Boolean Connexive Logic and Content Relationship: Boolean connexive logic and content relationship
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| Názov: | Boolean Connexive Logic and Content Relationship: Boolean connexive logic and content relationship |
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| Autori: | Mateusz Klonowski, Luis Estrada‐González |
| Zdroj: | Studia Logica. 112:207-248 |
| Informácie o vydavateľovi: | Springer Science and Business Media LLC, 2023. |
| Rok vydania: | 2023 |
| Predmety: | logic of content relationship, Geometry, Set (abstract data type), Computational linguistics, Mathematical logic and foundations, 0603 philosophy, ethics and religion, Mathematical analysis, 01 natural sciences, Description Logics, 12. Responsible consumption, Epistemic Logic, Theoretical computer science, Logic Programming and Knowledge Representation, Artificial Intelligence, Temporal Logic, set-assignment semantics, Fuzzy Logic and Residuated Lattices, FOS: Mathematics, Content (measure theory), 0101 mathematics, 10. No inequality, Axiom, relating semantics, Nonmonotonic Reasoning, Natural language processing, Physics, Semantics (computer science), Optics, Boolean connexive logic, 06 humanities and the arts, Focus (optics), Computer science, Programming language, 3. Good health, Computational Theory and Mathematics, Constraint Logic Programming, Computer Science, Physical Sciences, Semantic Web and Ontology Development, Mathematics |
| Popis: | We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. In the first part, we also identify axioms of Epstein’s logics that, together with the connexive principles, lead to contradiction. Moreover, we present some principles that will be equivalent to the connexive theses, but not to the content connexive theses we will propose. In the second part, we focus on the semantic analysis provided by relating- and set-assignment models. We define sound and complete relating semantics for all tested systems. We also indicate alternative relating models for the smallest BCL, which are not alternative models of the connexive counterparts of the considered CRLs. We provide a set-assignment semantics for some BCLs, giving thus a natural formalization of the content relationship understood either as content sharing or as content inclusion. |
| Druh dokumentu: | Article Other literature type |
| Popis súboru: | application/xml |
| Jazyk: | English |
| ISSN: | 1572-8730 0039-3215 |
| DOI: | 10.1007/s11225-023-10058-1 |
| DOI: | 10.60692/hkax5-mbm50 |
| DOI: | 10.60692/fjm0k-5a612 |
| Prístupová URL adresa: | https://zbmath.org/7830168 https://doi.org/10.1007/s11225-023-10058-1 |
| Rights: | CC BY |
| Prístupové číslo: | edsair.doi.dedup.....c5135aa51897e68d84534b593a15f1eb |
| Databáza: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. In the first part, we also identify axioms of Epstein’s logics that, together with the connexive principles, lead to contradiction. Moreover, we present some principles that will be equivalent to the connexive theses, but not to the content connexive theses we will propose. In the second part, we focus on the semantic analysis provided by relating- and set-assignment models. We define sound and complete relating semantics for all tested systems. We also indicate alternative relating models for the smallest BCL, which are not alternative models of the connexive counterparts of the considered CRLs. We provide a set-assignment semantics for some BCLs, giving thus a natural formalization of the content relationship understood either as content sharing or as content inclusion. |
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| ISSN: | 15728730 00393215 |
| DOI: | 10.1007/s11225-023-10058-1 |