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Weak Kleene and Other Weak Logics of Conditionals 弱Kleene和其他弱条件逻辑
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0008
Jeremiah Joven Joaquin
{"title":"Weak Kleene and Other Weak Logics of Conditionals","authors":"Jeremiah Joven Joaquin","doi":"10.1215/00294527-2023-0008","DOIUrl":"https://doi.org/10.1215/00294527-2023-0008","url":null,"abstract":"This paper presents a weak Kleene approach to conditionals that preserves some salient formal features of conditionals, particularly their interdefinability with Boolean logical connectives. I argue that such an approach fares better than other proposed weak logics of conditionals in this regard. In particular, it fares better than the logics proposed by Cooper, Cantwell, Farrell, De Finetti, Égré, Rossi, and Sprenger.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135005604","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}
引用次数: 0
Definable Version of Wedderburn–Artin Theorem in O-Minimal Structures o -极小结构中Wedderburn-Artin定理的可定义版本
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0010
Jaruwat Rodbanjong, Athipat Thamrongthanyalak
{"title":"Definable Version of Wedderburn–Artin Theorem in O-Minimal Structures","authors":"Jaruwat Rodbanjong, Athipat Thamrongthanyalak","doi":"10.1215/00294527-2023-0010","DOIUrl":"https://doi.org/10.1215/00294527-2023-0010","url":null,"abstract":"Here we work in an arbitrary o-minimal expansion of a divisible ordered abelian group. We say that a definable ring is definably semiprime if squares of nontrivial two-sided ideals definable in the expansion are nontrivial. We prove a definable version of Wedderburn–Artin theorem and give a characterization of definably semiprime rings.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135055593","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}
引用次数: 0
Geometric Modal Logic 几何模态逻辑
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0012
Brice Halimi
{"title":"Geometric Modal Logic","authors":"Brice Halimi","doi":"10.1215/00294527-2023-0012","DOIUrl":"https://doi.org/10.1215/00294527-2023-0012","url":null,"abstract":"The purpose of this paper is to generalize Kripke semantics for propositional modal logic by geometrizing it, that is, by considering the space underlying the collection of all possible worlds as an important semantic feature in its own right, so as to take the idea of accessibility seriously. The resulting new modal semantics is worked out in a setting coming from Riemannian geometry, where Kripke semantics is shown to correspond to a particular case, namely, the discrete one. Several correspondence results, established between variants of well-known modal systems and corresponding geometric properties, illustrate the import of this new framework.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135053037","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}
引用次数: 0
C. I. Lewis’s Intensional Semantics c.i.刘易斯的内涵语义学
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0006
Edwin Mares
{"title":"C. I. Lewis’s Intensional Semantics","authors":"Edwin Mares","doi":"10.1215/00294527-2023-0006","DOIUrl":"https://doi.org/10.1215/00294527-2023-0006","url":null,"abstract":"This paper begins with a discussion of C. I. Lewis’s theory of meaning in his book, An Analysis of Knowledge and Valuation (1946) and his pragmatic theory of analyticity and necessity. I bring this theories together with some remarks that he makes in an appendix to the second edition of Symbolic Logic to construct an algebraic semantics for his logics S2 and S3. These logics and their semantics are compared and evaluated with regard to how well they implement Lewis’s theories of meaning and analyticity.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135055594","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}
引用次数: 0
An Invitation to Extension Domination 对扩展统治的邀请
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0005
Kyle Gannon, Jinhe Ye
{"title":"An Invitation to Extension Domination","authors":"Kyle Gannon, Jinhe Ye","doi":"10.1215/00294527-2023-0005","DOIUrl":"https://doi.org/10.1215/00294527-2023-0005","url":null,"abstract":"Motivated by the theory of domination for types, we introduce a notion of domination for Keisler measures called extension domination. We argue that this variant of domination behaves similarly to its typesetting counterpart. We prove that extension domination extends domination for types and that it forms a preorder on the space of global Keisler measures. We then explore some basic properties related to this notion (e.g., approximations by formulas, closure under localizations, convex combinations). We also prove a few preservation theorems and provide some explicit examples.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135002828","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}
引用次数: 0
Substitutional Validity for Modal Logic 模态逻辑的替代有效性
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0007
Marco Grossi
{"title":"Substitutional Validity for Modal Logic","authors":"Marco Grossi","doi":"10.1215/00294527-2023-0007","DOIUrl":"https://doi.org/10.1215/00294527-2023-0007","url":null,"abstract":"In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135003739","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}
引用次数: 0
Definability of Boolean Functions in Kripke Semantics Kripke语义中布尔函数的可定义性
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0011
Naosuke Matsuda
{"title":"Definability of Boolean Functions in Kripke Semantics","authors":"Naosuke Matsuda","doi":"10.1215/00294527-2023-0011","DOIUrl":"https://doi.org/10.1215/00294527-2023-0011","url":null,"abstract":"A set F of Boolean functions is said to be functionally complete if every Boolean function is definable by combining functions in F. Post clarified when a set of Boolean functions is functionally complete (with respect to classical semantics). In this paper, by extending Post’s theorem, we clarify when a set of Boolean functions is functionally complete with respect to Kripke semantics.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135051656","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}
引用次数: 0
Lower Bounds of Sets of P-points p点集合的下界
3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-08-01 DOI: 10.1215/00294527-2023-0009
Borisa Kuzeljevic, Dilip Raghavan, Jonathan L. Verner
{"title":"Lower Bounds of Sets of P-points","authors":"Borisa Kuzeljevic, Dilip Raghavan, Jonathan L. Verner","doi":"10.1215/00294527-2023-0009","DOIUrl":"https://doi.org/10.1215/00294527-2023-0009","url":null,"abstract":"We show that $mathrm{MA}_{kappa}$ implies that each collection of ${P}_{mathfrak c}$-points of size at most $kappa$ which has a $P_{mathfrak c}$-point as an $RK$ upper bound also has a ${P}_{mathfrak c}$-point as an $RK$ lower bound.","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135005605","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}
引用次数: 0
Deduction Theorem in Congruential Modal Logics 同余模态逻辑中的演绎定理
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-05-01 DOI: 10.1215/00294527-10670082
Krzysztof A. Krawczyk
{"title":"Deduction Theorem in Congruential Modal Logics","authors":"Krzysztof A. Krawczyk","doi":"10.1215/00294527-10670082","DOIUrl":"https://doi.org/10.1215/00294527-10670082","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43973220","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}
引用次数: 0
Dialetheias and Numbers Distinct from Themselves 与自己不同的对偶和数字
IF 0.7 3区 数学
Notre Dame Journal of Formal Logic Pub Date : 2023-05-01 DOI: 10.1215/00294527-10670103
U. Petersen
{"title":"Dialetheias and Numbers Distinct from Themselves","authors":"U. Petersen","doi":"10.1215/00294527-10670103","DOIUrl":"https://doi.org/10.1215/00294527-10670103","url":null,"abstract":"","PeriodicalId":51259,"journal":{"name":"Notre Dame Journal of Formal Logic","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45434702","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}
引用次数: 0
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