Three Modern Roles for Logic in AI

We consider three modern roles for logic in artificial intelligence, which are based on the theory of tractable Boolean circuits: (1) logic as a basis for computation, (2) logic for learning from a combination of data and knowledge, and (3) logic for reasoning about the behavior of machine learning systems.Comment: To be published in PODS 202

Knowledge Compilation for Solving Computationally Hard Problems

Knowledge compilation is concerned with compiling problems encoded in some input language into some tractable, output language, with the goal of allowing one to solve such problems efficiently if the compilation is successful. This paradigm was originally motivated by the need to push much of the computational overhead into an offline compilation phase, which can then be amortized over a large number of queries in an online computation phase. In this dissertation, we study various new approaches to enhance the offline compilation phase, both theoretically and practically. We also study knowledge compilation from a perspective where it is employed as a general methodology for computation instead of just a paradigm that is concerned with the offline/online divide. In particular, we introduce a hierarchy of complexity parameters to bound the sizes of compiled representations. These new parameters are based on incorporating the logical content of the input representations, as opposed to existing parameters (e.g., treewidth) that are only based on the structure of the input. Our results improve some of the best known upper bounds on the compilation of influential representations, such as DNNFs, SDDs, and OBDDs. Moreover, we develop two new practical compilation algorithms for the DNNF and SDD languages, leading to orders of magnitude faster compilations. Finally, we study solving Beyond-NP problems using knowledge compilation, while particularly extending the reach of knowledge compilation to tackling problems in the highly intractable complexity class PP^PP. Our results show the applicability of knowledge compilers as black-box tools for solving Beyond-NP problems, similar to the use of SAT solvers for solving NP-complete problems

Generating Explanations for Complex Biomedical Queries

We present a computational method to generate explanations to answers of complex queries over biomedical ontologies and databases, using the high-level representation and efficient automated reasoners of Answer Set Programming. We show the applicability of our approach with some queries related to drug discovery over PHARMGKB, DRUGBANK, BI

A general formal framework for pathfinding problems with multiple agents

Pathfinding for a single agent is the problem of planning a route from an initial location to a goal location in an environment, going around obstacles. Pathfinding for multiple agents also aims to plan such routes for each agent, subject to different constraints, such as restrictions on the length of each path or on the total length of paths, no self-intersecting paths, no intersection of paths/plans, no crossing/meeting each other. It also has variations for finding optimal solutions, e.g., with respect to the maximum path length, or the sum of plan lengths. These problems are important for many real-life applications, such as motion planning, vehicle routing, environmental monitoring, patrolling, computer games. Motivated by such applications, we introduce a formal framework that is general enough to address all these problems: we use the expressive high-level representation formalism and efficient solvers of the declarative programming paradigm Answer Set Programming. We also introduce heuristics to improve the computational efficiency and/or solution quality. We show the applicability and usefulness of our framework by experiments, with randomly generated problem instances on a grid, on a real-world road network, and on a real computer game terrain