2022/05/27 by Andrea De Domenico, Ali Farjami, De Domenico, Andrea +9
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO) #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies #cs.LO #math.LO
paper · pdf · doi:10.48550/arxiv.2205.13903
arxiv created 2022/05/27 · openalex publication_date 2022/05/27 · arxiv updated 2022/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.