Mixed logical-linear programming
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Mathematical Programming Embeddings of Logic
Journal of Automated Reasoning
On the Use of Integer Programming Models in AI Planning
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Integer linear programming inference for conditional random fields
ICML '05 Proceedings of the 22nd international conference on Machine learning
Machine Learning
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Lifted first-order belief propagation
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
IBAL: a probabilistic rational programming language
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Lifted first-order probabilistic inference
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
BLOG: probabilistic models with unknown objects
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
The independent choice logic and beyond
Probabilistic inductive logic programming
A formal domain model for dietary and physical activity counseling
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part I
Automating mathematical program transformations
PADL'10 Proceedings of the 12th international conference on Practical Aspects of Declarative Languages
A general constraint-centric scheduling framework for spatial architectures
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations. First-order logic (FOL), on the other hand, excels at reasoning about classes of objects, but lacks a rich representation of uncertainty. While representing propositional logic in MILP has been extensively explored, no theory exists yet for fully combining FOL with MILP. We propose a new representation, called first-order programming or FOP, which subsumes both FOL and MILP. We establish formal methods for reasoning about first order programs, including a sound and complete lifted inference procedure for integer first order programs. Since FOP can offer exponential savings in representation and proof size compared to FOL, and since representations and proofs are never significantly longer in FOP than in FOL, we anticipate that inference in FOP will be more tractable than inference in FOL for corresponding problems.