统一了信念型ASP的多种语义,揭示其内在关联。
Pearce's Characterisation in an Epistemic Domain
- 基于佩斯的均衡模型思想,构建通用信念型ASP框架
- 证明不同信念逻辑语义可通过该框架相互对应
- 适合逻辑编程与非单调推理方向的研究者
答案集编程(ASP)是基于逻辑的人工智能问题求解方法,通过逻辑程序表示问题,以答案集识别解。均衡逻辑(EL)是一种基于‘这里-那里’逻辑的非单调推理形式化系统,由佩斯提出作为ASP的基础框架。信念型规范(ES)是带有主观字面量的ASP扩展,引入模态构造,可判断常规字面量是否在所有或某些答案集中为真。ES程序由世界视图解释,即答案集的集合。自信念逻辑(特别是反射式)用于建模理想理性主体的自我信念。近年来,一种新的ES语义结合了均衡逻辑与自信念逻辑。本文首先提出一个覆盖信念型ASP领域的统一框架,并基于佩斯对答案集作为均衡模型的刻画,建立现有各类(反射式)(自)信念均衡逻辑之间的对应关系。通过将费拉里斯关于命题理论答案集的工作扩展至信念情形,揭示了部分信念语义提案间的联系。
原文摘要 · Abstract (English)
Answer-set programming (ASP) is a successful problem-solving approach in logic-based AI. In ASP, problems are represented as declarative logic programs, and solutions are identified through their answer sets. Equilibrium logic (EL) is a general-purpose nonmonotonic reasoning formalism, based on a monotonic logic called here-and-there logic. EL was basically proposed by Pearce as a foundational framework of ASP. Epistemic specifications (ES) are extensions of ASP-programs with subjective literals. These new modal constructs in the ASP-language make it possible to check whether a regular literal of ASP is true in every (or some) answer-set of a program. ES-programs are interpreted by world-views, which are essentially collections of answer-sets. (Reflexive) autoepistemic logic is a nonmonotonic formalism, modeling self-belief (knowledge) of ideally rational agents. A relatively new semantics for ES is based on a combination of EL and (reflexive) autoepistemic logic. In this paper, we first propose an overarching framework in the epistemic ASP domain. We then establish a correspondence between existing (reflexive) (auto)epistemic equilibrium logics and our easily-adaptable comprehensive framework, building on Pearce's characterisation of answer-sets as equilibrium models. We achieve this by extending Ferraris' work on answer sets for propositional theories to the epistemic case and reveal the relationship between some ES-semantic proposals.
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