Pub Date : 2021-11-11DOI: 10.4324/9781003026532-10
L. Falkenstein, S. Stapleford, Molly Kao
While truth tables allow us to determine the validity or invalidity of arguments by searching for counter-examples, they are limited because as they grow in size, the chance of error increases and the time required to construct and read them becomes increasingly prohibitive. Reduction trees give us a more efficient way of exploring the possible substitution instances of an argument form. They also provide a different and more comprehensible picture of the structure of the argument. Reduction tree construction begins by listing the premises of the argument. The denial of the conclusion is then added as the last item in the list. If the argument is valid, then it is impossible to assert the premises along with the denial of the conclusion without contradiction. The process of developing the rest of the tree involves uncovering the contradictions that must occur if the argument is valid. Let's first consider a simple argument, one whose premises and conclusion consist only of truth functionally simple statements.
{"title":"Reduction Trees","authors":"L. Falkenstein, S. Stapleford, Molly Kao","doi":"10.4324/9781003026532-10","DOIUrl":"https://doi.org/10.4324/9781003026532-10","url":null,"abstract":"While truth tables allow us to determine the validity or invalidity of arguments by searching for counter-examples, they are limited because as they grow in size, the chance of error increases and the time required to construct and read them becomes increasingly prohibitive. Reduction trees give us a more efficient way of exploring the possible substitution instances of an argument form. They also provide a different and more comprehensible picture of the structure of the argument. Reduction tree construction begins by listing the premises of the argument. The denial of the conclusion is then added as the last item in the list. If the argument is valid, then it is impossible to assert the premises along with the denial of the conclusion without contradiction. The process of developing the rest of the tree involves uncovering the contradictions that must occur if the argument is valid. Let's first consider a simple argument, one whose premises and conclusion consist only of truth functionally simple statements.","PeriodicalId":208547,"journal":{"name":"Logic Works","volume":"574 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121736905","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 : 2021-11-11DOI: 10.4324/9781003026532-14
L. Falkenstein, S. Stapleford, Molly Kao
{"title":"Semantics and Trees for Modal and Intuitionistic Sentential Logic","authors":"L. Falkenstein, S. Stapleford, Molly Kao","doi":"10.4324/9781003026532-14","DOIUrl":"https://doi.org/10.4324/9781003026532-14","url":null,"abstract":"","PeriodicalId":208547,"journal":{"name":"Logic Works","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115480414","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":"Introduction to the Study of Logic","authors":"L. Falkenstein, S. Stapleford, Molly Kao","doi":"10.4324/9781003026532-1","DOIUrl":"https://doi.org/10.4324/9781003026532-1","url":null,"abstract":"","PeriodicalId":208547,"journal":{"name":"Logic Works","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127368832","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}
Infants are able to extract words from speech early in life. Here we show that the quality of forming longer-term representations for word forms at birth predicts expressive language ability at the age of two years. Seventy-five neonates were familiarized with two spoken disyllabic pseudowords. We then tested whether the neonate brain predicts the second syllable from the first one by presenting a familiarized pseudoword frequently, and occasionally violating the learned syllable combination by different rare pseudowords. Distinct brain responses were elicited by predicted and unpredicted word endings, suggesting that the neonates had learned the familiarized pseudowords. The difference between responses to predicted and unpredicted pseudowords indexing the quality of word-form learning during familiarization significantly correlated with expressive language scores (the mean length of utterance) at 24 months in the same infant. These findings suggest that 1) neonates can memorize disyllabic words so that a learned first syllable generates predictions for the word ending, and 2) early individual differences in the quality of word-form learning correlate with language skills. This relationship helps early identification of infants at risk for language impairment.
{"title":"A-2","authors":"L. Falkenstein, S. Stapleford, Molly Kao","doi":"10.4324/9781003026532-9","DOIUrl":"https://doi.org/10.4324/9781003026532-9","url":null,"abstract":"Infants are able to extract words from speech early in life. Here we show that the quality of forming longer-term representations for word forms at birth predicts expressive language ability at the age of two years. Seventy-five neonates were familiarized with two spoken disyllabic pseudowords. We then tested whether the neonate brain predicts the second syllable from the first one by presenting a familiarized pseudoword frequently, and occasionally violating the learned syllable combination by different rare pseudowords. Distinct brain responses were elicited by predicted and unpredicted word endings, suggesting that the neonates had learned the familiarized pseudowords. The difference between responses to predicted and unpredicted pseudowords indexing the quality of word-form learning during familiarization significantly correlated with expressive language scores (the mean length of utterance) at 24 months in the same infant. These findings suggest that 1) neonates can memorize disyllabic words so that a learned first syllable generates predictions for the word ending, and 2) early individual differences in the quality of word-form learning correlate with language skills. This relationship helps early identification of infants at risk for language impairment.","PeriodicalId":208547,"journal":{"name":"Logic Works","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133866559","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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