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.
翻译:在非古典逻辑两个研究领域之间,我们建立了新颖的联系,这些研究领域是迄今独立发展起来的:一方面,投入/产出逻辑的基本框架及其延伸,可以在一个研究方案内提出,发展哲学逻辑逻辑和AI的规范性推理的逻辑正规化;另一方面,在将地形学、代数学和双重理论理论技术纳入模型逻辑的语义研究方案范围内调查的从属代数;具体地说,我们提议,投入/产出逻辑及其延伸的基本框架可以正式地表述(简单概括)从属代数,这种解释的存在给两个研究领域都带来了好处:一方面,这种联系使人们能够从概念上理解从属代数作为规范属性和行为的数学模型;另一方面,由于从属代数和模式逻辑之间发展了良好的联系,投入/产出逻辑的输出操作者可以作为模型操作者获得新的正式代表,其特性可以明确地以适当的数学手段系统化地加以研究。