Positive logic with adjoint modalities: Proof theory, semantics, and reasoning about information
We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T,...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2010
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| _version_ | 1826301850664566784 |
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| author | Sadrzadeh, M Dyckhoff, R Sadrzadeh, M |
| author_facet | Sadrzadeh, M Dyckhoff, R Sadrzadeh, M |
| author_sort | Sadrzadeh, M |
| collection | OXFORD |
| description | We consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4, and S5, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of "nested" or "tree-sequent" calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario. Copyright © 2010 Association for Symbolic Logic. |
| first_indexed | 2024-03-07T05:38:37Z |
| format | Journal article |
| id | oxford-uuid:e4cab7fb-32bf-465f-b32f-044db9d352e9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T05:38:37Z |
| publishDate | 2010 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:e4cab7fb-32bf-465f-b32f-044db9d352e92022-03-27T10:19:10ZPositive logic with adjoint modalities: Proof theory, semantics, and reasoning about informationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e4cab7fb-32bf-465f-b32f-044db9d352e9EnglishSymplectic Elements at OxfordElsevier2010Sadrzadeh, MDyckhoff, RSadrzadeh, MWe consider a simple modal logic whose nonmodal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of axioms corresponding to the characteristic axioms of (e.g.) T, S4, and S5, such logics are useful, as shown in previous work by Baltag, Coecke, and the first author, for encoding and reasoning about information and misinformation in multiagent systems. For the propositional-only fragment of such a dynamic epistemic logic, we present an algebraic semantics, using lattices with agent-indexed families of adjoint pairs of operators, and a cut-free sequent calculus. The calculus exploits operators on sequents, in the style of "nested" or "tree-sequent" calculi; cut-admissibility is shown by constructive syntactic methods. The applicability of the logic is illustrated by reasoning about the muddy children puzzle, for which the calculus is augmented with extra rules to express the facts of the muddy children scenario. Copyright © 2010 Association for Symbolic Logic. |
| spellingShingle | Sadrzadeh, M Dyckhoff, R Sadrzadeh, M Positive logic with adjoint modalities: Proof theory, semantics, and reasoning about information |
| title | Positive logic with adjoint modalities: Proof theory, semantics, and reasoning about information |
| title_full | Positive logic with adjoint modalities: Proof theory, semantics, and reasoning about information |
| title_fullStr | Positive logic with adjoint modalities: Proof theory, semantics, and reasoning about information |
| title_full_unstemmed | Positive logic with adjoint modalities: Proof theory, semantics, and reasoning about information |
| title_short | Positive logic with adjoint modalities: Proof theory, semantics, and reasoning about information |
| title_sort | positive logic with adjoint modalities proof theory semantics and reasoning about information |
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