Cool: Coalgebras, Ontologies and Logic

酷：代数、本体论和逻辑

基本信息

批准号：
EP/H016317/1
负责人：
Dirk Pattinson
金额：
$ 50.17万
依托单位：
Imperial College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2010
资助国家：
英国
起止时间：
2010 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FH016317%2F1
关键词：
Cool Coalgebras Ontologies Logic

项目摘要

The main theme that underlies this research project is automatedreasoning, an applied sub-discipline of mathematical logic. Logichas found applications in many areas of computer sciencesuch as the verification of digital circuits, reasoning aboutprograms and knowledge representation. One of the most fundamentalaspects in this context is to automatically decide whether aparticular formula is a logical consequence of a given set ofassumptions. The set of assumptions may describe complex relationsbetween diseases and their symptoms, and one possible reasoning taskwould be to confirm or reject a diagnosis based on observed symptomsand medical history.In this research project, we investigate applications ofmathematical logic in knowledge representation. One of the primechallenges in this area is to design logical formalisms that strikea balance between the two conflicting goals of expressiveness (theability to formally represent the application domain) andcomputational tractability. The family of modal logics, conceived ina broad way, combines both aspects and serves as the mathematicalfoundation of a large number of knowledge representation formalisms.The core ingredient of modal logic is the possibility to qualifylogical assertions to hold in a certain way. Depending on thecontext, we may for instance stipulate that assertion holds `alwaysin the future', `with a likelihood of at least 50%' or `normally'.Together with names for individual entities, this allows us toformulate assertions like `the likelihood of congestion on Queen'sRoad is greater than 30%', and complex knowledge bases arise bycombining different logical primitives. Automated reasoning thenallows us to mechanically verify e.g. the consistency of scientifichypotheses against an existing knowledge base. Our goal is to builda modular and practical knowledge representation system that allowsto represent and reason about knowledge represented in this way,based on a large and diverse class of logical primitives, includinge.g. the coalitional behaviour of agents, quantitative uncertainty,counterfactual reasoning and default assumptions. This goes waybeyond the current state of the art, where only logical primitiveswith a relational interpretation are supported by automated tools.Recent research has shown these new logical features can beaccounted for in a uniform way by passing to a more generalmathematical model, known as `coalgebraic semantics'. This richerframework does not only provide a uniform umbrella for a largenumber of reasoning principles, but also supports a richmathematical theory that has by now matured to the extent which putsthe development of automated tools within reach. The researchchallenge that this proposal addresses is the further development of thesetheoretical results as to bring them to bear on practical applications.As a concrete case study, we will use the Cool system to formalisequantitative models in Systems Biology.

基于该研究项目的主要主题是自动化，这是数学逻辑的应用子学科。 logichas在计算机科学的许多领域中找到了应用程序，以验证数字电路，关于程序的推理和知识表示。在这种情况下，最基本的镜头之一是自动决定公共公式是否是给定垃圾集的逻辑结果。一组假设可以描述疾病及其症状之间的复杂关系，并且可能的推理是根据观察到的症状和病史确认或拒绝诊断。在这项研究项目中，我们调查了在知识表示中的神经逻辑的应用。该领域中的大量呼吁之一是设计逻辑形式主义，以在两个相互矛盾的表现力目标（正式代表应用域）和计算障碍性之间平衡。模态逻辑的家族构思了，这两个方面都结合在一起，并作为大量知识表示形式主义的数学基础。模态逻辑的核心成分是有可能以某种方式持有的合格主张。例如，我们可能会规定断言在“永远的未来”，“至少有50％或``正常''的可能性。自动推理然后将我们机械验证例如科学型对现有知识基础的一致性。我们的目标是建立模块化和实用的知识表示系统，该系统允许Sto代表和理由以这种方式代表的知识，基于包括e.g在内的大量多样化的逻辑原始人。代理人的联盟行为，定量不确定性，反事实推理和默认假设。这是当前的最新状态，在该状态下，只有自动化工具支持关系解释的逻辑原始。这种Richerframework不仅为推理原则的大量象征提供了统一的雨伞，而且还支持一种富裕的理论，该理论现在已经成熟到使自动化工具开发的范围内的范围。该提案所解决的研究挑战是将它们带来实际应用的进一步发展。作为具体的案例研究，我们将使用凉爽的系统来实现系统生物学中的福尔马斯定质模型。