Pub Date : 2022-04-21DOI: 10.1007/s10849-022-09362-1
Dan Constantin Radulescu
One lists the distinct pairs of categorical premises (PCPs) formulable via only the positive terms, S,P,M, by constructing a six by six matrix obtained by pairing the six categorical P-premises, A(P,M), O(P,M), A(M,P*), O(M,P*), where P* ∈ {P,P′}, with the six, similar, categorical S-premises. One shows how five rules of valid syllogism (RofVS), select only 15 distinct PCPs that entail logical consequences (LCs) belonging to the set L+: = {A(P,S), O(P,S), A(S,P), E(S,P), O(S,P), I(S,P)}. The choice of admissible LCs can be regarded as a condition separated from the conditions (or axioms) contained in the RofVS: the usual eight (Boolean) PCPs that generate valid syllogisms are obtained when the only admissible LCs belong to the set L: = {A(S,P), E(S,P), O(S,P), I(S,P)} and no existential imports are addressed. A 64 PCP-matrix obtains when both PCPs and LCs may contain indefinite terms—the positive, S,P,M, terms, and their complementary sets, S′,P′, M′, in the universe of discourse, U, called the negative terms. Now one can accept eight LCs: A(S*,P*), I(S*,P*), where P* ∈ {P,P′}, S* ∈ {S,S′}, and there are 32 conclusive PCPs, entailing precise, “one partitioning subset of U” LCs. The four rules of conclusive syllogisms (RofCS) predict the less precise LCs, left after eliminating the middle term from the exact LCs. The RofCS also predict that the other 32 PCPs of the 64 PCP-matrix are non-conclusive. The RofVS and the RofCS are generalized, and arguments are given, for also accepting as valid syllogisms the conclusive syllogisms formulable via positive terms which entail the LCs A(P,S) and O(P,S).
{"title":"A Matricial Vue of Classical Syllogistic and an Extension of the Rules of Valid Syllogism to Rules of Conclusive Syllogisms with Indefinite Terms","authors":"Dan Constantin Radulescu","doi":"10.1007/s10849-022-09362-1","DOIUrl":"https://doi.org/10.1007/s10849-022-09362-1","url":null,"abstract":"<p>One lists the distinct pairs of categorical premises (PCPs) formulable via only the positive terms, S,P,M, by constructing a six by six matrix obtained by pairing the six categorical P-premises, A(P,M), O(P,M), A(M,P*), O(M,P*), where P* ∈ {P,P′}, with the six, similar, categorical S-premises. One shows how five rules of valid syllogism (RofVS), select only 15 distinct PCPs that entail logical consequences (LCs) belonging to the set L<sup>+</sup>: = {A(P,S), O(P,S), A(S,P), E(S,P), O(S,P), I(S,P)}. The choice of admissible LCs can be regarded as a condition separated from the conditions (or axioms) contained in the RofVS: the usual eight (Boolean) PCPs that generate valid syllogisms are obtained when the only admissible LCs belong to the set L: = {A(S,P), E(S,P), O(S,P), I(S,P)} and no existential imports are addressed. A 64 PCP-matrix obtains when both PCPs and LCs may contain indefinite terms—the positive, S,P,M, terms, and their complementary sets, S′,P′, M′, in the universe of discourse, U, called the negative terms. Now one can accept eight LCs: A(S*,P*), I(S*,P*), where P* ∈ {P,P′}, S* ∈ {S,S′}, and there are 32 conclusive PCPs, entailing precise, “one partitioning subset of U” LCs. The four rules of conclusive syllogisms (RofCS) predict the less precise LCs, left after eliminating the middle term from the exact LCs. The RofCS also predict that the other 32 PCPs of the 64 PCP-matrix are non-conclusive. The RofVS and the RofCS are generalized, and arguments are given, for also accepting as valid syllogisms the conclusive syllogisms formulable via positive terms which entail the LCs A(P,S) and O(P,S).</p>","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"48 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516543","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 : 2022-04-21DOI: 10.1007/s10849-022-09361-2
Dylan Bumford
{"title":"Composition Under Distributive Natural Transformations: Or, When Predicate Abstraction is Impossible","authors":"Dylan Bumford","doi":"10.1007/s10849-022-09361-2","DOIUrl":"https://doi.org/10.1007/s10849-022-09361-2","url":null,"abstract":"","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"31 1","pages":"287 - 307"},"PeriodicalIF":0.8,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48952564","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 : 2022-04-10DOI: 10.1007/s10849-022-09370-1
Prosenjit Howlader, M. Banerjee
{"title":"Kripke Contexts, Double Boolean Algebras with Operators and Corresponding Modal Systems","authors":"Prosenjit Howlader, M. Banerjee","doi":"10.1007/s10849-022-09370-1","DOIUrl":"https://doi.org/10.1007/s10849-022-09370-1","url":null,"abstract":"","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"32 1","pages":"117 - 146"},"PeriodicalIF":0.8,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44186931","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 : 2022-04-10DOI: 10.1007/s10849-022-09364-z
Michal Sikorski
The Ramsey Test is considered to be the default test for the acceptability of indicative conditionals. I will argue that it is incompatible with some of the recent developments in conceptualizing conditionals, namely the growing empirical evidence for the Relevance Hypothesis. According to the hypothesis, one of the necessary conditions of acceptability for an indicative conditional is its antecedent being positively probabilistically relevant for the consequent. The source of the idea is Evidential Support Theory presented in Douven (2008). I will defend the hypothesis against alleged counterexamples, and show that it is supported by growing empirical evidence. Finally, I will present a version of the Ramsey test which incorporates the relevance condition and therefore is consistent with growing empirical evidence for the relevance hypothesis.
