{"title":"Propositional Logic for Infinitive Sentences","authors":"Nicola Spinelli","doi":"10.1007/s10849-024-09418-4","DOIUrl":null,"url":null,"abstract":"<p>This paper is about sentences of form <i>To be human is to be an animal</i>, <i>To live is to fight</i>, etc. I call them ‘infinitive sentences’. I define an augmented propositional language able to express them and give a matrix-based semantics for it. I also give a tableau proof system, called <b>IL</b> for Infinitive Logic. I prove soundness, completeness and a few basic theorems.</p>","PeriodicalId":48732,"journal":{"name":"Journal of Logic Language and Information","volume":"24 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Logic Language and Information","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s10849-024-09418-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is about sentences of form To be human is to be an animal, To live is to fight, etc. I call them ‘infinitive sentences’. I define an augmented propositional language able to express them and give a matrix-based semantics for it. I also give a tableau proof system, called IL for Infinitive Logic. I prove soundness, completeness and a few basic theorems.
本文讨论的是 "To be human is to be an animal"、"To live is to fight "等形式的句子。我称它们为 "不定式句子"。我定义了一种能够表达它们的增强命题语言，并给出了基于矩阵的语义。我还给出了一个表证明系统，称为 "不定式逻辑 IL"。我证明了健全性、完备性和一些基本定理。
期刊介绍：
The scope of the journal is the logical and computational foundations of natural, formal, and programming languages, as well as the different forms of human and mechanized inference. It covers the logical, linguistic, and information-theoretic parts of the cognitive sciences.
Examples of main subareas are Intentional Logics including Dynamic Logic; Nonmonotonic Logic and Belief Revision; Constructive Logics; Complexity Issues in Logic and Linguistics; Theoretical Problems of Logic Programming and Resolution; Categorial Grammar and Type Theory; Generalized Quantification; Information-Oriented Theories of Semantic Structure like Situation Semantics, Discourse Representation Theory, and Dynamic Semantics; Connectionist Models of Logical and Linguistic Structures. The emphasis is on the theoretical aspects of these areas.
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