Plausible Reasoning and Revision in AI Along Two Dimensions: Syntax Splitting and Kinematics Principles

这个项目的主要目标是通过在深刻的方法论基础上集成来自概率推理的两种技术来丰富和扩展符号人工智能中的似然推理和信念修正的框架，这两种技术是允许通过条件对小个子签名进行局部推理的基础：句法分裂和运动学。语法拆分根据签名的子集划分模型的语义空间；运动学允许根据(排他的)情况进一步划分。这样，句法拆分和运动学原理沿两个维度组织推理和修改任务，并支持它们在局部子空间上更有效的求解。局部推理和局部修正(关于语义子空间。基于信念基础的子集)是该项目的关键概念。一个主要的挑战是(重新)构造归纳推理的全局解。从局部解出发，对整个语义空间进行修正。该项目的结果将具有深远的实践和理论影响，通过提供更有效的算法和实现，并通过处理归纳推理和信念修改的条件集的处理，支持解决归纳推理和迭代修改的两个分裂维度的基准问题存储库，并使用工作台和演示系统进行评估。将开发远远超出当前技术状态的新技术，以及可能支配高级推理和修改方法的新公理。这将通过建立一个连贯和统一的推理和修改框架来实现，该框架完全基于认知状态和条件句。对于认知状态的表示，我们依赖于两个最广泛使用的非单调推理和信念修正的语义框架，即总前序(TPO)和有序条件函数(OCF)。我们的目标是从这两种语义之间的相互关系中获得最大的好处，同时为TPO方法利用OCFs的更强结构。此外，我们还使用了受到概率推理/修改启发的OCFs的c-表示和c-修改，以及以连贯和原则性的方式控制条件句在推理/修改任务中的影响的策略。他们将局部解决方案合并为全球解决方案的做法为(有条件的)合并提供了一个全新的视角。C-表示/c-修改策略的公理化描述不仅对定义合适的算子具有实际意义。这也传达了对条件推理和条件修正的深刻方法论见解，这是由于在归纳推理/信念修正下支配条件信念集合的相互作用。这样，我们方法的基本思想和主要结果将可以转移到其他归纳推理和修改的方法中。

The main goal of this project is to enrich and extend the frameworks of plausible reasoning and belief revision in symbolic Artificial Intelligence by integrating on a deep methodological base two techniques from probabilistic reasoning which are fundamental to allow for local reasoning on small subsignatures via conditionals: syntax splitting and kinematics. Syntax splitting divides the semantic space of models according to subsets of the signature; kinematics allows for further dividing it according to (exclusive) cases. In this way, syntax splitting and kinematics principles structure reasoning and revision tasks along two dimensions, and support their more efficient solution on local subspaces. Local reasoning and local revision (on semantic subspaces resp. on subsets of the belief bases) are key concepts of this project. A major challenge is to (re)construct a global solution of the inductive reasoning resp. revision task on the whole semantic space from the local solutions. The results of the project will have far-reaching both practical and theoretical impacts, supported by a repository of benchmark problems addressing the two splitting dimensions of inductive reasoning and iterated revision and evaluated with a workbench and demonstrator system, by providing more efficient algorithms and implementations, and by dealing with the processing of sets of conditionals for inductive reasoning and belief revision. Novel techniques far beyond the current state of the art and also novel axioms that may govern advanced reasoning and revision approaches will be developed. This will be possible by setting up a coherent and unified framework for reasoning and revision which is based thoroughly on epistemic states and conditionals. For representing epistemic states, we rely on two of the most broadly used semantic frameworks for nonmonotonic inference and belief revision, namely total preorders (TPO) and ordinal conditional functions (OCF). We aim at taking maximal benefit from the interrelationships between both semantics while exploiting the stronger structure of OCFs for TPO methods. Moreover, we make use of c-representations and c-revisions for OCFs which have been inspired by probabilistic reasoning/revision, together with strategies which govern the impacts of conditionals in reasoning/revision tasks in a coherent and principled way. Their employment for merging local solutions into global solutions offers a completely novel perspective on (conditional) merging. The axiomatic description of suitable strategies for c-representations/c-revisions is not only of practical relevance to define suitable operators. This also conveys deep methodological insights into reasoning with and revision by conditionals due to governing the interactions of sets of conditional beliefs under inductive reasoning/belief revision. In this way, basic ideas and main results of our approach will be transferrable to other approaches to inductive reasoning and revision.