{"title":"The Ramsey Test and Evidential Support Theory","authors":"Michal Sikorski","doi":"10.1007/s10849-022-09364-z","DOIUrl":"https://doi.org/10.1007/s10849-022-09364-z","url":null,"abstract":"<p>The Ramsey Test is considered to be the default test for the acceptability of indicative conditionals. I will argue that it is incompatible with some of the recent developments in conceptualizing conditionals, namely the growing empirical evidence for the <i>Relevance Hypothesis</i>. According to the hypothesis, one of the necessary conditions of acceptability for an indicative conditional is its antecedent being positively probabilistically relevant for the consequent. The source of the idea is <i>Evidential Support Theory</i> presented in Douven (2008). I will defend the hypothesis against alleged counterexamples, and show that it is supported by growing empirical evidence. Finally, I will present a version of the Ramsey test which incorporates the relevance condition and therefore is consistent with growing empirical evidence for the relevance hypothesis.</p>","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"9 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516496","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 : 2022-04-06DOI: 10.1007/s10849-022-09360-3
Zhen Zhao
This paper is based on Tarski’s theory of truth. The purpose of this paper is to solve the liar paradox (and its cousins) and keep both of the deductive power of classical logic and the expressive power of the word “true” in natural language. The key of this paper lies in the distinction between the predicate usage and the operator usage of the word “true”. The truth operator is primarily used for characterizing the semantics of the language. Then, we do not need the hierarchy of languages. The truth predicate is mainly used for grammatical function. Tarski’s schema of the truth predicate is not necessary in this proposal. The schema of the word "true" is the schema of the truth operator. The liar paradox (and its cousins) can be solved in this way. In the appendix, I show a consistent model for both of the truth predicate and the truth operator.
{"title":"An Update of Tarski: Two Usages of the Word “True”","authors":"Zhen Zhao","doi":"10.1007/s10849-022-09360-3","DOIUrl":"https://doi.org/10.1007/s10849-022-09360-3","url":null,"abstract":"<p>This paper is based on Tarski’s theory of truth. The purpose of this paper is to solve the liar paradox (and its cousins) and keep both of the deductive power of classical logic and the expressive power of the word “true” in natural language. The key of this paper lies in the distinction between the predicate usage and the operator usage of the word “true”. The truth operator is primarily used for characterizing the semantics of the language. Then, we do not need the hierarchy of languages. The truth predicate is mainly used for grammatical function. Tarski’s schema of the truth predicate is not necessary in this proposal. The schema of the word \"true\" is the schema of the truth operator. The liar paradox (and its cousins) can be solved in this way. In the appendix, I show a consistent model for both of the truth predicate and the truth operator.\u0000</p>","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"29 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516535","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 : 2022-03-28DOI: 10.1007/s10849-022-09359-w
A. Baltag, Dazhu Li, Mina Young Pedersen
{"title":"A Modal Logic for Supervised Learning","authors":"A. Baltag, Dazhu Li, Mina Young Pedersen","doi":"10.1007/s10849-022-09359-w","DOIUrl":"https://doi.org/10.1007/s10849-022-09359-w","url":null,"abstract":"","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"31 1","pages":"213 - 234"},"PeriodicalIF":0.8,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43068186","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 : 2022-03-24DOI: 10.1007/s10849-022-09355-0
T. Ågotnes, N. Alechina, R. Galimullin
{"title":"Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power","authors":"T. Ågotnes, N. Alechina, R. Galimullin","doi":"10.1007/s10849-022-09355-0","DOIUrl":"https://doi.org/10.1007/s10849-022-09355-0","url":null,"abstract":"","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"31 1","pages":"141 - 166"},"PeriodicalIF":0.8,"publicationDate":"2022-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46455186","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 : 2022-02-24DOI: 10.1007/s10849-022-09353-2
J. J. Joaquin
{"title":"A Reinterpretation of Beall’s ‘Off-Topic’ Semantics","authors":"J. J. Joaquin","doi":"10.1007/s10849-022-09353-2","DOIUrl":"https://doi.org/10.1007/s10849-022-09353-2","url":null,"abstract":"","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"31 1","pages":"409 - 421"},"PeriodicalIF":0.8,"publicationDate":"2022-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43726709","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 : 2022-02-09DOI: 10.1007/s10849-022-09350-5
R. Zuber
{"title":"Anaphoric Conservativity","authors":"R. Zuber","doi":"10.1007/s10849-022-09350-5","DOIUrl":"https://doi.org/10.1007/s10849-022-09350-5","url":null,"abstract":"","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"31 1","pages":"113 - 128"},"PeriodicalIF":0.8,"publicationDate":"2022-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52371974","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 : 2022-01-01DOI: 10.1007/s10849-022-09354-1
Holger Andreas
{"title":"A Simple and Non-Trivial Ramsey Test","authors":"Holger Andreas","doi":"10.1007/s10849-022-09354-1","DOIUrl":"https://doi.org/10.1007/s10849-022-09354-1","url":null,"abstract":"","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"31 1","pages":"309-325"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"52372407","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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