather than infinitary weak disjunction/conjunction. Moreover, we show that these models cannot be used to provide a new consistency proof for the theory of truth IKTω obtained by expanding IKω with transparent truth, because the models are inconsistent with transparent truth. Finally, we show that whether or not this inconsistency can be reproduced in the sequent calculus for IKTω depends on how vacuous quantification is treated.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87275547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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