Bipolar Argumentation Frameworks (BAF) are a natural extension of Dung's Argumentation Frameworks (AF) where a relation of support between arguments is added to the standard attack relation. Despite their interest, BAF present several difficulties and their semantics are quite complex. This paper provides a definition of semantic concepts for BAF in terms of fixpoints of the functions of neutrality and defense, thus preserving most of the fundamental properties of Dung's AF. From this angle it becomes easy to show that propositional dynamic logic provides an adequate language to talk about BAF. Finally, we illustrate how this framework allows to encode the structure of the referential discourse involved in semantic paradoxes such as the Liar. It turns out that such paradoxes can be seen as BAF without a stable extension.
Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes
Carlo Proietti;
2019
Abstract
Bipolar Argumentation Frameworks (BAF) are a natural extension of Dung's Argumentation Frameworks (AF) where a relation of support between arguments is added to the standard attack relation. Despite their interest, BAF present several difficulties and their semantics are quite complex. This paper provides a definition of semantic concepts for BAF in terms of fixpoints of the functions of neutrality and defense, thus preserving most of the fundamental properties of Dung's AF. From this angle it becomes easy to show that propositional dynamic logic provides an adequate language to talk about BAF. Finally, we illustrate how this framework allows to encode the structure of the referential discourse involved in semantic paradoxes such as the Liar. It turns out that such paradoxes can be seen as BAF without a stable extension.| Campo DC | Valore | Lingua |
|---|---|---|
| dc.authority.orgunit | Istituto di linguistica computazionale "Antonio Zampolli" - ILC | - |
| dc.authority.people | Carlo Proietti | it |
| dc.authority.people | Davide Grossi | it |
| dc.authority.people | Sonja Smets | it |
| dc.authority.people | Fernando VelazquezQuesada | it |
| dc.collection.id.s | 71c7200a-7c5f-4e83-8d57-d3d2ba88f40d | * |
| dc.collection.name | 04.01 Contributo in Atti di convegno | * |
| dc.contributor.appartenenza | Istituto di linguistica computazionale "Antonio Zampolli" - ILC | * |
| dc.contributor.appartenenza.mi | 918 | * |
| dc.date.accessioned | 2024/02/21 09:51:39 | - |
| dc.date.available | 2024/02/21 09:51:39 | - |
| dc.date.issued | 2019 | - |
| dc.description.abstracteng | Bipolar Argumentation Frameworks (BAF) are a natural extension of Dung's Argumentation Frameworks (AF) where a relation of support between arguments is added to the standard attack relation. Despite their interest, BAF present several difficulties and their semantics are quite complex. This paper provides a definition of semantic concepts for BAF in terms of fixpoints of the functions of neutrality and defense, thus preserving most of the fundamental properties of Dung's AF. From this angle it becomes easy to show that propositional dynamic logic provides an adequate language to talk about BAF. Finally, we illustrate how this framework allows to encode the structure of the referential discourse involved in semantic paradoxes such as the Liar. It turns out that such paradoxes can be seen as BAF without a stable extension. | - |
| dc.description.affiliations | University of Amsterdam - ILLC, University of Groningen | - |
| dc.description.allpeople | Proietti, Carlo; Grossi, Davide; Smets, Sonja; Velazquezquesada, Fernando | - |
| dc.description.allpeopleoriginal | Carlo Proietti and Davide Grossi and Sonja Smets and Fernando Velazquez-Quesada | - |
| dc.description.fulltext | none | en |
| dc.description.numberofauthors | 4 | - |
| dc.identifier.isbn | 9783662602911 | - |
| dc.identifier.scopus | 2-s2.0-85075688361 | - |
| dc.identifier.uri | https://hdl.handle.net/20.500.14243/404076 | - |
| dc.language.iso | eng | - |
| dc.miur.last.status.update | 2026-05-18T13:00:00Z | * |
| dc.relation.alleditors | Patrick Blackburn, Emiliano Lorini, Meiyun Guo | - |
| dc.relation.conferencedate | 18-21/10/2019 | - |
| dc.relation.conferencename | 7th International Workshop on Logic, Rationality, and Interaction, LORI 2019 | - |
| dc.relation.conferenceplace | Chongqing (China) | - |
