Related papers: Generalizing Redundancy in Propositional Logic: Fo…
The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the…
In this paper, we address the problem of enumerating all models of a Boolean formula in conjunctive normal form (CNF). We propose an extension of CDCL-based SAT solvers to deal with this fundamental problem. Then, we provide an experimental…
In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
Decomposition of text into atomic propositions is a flexible framework allowing for the closer inspection of input and output text. We use atomic decomposition of hypotheses in two natural language reasoning tasks, traditional NLI and…
We introduce a new canonical form of lattices called the systematic normal form (SNF). We show that for every lattice there is an efficiently computable "nearby" SNF lattice, such that for any lattice one can solve lattice problems on its…
We consider the problem of elimination of existential quantifiers from a Boolean CNF formula. Our approach is based on the following observation. One can get rid of dependency on a set of variables of a quantified CNF formula F by adding…
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…
The extent to which neural networks are able to acquire and represent symbolic rules remains a key topic of research and debate. Much current work focuses on the impressive capabilities of large language models, as well as their often…
A challenging open question in deep learning is how to handle tabular data. Unlike domains such as image and natural language processing, where deep architectures prevail, there is still no widely accepted neural architecture that dominates…
In this paper, we propose a first application of data mining techniques to propositional satisfiability. Our proposed Mining4SAT approach aims to discover and to exploit hidden structural knowledge for reducing the size of propositional…
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
Recurrent neural networks (RNNs) are a widely used deep architecture for sequence modeling, generation, and prediction. Despite success in applications such as machine translation and voice recognition, these stateful models have several…
We study cut elimination for a multifocused variant of full linear logic in the sequent calculus. The multifocused normal form of proofs yields problems that do not appear in a standard focused system, related to the constraints in grouping…
The Fourier representation for the uniform distribution over the Boolean cube has found numerous applications in algorithms and complexity analysis. Notably, in learning theory, learnability of Disjunctive Normal Form (DNF) under uniform as…
This document is written in order to establish a common base ground on which the majority of the relevant research about linear fountain codes can be analyzed and compared. As far as I am concerned, there is no unified approach that…
Advancements in computer science and AI lead to the development of larger, more complex knowledge bases. These are susceptible to contradictions, particularly when multiple experts are involved. To ensure integrity during changes,…
Whether the satisfiability of any formula F of propositional calculus can be determined in polynomial time is an open question. I propose a simple procedure based on some real world mechanisms to tackle this problem. The main result is the…
We propose analyzing conditional reasoning by appeal to a notion of intervention on a simulation program, formalizing and subsuming a number of approaches to conditional thinking in the recent AI literature. Our main results include a…
In this thesis, a detailed study shows that closed itemsets and minimal generators play a key role for concisely representing both frequent itemsets and association rules. These itemsets structure the search space into equivalence classes…