Description logics are a powerful tool for describing ontological knowledge bases. That is, they give a factual account of the world in terms of individuals, concepts and relations. In the presence of uncertainty, such factual accounts are not feasible, and a subjective or epistemic approach is required. Aleatoric description logic models uncertainty in the world as aleatoric events, by the roll of the dice, where an agent has subjective beliefs about the bias of these dice. This provides a subjective Bayesian description logic, where propositions and relations are assigned probabilities according to what a rational agent would bet, given a configuration of possible individuals and dice. Aleatoric description logic is shown to generalise the description logic ALC, and can be seen to describe a probability space of interpretations of a restriction of ALC where all roles are functions. Several computational problems are considered and model-checking and consistency checking algorithms are presented. Finally, aleatoric description logic is shown to be able to model learning, where agents are able to condition their beliefs on the bias of dice according to observations.
翻译:描述逻辑是描述本体知识基础的有力工具。 也就是说, 描述逻辑是描述本体知识基础的有力工具。 也就是说, 以个人、 概念和关系来对世界进行事实描述。 在存在不确定性的情况下, 这种事实描述是不可行的, 并且需要主观或认知的方法。 使用解说性描述逻辑模型, 以世界的不确定性作为解析事件, 由骰子卷进行, 代理商对这些 dice 的偏向有主观的信念。 这提供了一种主观的巴伊西亚描述逻辑, 即根据理性代理人的组合, 将各种主张和关系分配为概率, 并给一个理性代理人配置个人和 dice 。 解说性描述逻辑被显示为概括描述逻辑 ALC, 并且可以被看成描述解说 ALC 限制所有角色都具有功能的概率空间。 一些计算问题得到了考虑, 示范性核对和一致性核对算法。 最后, 解说性描述逻辑被证明能够模拟学习, 在那里, 代理商能够根据观察来决定对 dice 的偏向的信念。