报告人：顾韬 (UCL)

题目：Probabilistic logic programming and Bayesian networks: a string diagram perspective

时间：2021/6/15 15:10-18:00

线上腾讯会议ID ：440 883 947

摘要：Probabilistic logic programming (PLP) is an emerging subfield of artificial intelligence as a formalism to reason about uncertainty. It generalises logic programming by allowing annotation of clauses with probability values. We develop a categorical perspective of PLP based on a clear distinction between the syntax and semantics. In the spirit of Lawvere's functorial semantics of algebraic theories, we identify ground PLP with functors from some syntax categories (as freely generated categories of string diagrams) to a semantics category (of probabilistic transitions). Based on this, we retrieve the transformations between acyclic ground PLP and boolean-valued Bayesian networks at a functorial levels. Thanks to the syntax/semantics distinction as different categories, we can make precise the intuition that such transformations are syntactic. At the end of the talk we will briefly present how this framework can be adapted to the settings of classical logic programming and weighted logic programming

相关背景文献:

1. Symmetric monoidal categories (SMC) and their string diagrammatic representations: ''Causal Theories: A Categorical Perspective on Bayesian Reasoning".
2. String diagram perspective of Bayesian networks: "Causal Inference by String Diagram Surgery" (Sec 2, 3), ''Causal Theories: A Categorical Perspective on Bayesian Reasoning".
3. For probabilistic logic programming (PLP): "ProbLog: A Probabilistic Prolog and its Application in Link  Discovery" (Sec 2, 3), "Probabilistic (logic) programming concepts" (Sec 1, 2.1). Ground (propositional) case is enough.
4. How to turn a PLP into a Bayesian network: "Learning ground CP-logic by leveraging Bayesian network learning techniques". This paper is written in the more general context of CP-logic --- see Sec 5.2 for comments on ProbLog.
5. Familarity with functors, the distribution monad, Kleisli categories is a plus. See any standard textbook on category theory.