Probabilistic Tabled Logic Programming

表归结使用记忆来解决PROLOG风格归结的主要缺点，即弱终止性、重复子计算和对否定的弱语义。针对需要定点计算的几个复杂问题，包括模型检测和程序分析问题，将其转化为逻辑程序上的查询求值问题，并利用表化归结有效地解决了这一问题，旨在将演绎，特别是表化化归结与概率推理相结合，以便于对具有概率行为的系统进行声明性建模和推理.该项目包括(A)概率表解语义的基础研究，(B)研究结果在健壮原型中的实现，以及(C)结合逻辑和概率推理的应用程序的开发，例如有限状态和下推模型的概率模型检查和概率程序分析。该项目解决了语义学水平上的几个问题，包括处理混合了连续和离散随机变量的程序，编码无限但离散时间上的动态模型的程序，以及可伸缩的概率推理技术(例如抽样)与演绎的集成。在实现层面，该项目开发了将概率推理和参数学习合并到称为概率表逻辑编程(PTLP)的声明性编程框架中的轻量级方法。该框架为逻辑推理和概率推理的结合提供了坚实的语义和计算基础。将计算逻辑、统计和约束处理紧密结合在一起的计算基础设施将对系统开发和验证、规划、物流和优化控制等领域产生立竿见影的影响，在科学和工程中具有广泛的应用。

Tabled resolution uses memoization to address the major shortcomings of Prolog-style resolution, namely, weak termination, repeated subcomputations, and weak semantics for negation. Several complex problems requiring fixed-point computation, including several model checking and program analysis problems, have been cast as query evaluation over logic programs and solved efficiently using tabled resolution.This project aims to combine deduction, especially tabled resolution, with probabilistic inference in order to facilitate declarative modeling and reasoning of systems with probabilistic behavior. The project includes (a) fundamental research on the semantics of probabilistic tabled resolution, (b) implementation of the research results in a robust prototype, and (c) development of applications that combine logical and probabilistic reasoniong such as probabilistic model checking of finite-state and pushdown models and probabilistic program analysis. The project addresses several problems at the level of semantics, including the treatment of programs with a mixture of continuous and discrete random variables, programs that encode dynamic models over unbounded but discrete time, and the integration of scalable probabilistic inference techniques (e.g. sampling) with deduction. At the implementation level, the project develops light-weight methods for incorporating probabilistic inference and parameter learning into a declarative programming framework called Probabilistic Tabled Logic Programming (PTLP). This framework provides a firm semantic and computational basis for combining logical and probabilistic reasoning. A computing infrastructure that tightly integrates computational logic, statistics, and constraint processing will have an immediate impact on the areas of system development and verification, planning, logistics, and optimization and control, with broad application in science and engineering.