Subordination Algebras as Semantic Environment of Input/Output Logic

Andrea De Domenico; Ali Farjami; Krishna Manoorkar; Alessandra Palmigiano; Mattia Panettiere; Xiaolong Wang

doi:10.1007/978-3-031-15298-6_21

Subordination Algebras as Semantic Environment of Input/Output Logic

Andrea De Domenico^*
, Ali Farjami
, Krishna Manoorkar
, Alessandra Palmigiano
, Mattia Panettiere
, Xiaolong Wang

^*Corresponding author for this work

Ethics, Governance and Society

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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Abstract

We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical formalizations of normative reasoning in philosophical logic and AI; on the other hand, subordination algebras, investigated in the context of a research program integrating topological, algebraic, and duality-theoretic techniques in the study of the semantics of modal logic. Specifically, we propose that the basic framework of input/output logic, as well as its extensions, can be given formal semantics on (slight generalizations of) subordination algebras. The existence of this interpretation brings benefits to both research areas: on the one hand, this connection allows for a novel conceptual understanding of subordination algebras as mathematical models of the properties and behaviour of norms; on the other hand, thanks to the well developed connection between subordination algebras and modal logic, the output operators in input/output logic can be given a new formal representation as modal operators, whose properties can be explicitly axiomatised in a suitable language, and be systematically studied by means of mathematically established and powerful tools.

Original language	English
Title of host publication	Logic, Language, Information, and Computation
Subtitle of host publication	28th International Workshop, WoLLIC 2022, Iași, Romania, September 20–23, 2022, Proceedings
Editors	Agata Ciabattoni, Elaine Pimentel, Ruy J.G.B. de Queiroz
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	326-343
Number of pages	18
ISBN (Electronic)	9783031152986
ISBN (Print)	9783031152979
DOIs	https://doi.org/10.1007/978-3-031-15298-6_21
Publication status	Published - 2022
Event	28th International Workshop on Logic, Language, Information and Computation, WoLLIC 2022 - Iaşi, Romania Duration: 20 Sept 2022 → 23 Sept 2022

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13468 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	28th International Workshop on Logic, Language, Information and Computation, WoLLIC 2022
Country/Territory	Romania
City	Iaşi
Period	20/09/22 → 23/09/22

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

input/output logic
modal logic
Sahlqvist theory
subordination algebra

Access to Document

10.1007/978-3-031-15298-6_21

Subordination Algebras as Semantic Environment of Input or Output LogicFinal published version, 375 KBLicence: Article 25fa Dutch Copyright Act

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Cite this

De Domenico, A., Farjami, A., Manoorkar, K., Palmigiano, A., Panettiere, M., & Wang, X. (2022). Subordination Algebras as Semantic Environment of Input/Output Logic. In A. Ciabattoni, E. Pimentel, & R. J. G. B. de Queiroz (Eds.), Logic, Language, Information, and Computation: 28th International Workshop, WoLLIC 2022, Iași, Romania, September 20–23, 2022, Proceedings (pp. 326-343). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13468 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-15298-6_21

De Domenico, Andrea ; Farjami, Ali ; Manoorkar, Krishna et al. / Subordination Algebras as Semantic Environment of Input/Output Logic. Logic, Language, Information, and Computation: 28th International Workshop, WoLLIC 2022, Iași, Romania, September 20–23, 2022, Proceedings. editor / Agata Ciabattoni ; Elaine Pimentel ; Ruy J.G.B. de Queiroz. Springer Science and Business Media Deutschland GmbH, 2022. pp. 326-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical formalizations of normative reasoning in philosophical logic and AI; on the other hand, subordination algebras, investigated in the context of a research program integrating topological, algebraic, and duality-theoretic techniques in the study of the semantics of modal logic. Specifically, we propose that the basic framework of input/output logic, as well as its extensions, can be given formal semantics on (slight generalizations of) subordination algebras. The existence of this interpretation brings benefits to both research areas: on the one hand, this connection allows for a novel conceptual understanding of subordination algebras as mathematical models of the properties and behaviour of norms; on the other hand, thanks to the well developed connection between subordination algebras and modal logic, the output operators in input/output logic can be given a new formal representation as modal operators, whose properties can be explicitly axiomatised in a suitable language, and be systematically studied by means of mathematically established and powerful tools.",

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De Domenico, A, Farjami, A, Manoorkar, K, Palmigiano, A, Panettiere, M & Wang, X 2022, Subordination Algebras as Semantic Environment of Input/Output Logic. in A Ciabattoni, E Pimentel & RJGB de Queiroz (eds), Logic, Language, Information, and Computation: 28th International Workshop, WoLLIC 2022, Iași, Romania, September 20–23, 2022, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13468 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 326-343, 28th International Workshop on Logic, Language, Information and Computation, WoLLIC 2022, Iaşi, Romania, 20/09/22. https://doi.org/10.1007/978-3-031-15298-6_21

Subordination Algebras as Semantic Environment of Input/Output Logic. / De Domenico, Andrea; Farjami, Ali; Manoorkar, Krishna et al.
Logic, Language, Information, and Computation: 28th International Workshop, WoLLIC 2022, Iași, Romania, September 20–23, 2022, Proceedings. ed. / Agata Ciabattoni; Elaine Pimentel; Ruy J.G.B. de Queiroz. Springer Science and Business Media Deutschland GmbH, 2022. p. 326-343 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 13468 LNCS).

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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AB - We establish a novel connection between two research areas in non-classical logics which have been developed independently of each other so far: on the one hand, input/output logic, introduced within a research program developing logical formalizations of normative reasoning in philosophical logic and AI; on the other hand, subordination algebras, investigated in the context of a research program integrating topological, algebraic, and duality-theoretic techniques in the study of the semantics of modal logic. Specifically, we propose that the basic framework of input/output logic, as well as its extensions, can be given formal semantics on (slight generalizations of) subordination algebras. The existence of this interpretation brings benefits to both research areas: on the one hand, this connection allows for a novel conceptual understanding of subordination algebras as mathematical models of the properties and behaviour of norms; on the other hand, thanks to the well developed connection between subordination algebras and modal logic, the output operators in input/output logic can be given a new formal representation as modal operators, whose properties can be explicitly axiomatised in a suitable language, and be systematically studied by means of mathematically established and powerful tools.

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De Domenico A, Farjami A, Manoorkar K, Palmigiano A, Panettiere M, Wang X. Subordination Algebras as Semantic Environment of Input/Output Logic. In Ciabattoni A, Pimentel E, de Queiroz RJGB, editors, Logic, Language, Information, and Computation: 28th International Workshop, WoLLIC 2022, Iași, Romania, September 20–23, 2022, Proceedings. Springer Science and Business Media Deutschland GmbH. 2022. p. 326-343. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). Epub 2022 Sept 9. doi: 10.1007/978-3-031-15298-6_21