Related papers: The Horn Non-Clausal Class and its Polynomiality

Brown clustering is a hard, hierarchical, bottom-up clustering of words in a vocabulary. Words are assigned to clusters based on their usage pattern in a given corpus. The resulting clusters and hierarchical structure can be used in…

Computer vision systems in real-world applications need to be robust to partial occlusion while also being explainable. In this work, we show that black-box deep convolutional neural networks (DCNNs) have only limited robustness to partial…

Automatically verifying safety properties of programs is hard, and it is even harder if the program acts upon arrays or other forms of maps. Many approaches exist for verifying programs operating upon Boolean and integer values (e.g.…

We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several…

We show how automatic tools for the verification of linear and branching time properties of procedural, multi-threaded, and functional programs as well as program synthesis can be naturally and uniformly seen as solvers of constraints in…

Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related…

Efficient implementations of DPLL with the addition of clause learning are the fastest complete Boolean satisfiability solvers and can handle many significant real-world problems, such as verification, planning and design. Despite its…

Questions concerning the proof-theoretic strength of classical versus non-classical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of…

We introduce Hausdorff (complexity) classes, which provide canonical characterizations of the intermediate levels of the iterated exponential hierarchies, including the Polynomial Hierarchy, the (Weak) Exponential Hierarchy, and…

The enumeration of minimal unsatisfiable subsets (MUSes) finds a growing number of practical applications, that includes a wide range of diagnosis problems. As a concrete example, the problem of axiom pinpointing in the EL family of…

We present a unified formalism for structure discovery of causal models and predictive state representation (PSR) models in reinforcement learning (RL) using higher-order category theory. Specifically, we model structure discovery in both…

Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. Both instances of coinductive reasoning appeared in…

In this paper, we investigate the extent to which knowledge compilation can be used to improve inference from propositional weighted bases. We present a general notion of compilation of a weighted base that is parametrized by any…

Verification conditions (VCs) are logical formulas whose satisfiability guarantees program correctness. We consider VCs in the form of constrained Horn clauses (CHC) which are automatically generated from the encoding of (an interpreter of)…

In many classification tasks there is a requirement of monotonicity. Concretely, if all else remains constant, increasing (resp. decreasing) the value of one or more features must not decrease (resp. increase) the value of the prediction.…

We consider a class of formula equations in first-order logic, Horn formula equations, which are defined by a syntactic restriction on the occurrences of predicate variables. Horn formula equations play an important role in many…

CNNs, RNNs, GCNs, and CapsNets have shown significant insights in representation learning and are widely used in various text mining tasks such as large-scale multi-label text classification. However, most existing deep models for…

We investigate a class of polyhedral convex cones, with $R^k_+$ (the nonegative orthant in $\mathbb{R}^k$) as a special case. We start with the observation that for convex cones contained in $\mathbb{R}^k$, the respective cone efficiency is…

Deep learning models often suffer from a lack of interpretability due to polysemanticity, where individual neurons are activated by multiple unrelated semantics, resulting in unclear attributions of model behavior. Recent advances in…

Recent findings show that deep convolutional neural networks (DCNNs) do not generalize well under partial occlusion. Inspired by the success of compositional models at classifying partially occluded objects, we propose to integrate…