{"title":"反事实的因果建模语义学","authors":"Giuliano Rosella, Jan Sprenger","doi":"10.1016/j.apal.2023.103336","DOIUrl":null,"url":null,"abstract":"<div><p><span>Causal Modeling Semantics (CMS, e.g., </span><span>[6]</span>, <span>[22]</span>, <span>[12]</span><span>) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual </span><figure><img></figure><span> at a causal model </span><span><math><mi>M</mi></math></span> as a weighted average of the probability of <em>C</em> in those submodels that <em>truthmake</em> <span><math><mi>A</mi><mo>∨</mo><mi>B</mi></math></span> <span>[1]</span>, <span>[3]</span>, <span>[4]</span>. The weights of the submodels are given by the inverse distance to the original model <span><math><mi>M</mi></math></span>, based on a distance metric proposed by Eva et al. <span>[2]</span>. Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined.</p></div>","PeriodicalId":50762,"journal":{"name":"Annals of Pure and Applied Logic","volume":"175 9","pages":"Article 103336"},"PeriodicalIF":0.6000,"publicationDate":"2023-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Causal modeling semantics for counterfactuals with disjunctive antecedents\",\"authors\":\"Giuliano Rosella, Jan Sprenger\",\"doi\":\"10.1016/j.apal.2023.103336\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p><span>Causal Modeling Semantics (CMS, e.g., </span><span>[6]</span>, <span>[22]</span>, <span>[12]</span><span>) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual </span><figure><img></figure><span> at a causal model </span><span><math><mi>M</mi></math></span> as a weighted average of the probability of <em>C</em> in those submodels that <em>truthmake</em> <span><math><mi>A</mi><mo>∨</mo><mi>B</mi></math></span> <span>[1]</span>, <span>[3]</span>, <span>[4]</span>. The weights of the submodels are given by the inverse distance to the original model <span><math><mi>M</mi></math></span>, based on a distance metric proposed by Eva et al. <span>[2]</span>. Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined.</p></div>\",\"PeriodicalId\":50762,\"journal\":{\"name\":\"Annals of Pure and Applied Logic\",\"volume\":\"175 9\",\"pages\":\"Article 103336\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Pure and Applied Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0168007223000933\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Pure and Applied Logic","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168007223000933","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"LOGIC","Score":null,"Total":0}
引用次数: 0
摘要
因果建模语义学(CMS,例如 [6]、[22]、[12])是一个强大的框架,用于评估前因是原子公式组合的反事实。我们将 CMS 扩展到了对前件为非连接词的反事实的概率评估,更广泛地说,扩展到了前件为原子公式的任意布尔组合的反事实。我们的主要想法是在因果模型 M 中给反事实分配一个概率,作为 C 在真值为 A∨B 的子模型中的概率的加权平均值 [1], [3], [4]。子模型的权重由与原始模型 M 的反距离给出,该反距离基于 Eva 等人提出的距离度量[2]。除了解决了反事实认识论中的一个主要问题,我们的论文还展示了如何将语义学、因果推理和形式认识论的工作富有成效地结合起来。
Causal modeling semantics for counterfactuals with disjunctive antecedents
Causal Modeling Semantics (CMS, e.g., [6], [22], [12]) is a powerful framework for evaluating counterfactuals whose antecedent is a conjunction of atomic formulas. We extend CMS to an evaluation of the probability of counterfactuals with disjunctive antecedents, and more generally, to counterfactuals whose antecedent is an arbitrary Boolean combination of atomic formulas. Our main idea is to assign a probability to a counterfactual at a causal model as a weighted average of the probability of C in those submodels that truthmake[1], [3], [4]. The weights of the submodels are given by the inverse distance to the original model , based on a distance metric proposed by Eva et al. [2]. Apart from solving a major problem in the epistemology of counterfactuals, our paper shows how work in semantics, causal inference and formal epistemology can be fruitfully combined.
期刊介绍:
The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.