Inspired by empirical work in neuroscience for Bayesian approaches to brain
function, we give a unified probabilistic account of various types of symbolic
reasoning from data. We characterise them in terms of formal logic using the
classical consequence relation, an empirical consequence relation, maximal
consistent sets, maximal possible sets and maximum likelihood estimation. The
theory gives new insights into reasoning towards human-like machine
intelligence.

从神经科学的贝叶斯方法论中汲取灵感，我们提供了一种统一的概率模型，用于从数据中进行各种类型的符号推理。我们使用经典后果关系、经验后果关系、最大一致集、最大可能集和最大似然估计来描述它们，该理论为实现类人机智能的推理过程提供了新的见解。

从数据中推断抽象的统一符号推理模型

Inference of Abstraction for a Unified Account of Symbolic Reasoning  from Data

This proceedings contains abstracts and position papers for the work
presented at the second Logic and Practice of Programming (LPOP) Workshop. The
workshop was held online, virtually in place of Chicago, USA, on November 15,
2010, in conjunction with the ACM SIGPLAN Conference on Systems, Programming,
Languages, and Applications: Software for Humanity (SPLASH) 2020. The purpose
of this workshop is to be a bridge between different areas of computer science
that use logic as a practical tool. We take advantage of the common language of
formal logic to exchange ideas between these different areas.

本文介绍了第二届逻辑与程序设计工作坊（Logic and Practice of Programming，LPOP）的论文摘要和立场论文，旨在作为计算机科学中使用逻辑作为实用工具的不同领域之间的桥梁，利用形式逻辑的公共语言交换思想。

第二届逻辑与编程实践研讨会论文集 (LPOP)

Proceedings of the 2nd Workshop on Logic and Practice of Programming (LPOP)

This paper gives a generative model of the interpretation of formal logic for
data-driven logical reasoning. The key idea is to represent the interpretation
as likelihood of a formula being true given a model of formal logic. Using the
likelihood, Bayes' theorem gives the posterior of the model being the case
given the formula. The posterior represents an inverse interpretation of formal
logic that seeks models making the formula true. The likelihood and posterior
cause Bayesian learning that gives the probability of the conclusion being true
in the models where all the premises are true. This paper looks at statistical
and logical properties of the Bayesian learning. It is shown that the
generative model is a unified theory of several different types of reasoning in
logic and statistics.

本文基于生成模型的思想，采用 Bayesian learning 方法，探究形式逻辑及其数理统计特性，构建了一个统一的形式逻辑和统计推理理论。

统一逻辑蕴涵和统计估计

Towards Unifying Logical Entailment and Statistical Estimation

Logic Artificial Intelligence (AI) is a subfield of AI where variables can
take two defined arguments, True or False, and are arranged in clauses that
follow the rules of formal logic. Several problems that span from physical
systems to mathematical conjectures can be encoded into these clauses and
solved by checking their satisfiability (SAT). In contrast to machine learning
approaches where the results can be approximations or local minima, Logic AI
delivers formal and mathematically exact solutions to those problems. In this
work, we propose the use of logic AI for the design of optical quantum
experiments. We show how to map into a SAT problem the experimental preparation
of an arbitrary quantum state and propose a logic-based algorithm, called
Klaus, to find an interpretable representation of the photonic setup that
generates it. We compare the performance of Klaus with the state-of-the-art
algorithm for this purpose based on continuous optimization. We also combine
both logic and numeric strategies to find that the use of logic AI
significantly improves the resolution of this problem, paving the path to
developing more formal-based approaches in the context of quantum physics
experiments.

本文介绍了利用逻辑人工智能（Logic AI）来设计光量子实验的方法，使用基于逻辑的算法 Klaus 将实验准备转化为满足性 (SAT) 问题，并将其与基于连续优化的最先进算法进行比较，证明逻辑 AI 明显提高了问题的解决效率，并有望在量子物理实验的研究中推广。