About Me


I am currently a PhD student in the Machine Learning Group at the University of Toronto, advised by Dr. Sanja Fidler and Dr. Raquel Urtasun.

I obtained my Master's degree in Computer Science at Simon Fraser University, advised by Dr. James Delgrande. My MSc research focused on belief change, which is a subfield of knowledge representation concerned with updating knowledge bases in light of new information. I worked on belief change in multi-agent systems, studying the dynamics of belief propagation. I developed a Python package called Equibel to make it easier for researchers to experiment with belief change in multi-agent systems. The core of Equibel uses Answer Set Programming, which is a declarative logic programming paradigm tailored to solve NP-hard combinatorial search problems.

I received my BSc in computer science from Simon Fraser University in Winter 2014, and began my Master's in Spring 2015.

I am interested in machine learning, computer vision, knowledge representation, and generally all areas of AI. Specifically, I am interested in object recognition, 3D scene understanding, object detection and tracking, segmentation, action recognition, and image captioning. I am also interested in many areas of machine learning, including generative models and reinforcement learning. Additionally, I think that KRR can complement scene understanding to determine what future steps a robot could take.

I am also interested in ways to apply research to real-world problems and start a company that makes people's lives better!

Check out my blog!


As a Canadian, I enjoy salmon, maple syrup, and their combination (salmon candy)! I also like sports based on water in different physical phases: swimming, skating, and skiing. As a music-lover, I support the Vancouver Symphony Orchestra and the Vancouver Opera. I myself play the saxophone and the guitar.

A collection of my favorite books can be found on my bookshelf!


September, 2016 Started PhD at the University of Toronto
June 22, 2016 One paper accepted to ECAI 2016
June 6, 2015 One paper accepted to LPNMR 2015
May 7, 2015 Awarded the Governor General's Silver Medal for highest graduating GPA
December 20, 2014 Finished my BSc in Computer Science at Simon Fraser University


An example model graph

A Minimization-Based Approach to Iterated Multi-Agent Belief Change

Paul Vicol, James Delgrande, Torsten Schaub

Abstract: We investigate minimization-based approaches to iterated belief change in multi-agent systems. A network of agents is represented by an undirected graph, where propositional formulas are associated with vertices. Information is shared between vertices via a procedure where each vertex minimizes disagreement with other vertices in the graph. Each iterative approach takes into account the proximity between vertices, with the underlying assumption that information from nearby sources is given higher priority than information from more distant sources. We have identified two main approaches to iteration: in the first approach, a vertex takes into account the information at its immediate neighbours only, and information from more distant vertices is propagated via iteration; in the second approach, a vertex first takes into account information from distance-1 neighbours, then from distance-2 neighbours, and so on, in a prioritized fashion. There prove to be three distinct ways to define the second approach, so in total we have four types of iteration. We define these types formally, find relationships between them, and investigate their basic logical properties. We also implemented the approaches in a software system called Equibel.

Equibel System Architecture

An Implementation of Consistency-Based Multi-Agent Belief Change using ASP

Paul Vicol, James Delgrande, Torsten Schaub

Abstract: This paper presents an implementation of a general framework for consistency-based belief change using Answer Set Programming (ASP). We describe Equibel, a software system for working with belief change operations on arbitrary graph topologies. The system has an ASP component that performs a core maximization procedure, and a Python component that performs additional processing on the output of the ASP solver. The Python component also provides an interactive interface that allows users to create a graph, set formulas at nodes, perform belief change operations, and query the resulting graph.


Equibel Logo


A Python toolkit for equivalence-based belief change.

Examples flower images from all near/far classes

The Delicate Art of Flower Classification

Abstract: In this paper, we study the feasibility of identifying flowers in real-world Flickr photos. Established datasets for flower recognition contain only close-up, centered images of flowers, which are not representative of the large variety found on Flickr. We introduce a new dataset of close-up images that has greater variation in the orientation, shape, colour, and lighting than existing datasets. We also introduce a new dataset that contains both close-up and far-away images of certain species of flowers. We show that it is possible to identify fields of flowers, as well as individual flowers, in images downloaded from Flickr. This could provide a way to mine Flickr for information about nature, that could impact our understanding of the consequences of climate change.


A solution to a graph coloring problem

An Introduction to Answer Set Programming

Paul Vicol

Guest Lecture for Artificial Intelligence Survey (CMPT 310)

Abstract: Answer Set Programming (ASP) is a declarative logic programming paradigm tailored to solve NP-hard combinatorial search problems. ASP separates problem specification from solving by combining a rich modeling language with a general-purpose, high-performance solver. This allows it to solve a wide variety of search problems in a uniform way. This talk introduces ASP with a focus on practical problem solving. By looking at classic problems like graph colouring and n-queens, we see how to model problems in the language of ASP and use off-the-shelf tools to obtain solutions. Answer Set Programming is a powerful paradigm that has been used in applications ranging from robotics to music composition and genomics. This talk shows you how to get started with ASP, so that you can apply it to your own problems!

Latest from the Blog

A Glimpse of My Research in Multi-Agent Belief Change

A look at my recent work in comparing different forms of iterated belief change in multi-agent systems.

Read more!

Recommended from the Bookshelf


by Michael Sandel
Illustrates philosophical concepts with real examples from today's world. Makes it fun to learn the differences between categorical and consequentialist moral reasoning. One of my favorite books ever! You can also watch Sandel's Harvard lectures online!