| dc.relation.firstpage | 214 | - |
| dc.relation.ispartofbook | Logic, Rationality, and Interaction - 7th International Workshop, LORI 2019, Proceedings | - |
| dc.relation.lastpage | 229 | - |
| dc.relation.numberofpages | 16 | - |
| dc.relation.volume | 11813 | - |
| dc.subject.keywords | abstract argumentation | - |
| dc.subject.keywords | bipolar argumentation frameworks | - |
| dc.subject.keywords | modal logic | - |
| dc.subject.keywords | semantic paradoxes | - |
| dc.subject.singlekeyword | abstract argumentation | * |
| dc.subject.singlekeyword | bipolar argumentation frameworks | * |
| dc.subject.singlekeyword | modal logic | * |
| dc.subject.singlekeyword | semantic paradoxes | * |
| dc.title | Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes | en |
| dc.type.driver | info:eu-repo/semantics/conferenceObject | - |
| dc.type.full | 04 Contributo in convegno::04.01 Contributo in Atti di convegno | it |
| dc.type.miur | 273 | - |
| dc.type.referee | Sì, ma tipo non specificato | - |
| dc.ugov.descaux1 | 429605 | - |
| iris.orcid.lastModifiedDate | 2026/05/18 20:14:52 | * |
| iris.orcid.lastModifiedMillisecond | 1779128092380 | * |
| iris.scopus.extIssued | 2019 | - |
| iris.scopus.extTitle | Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes | - |
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| scopus.contributor.affiliation | University of Amsterdam | - |
| scopus.contributor.affiliation | University of Groningen | - |
| scopus.contributor.affiliation | University of Bergen | - |
| scopus.contributor.affiliation | University of Amsterdam | - |
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| scopus.contributor.country | Netherlands | - |
| scopus.contributor.country | Netherlands | - |
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| scopus.contributor.dptid | 123523189 | - |
| scopus.contributor.dptid | - | |
| scopus.contributor.name | Carlo | - |
| scopus.contributor.name | Davide | - |
| scopus.contributor.name | Sonja | - |
| scopus.contributor.name | Fernando R. | - |
| scopus.contributor.subaffiliation | ILLC; | - |
| scopus.contributor.subaffiliation | - | |
| scopus.contributor.subaffiliation | Logic;Information and Interaction Group; | - |
| scopus.contributor.subaffiliation | ILLC; | - |
| scopus.contributor.surname | Proietti | - |
| scopus.contributor.surname | Grossi | - |
| scopus.contributor.surname | Smets | - |
| scopus.contributor.surname | Velázquez-Quesada | - |
| scopus.date.issued | 2019 | * |
| scopus.description.abstracteng | Bipolar Argumentation Frameworks (BAF) are a natural extension of Dung’s Argumentation Frameworks (AF) where a relation of support between arguments is added to the standard attack relation. Despite their interest, BAF present several difficulties and their semantics are quite complex. This paper provides a definition of semantic concepts for BAF in terms of fixpoints of the functions of neutrality and defense, thus preserving most of the fundamental properties of Dung’s AF. From this angle it becomes easy to show that propositional dynamic logic provides an adequate language to talk about BAF. Finally, we illustrate how this framework allows to encode the structure of the referential discourse involved in semantic paradoxes such as the Liar. It turns out that such paradoxes can be seen as BAF without a stable extension. | * |
| scopus.description.allpeopleoriginal | Proietti C.; Grossi D.; Smets S.; Velazquez-Quesada F.R. | * |
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| scopus.funding.funders | 100010661 - Horizon 2020 Framework Programme; 501100000780 - European Commission; | * |
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| scopus.identifier.doi | 10.1007/978-3-662-60292-8_16 | * |
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| scopus.relation.conferencedate | 2019 | * |
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| scopus.relation.conferenceplace | chn | * |
| scopus.relation.firstpage | 214 | * |
| scopus.relation.lastpage | 229 | * |
| scopus.relation.volume | 11813 | * |
| scopus.title | Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes | * |
| scopus.titleeng | Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes | * |
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