Probabilistic Description Logic as a Fragment of Probabilistic First-Order Logic

概率描述逻辑作为概率一阶逻辑的片段

基本信息

项目摘要

Description logics are core formalisms in formal knowledge representation. They are concerned on the one hand with terminological knowledge, i.e. with interrelations among concepts, and on the other hand with assertional knowledge, i.e. knowledge about interrelations between concrete individuals and their description by abstract concepts. Knowledge is often subject to various forms of uncertainty; e.g. knowledge can be statistical ("90% of all birds fly") or subjectively uncertain due to lack of complete knowledge about the actual state of the world ("Patient X exhibits erythema, and therefore suffers from Lyme borreliosis with 80% probability"). Probabilistic description logics aim to formalize such uncertain knowledge using probabilistic methods. Technically, probabilistic description logics are many-dimensional modal logics; models are based on probability distributions on a set of worlds, each of which is associated with a standard interpretation of the description logical dimension. The latter represents the set of individuals, possibly equipped with a statistical distribution. By dint of this notion of model, probabilistic description logic embeds as a fragment into Halpern's probabilistic first-order logic, in analogy to the embedding of classical modal logic into classical first-order logic. This puts the semantics of probabilistic description logics on a firm footing and provides a framework for the estimation and comparison of their expressive power. As in the classical case, central questions concern the decidability and complexity of the core reasoning problems in probabilistic description logics of various levels of expressivity. This includes in particular lightweight dialects such probabilistic EL, which limits expressivity rather substantially but in return allows for tractable reasoning.The aims of the second project phase include a broadening of the metatheory to cover also questions of axiomatization and formal bounds on expressivity, as well as an extension of the expressive means made available; in particular, we will target fixpoint extensions and probabilistic logics featuring fuzzy truth values, such as the fuzzy logic of `probably'. Moreover, the relationship between subjective and statistical probabilities remains in the focus of attention. We will aim to design logics that support intuitively expected reasoning patterns such as direct inference of subjective from statistical probabilities while at the same time having decidable reasoning problems.
描述逻辑是形式知识表示的核心形式。它们一方面涉及术语知识,即概念之间的相互关系,另一方面涉及断言知识,即关于具体个体之间的相互关系以及抽象概念对其描述的知识。知识通常受到各种形式的不确定性的影响;例如,知识可以是统计学的(“所有鸟类中有90%会飞”),也可以是由于缺乏关于世界实际状态的完整知识而主观上不确定的(“患者X表现出红斑,因此患有莱姆疏螺旋体病的概率为80%”)。概率描述逻辑旨在使用概率方法来形式化这种不确定性知识。从技术上讲,概率描述逻辑是多维模态逻辑;模型基于一组世界上的概率分布,每个世界都与描述逻辑维度的标准解释相关联。后者代表了一组个体,可能具有统计分布。借助于模型的概念,概率描述逻辑作为一个片段嵌入到Halpern的概率一阶逻辑中,类似于经典模态逻辑嵌入到经典一阶逻辑中。这使得概率描述逻辑的语义学有了坚实的基础,并为估计和比较它们的表达能力提供了一个框架。在经典的情况下,中心问题关注的可判定性和复杂性的概率描述逻辑的表达能力的各种水平的核心推理问题。这包括在特别轻量级的方言,如概率EL,这限制了表现力,而实质上,但在回报允许易处理的reasoning.The第二个项目阶段的目标包括扩大元理论,以涵盖也公理化和形式上的界限问题的表现力,以及扩展的表达手段提供;特别地,我们将针对不动点扩展和具有模糊真值的概率逻辑,例如“probably”的模糊逻辑。此外,主观和统计概率之间的关系仍然是关注的焦点。我们的目标是设计逻辑,支持直观预期的推理模式,如从统计概率的主观直接推理,而在同一时间有可判定的推理问题。

项目成果

期刊论文数量(4)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
A Quantified Coalgebraic van Benthem Theorem
量化的山地范·本蒂姆定理
Probabilistic Description Logics For Subjective Uncertainty
  • DOI:
    10.1613/jair.5222
  • 发表时间:
    2017-01-01
  • 期刊:
  • 影响因子:
    5
  • 作者:
    Gutierrez-Basulto, Victor;Jung, Jean Christoph;Schroeder, Lutz
  • 通讯作者:
    Schroeder, Lutz
A Characterization Theorem for a Modal Description Logic
模态描述逻辑的表征定理
  • DOI:
    10.24963/ijcai.2017/181
  • 发表时间:
    2017
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Paul Wild;Lutz Schröder
  • 通讯作者:
    Lutz Schröder
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Professor Dr. Lutz Schröder其他文献

Professor Dr. Lutz Schröder的其他文献

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{{ truncateString('Professor Dr. Lutz Schröder', 18)}}的其他基金

Coalgebra-based generic decision procedures and complexity bounds for modal and hybrid logics
基于代数的通用决策程序以及模态和混合逻辑的复杂性界限
  • 批准号:
    59369218
  • 财政年份:
    2007
  • 资助金额:
    --
  • 项目类别:
    Research Grants
Coalgebraic Reasoning for Quantitative System Analysis
定量系统分析的代数推理
  • 批准号:
    531706730
  • 财政年份:
  • 资助金额:
    --
  • 项目类别:
    Research Grants

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Research on Quantum Field Theory without a Lagrangian Description
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