A Proof Theoretic View of Constraint Programming

We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and illustrate their use by analyzing the constraint propagation process for the {\tt SEND + MORE = MONEY} puzzle. We also show how this approach allows one to build new constraint solvers.Comment: 25 page

Learning Weak Constraints in Answer Set Programming

This paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, called Learning from Ordered Answer Sets, generalises our previous work on learning ASP programs without weak constraints, by considering a new notion of examples as ordered pairs of partial answer sets that exemplify which answer sets of a learned hypothesis (together with a given background knowledge) are preferred to others. In this new learning task inductive solutions are searched within a hypothesis space of normal rules, choice rules, and hard and weak constraints. We propose a new algorithm, ILASP2, which is sound and complete with respect to our new learning framework. We investigate its applicability to learning preferences in an interview scheduling problem and also demonstrate that when restricted to the task of learning ASP programs without weak constraints, ILASP2 can be much more efficient than our previously proposed system.Comment: To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 201

Constrained superfields in Supergravity

We analyze constrained superfields in supergravity. We investigate the consistency and solve all known constraints, presenting a new class that may have interesting applications in the construction of inflationary models. We provide the superspace Lagrangians for minimal supergravity models based on them and write the corresponding theories in component form using a simplifying gauge for the goldstino couplings.Comment: 24 pages. v2: JHEP final version (fixed typos, references added

Bayesian Matrix Completion via Adaptive Relaxed Spectral Regularization

Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization formulation. We fill this gap by presenting a novel Bayesian matrix completion method based on spectral regularization. In order to circumvent the difficulties of dealing with the orthonormality constraints of singular vectors, we derive a new equivalent form with relaxed constraints, which then leads us to design an adaptive version of spectral regularization feasible for Bayesian inference. Our Bayesian method requires no parameter tuning and can infer the number of latent factors automatically. Experiments on synthetic and real datasets demonstrate encouraging results on rank recovery and collaborative filtering, with notably good results for very sparse matrices.Comment: Accepted to AAAI 201

New Integrality Gap Results for the Firefighters Problem on Trees

The firefighter problem is NP-hard and admits a $(1-1/e)$ approximation based on rounding the canonical LP. In this paper, we first show a matching integrality gap of $(1-1/e+\epsilon)$ on the canonical LP. This result relies on a powerful combinatorial gadget that can be used to prove integrality gap results for many problem settings. We also consider the canonical LP augmented with simple additional constraints (as suggested by Hartke). We provide several evidences that these constraints improve the integrality gap of the canonical LP: (i) Extreme points of the new LP are integral for some known tractable instances and (ii) A natural family of instances that are bad for the canonical LP admits an improved approximation algorithm via the new LP. We conclude by presenting a $5/6$ integrality gap instance for the new LP.Comment: 22 page