Related papers: Enumeration Problems Related to Ground Horn Theori…
We propose a norm of consistency for a mixed set of defeasible and strict sentences, based on a probabilistic semantics. This norm establishes a clear distinction between knowledge bases depicting exceptions and those containing outright…
Many Program Verification and Synthesis problems of interest can be modeled directly using Horn clauses and many recent advances in the CLP and CAV communities have centered around efficiently solving problems presented as Horn clauses. The…
We introduce a novel, logic-independent framework for the study of sequent-style proof systems, which covers a number of proof-theoretic formalisms and concrete proof systems that appear in the literature. In particular, we introduce a…
Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…
Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art…
The growing need for trustworthy machine learning has led to the blossom of interpretability research. Numerous explanation methods have been developed to serve this purpose. However, these methods are deficiently and inappropriately…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
This paper presents a simple framework for Horn clause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The…
We investigate the problem of extracting rules, expressed in Horn logic, from neural network models. Our work is based on the exact learning model, in which a learner interacts with a teacher (the neural network model) via queries in order…
We derive formulas for counting certain classes of vacua in the string/M theory landscape. We do so in the context of the moduli space of M-theory compactifications on singular manifolds with G_2 holonomy. Particularly, we count the numbers…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
We study the enumeration of bargraphs with respect to some corner statistics. We find generating functions for the number of bargraphs that tracks the corner statistics of interest, the number of cells, and the number of columns. The…
We provide a comparative study between neural word representations and traditional vector spaces based on co-occurrence counts, in a number of compositional tasks. We use three different semantic spaces and implement seven tensor-based…
Word embeddings are real-valued word representations able to capture lexical semantics and trained on natural language corpora. Models proposing these representations have gained popularity in the recent years, but the issue of the most…
By considering probability distributions over the set of assignments the expected truth values assignment to propositional variables are extended through linear operators, and the expected truth values of the clauses at any given…
This paper proposes a set of criteria to evaluate the objectiveness of explanation methods of neural networks, which is crucial for the development of explainable AI, but it also presents significant challenges. The core challenge is that…
Currently, knowledge discovery in databases is an essential step to identify valid, novel and useful patterns for decision making. There are many real-world scenarios, such as bankruptcy prediction, option pricing or medical diagnosis,…
The multiplicative multiple Horn problem is asking to determine possible singular values of the combinations $AB, BC$ and $ABC$ for a triple of invertible matrices $A,B,C$ with given singular values. There are similar problems for…