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

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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.