Related papers: Safe Formulas in the General Theory of Stable Mode…
Blocked clauses provide the basis for powerful reasoning techniques used in SAT, QBF, and DQBF solving. Their definition, which relies on a simple syntactic criterion, guarantees that they are both redundant and easy to find. In this paper,…
This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…
Fair classification has been a topic of intense study in machine learning, and several algorithms have been proposed towards this important task. However, in a recent study, Friedler et al. observed that fair classification algorithms may…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
We present a generalization of first-order unification to a term algebra where variable indexing is part of the object language. We exploit variable indexing by associating some sequences of variables ($X_0,\ X_1,\ X_2,\dots$) with a…
In this short note, we mimic the proof of the simplicity of the theory ACFA of generic difference fields in order to provide a criterion, valid for certain theories of pure fields and fields equipped with operators, which shows that a…
This paper discusses a general and useful stability principle which, roughly speaking, says that given a uniformly continuous function defined on an arbitrary metric space, if the function is bounded on the constraint set and we slightly…
The safety of automated driving systems must be justified by convincing arguments and supported by compelling evidence to persuade certification agencies, regulatory entities, and the general public to allow the systems on public roads.…
We first partly develop a mathematical notion of stable consistency intended to reflect the actual consistency property of human beings. Then we give a generalization of the first and second G\"odel incompleteness theorem to stably…
The module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets.…
We investigate the presence of twinlike models in theories described by several real scalar fields. We focus on the first-order formalism, and we show how to build distinct scalar field theories that support the same extended solution, with…
Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that…
The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then…
We prove in this note a stabilized version of a conjecture on $\A^1$-connectedness. For the stabilized version of this conjecture, we introduce the notion of stable $\A^1$-connectedness, which is can be seen as the stabilization of…
Understanding what constitutes safe text is an important issue in natural language processing and can often prevent the deployment of models deemed harmful and unsafe. One such type of safety that has been scarcely studied is commonsense…
Given a first-order theory and a proof that it is consistent, can we design a proof-search method for this theory that fails in finite time when it attempts to prove the formula False?
Effective software safety standards will contribute to confidence, or assurance, in the safety of the systems in which the software is used. It is infeasible to demonstrate a correlation between standards and accidents, but there is an…
A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…