Related papers: A Two-Watched Literal Scheme for First-Order Logic

Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…

The size and the computational load of fine-tuning large-scale pre-trained neural network are becoming two major obstacles in adopting machine learning in many applications. Continual learning (CL) can serve as a remedy through enabling…

We show that SCL(FOL) can simulate the derivation of non-redundant clauses by superposition for first-order logic without equality. Superposition-based reasoning is performed with respect to a fixed reduction ordering. The completeness…

We will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…

A verification method for distributed systems based on decoupling forward and backward behaviour is proposed. This method uses an event structure based algorithm that, given a CCS process, constructs its causal compression relative to a…

While many-shot ICL achieves remarkable performance, prior studies of its scaling behavior have mainly focused on non-reasoning tasks. In this work, we study many-shot ICL on reasoning tasks, with a particular focus on many-shot…

We show that the first-order logical theory of the binary overlap-free words (and, more generally, the ${\alpha}$-free words for rational ${\alpha}$, $2 < {\alpha} \leq 7/3$), is decidable. As a consequence, many results previously obtained…

Controlled natural languages (CNL) with a direct mapping to formal logic have been proposed to improve the usability of knowledge representation systems, query interfaces, and formal specifications. Predictive editors are a popular approach…

Classification of ordinal data is one of the most important tasks of relation learning. In this thesis a novel framework for ordered classes is proposed. The technique reduces the problem of classifying ordered classes to the standard…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…

We study the finite satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers (C2) and interpreted over linearly ordered structures. We show that the problem is undecidable in the case of…

Given two languages, a separator is a third language that contains the first one and is disjoint from the second one. We investigate the following decision problem: given two regular input languages of finite words, decide whether there…

Large Language Models (LLMs) demonstrate strong in-context learning abilities, yet their effectiveness in text classification depends heavily on prompt design and incurs substantial computational cost. Conformal In-Context Learning (CICLe)…

We study the detection of propagandistic text fragments in news articles. Instead of merely learning from input-output datapoints in training data, we introduce an approach to inject declarative knowledge of fine-grained propaganda…

Uncertainty in Logic Programming has been investigated during the last decades, dealing with various extensions of the classical LP paradigm and different applications. Existing proposals rely on different approaches, such as clause…

In this paper we propose a general framework to integrate supervised and unsupervised examples with background knowledge expressed by a collection of first-order logic clauses into kernel machines. In particular, we consider a multi-task…

One of the long-standing problems on logic programming is to express {\it priority}-related operations -- default reasoning, if-then-else, cut, exception handling, etc -- in a high-level way. We argue that this problem can be solved by…

Large Language Models (LLMs) suffer from critical reasoning gaps, including a tendency to hallucinate and poor accuracy in classifying logical fallacies. This limitation stems from their default System 1 processing, which is fast and…

Active automata learning algorithms cannot easily handle conflict in the observation data (different outputs observed for the same inputs). This inherent inability to recover after a conflict impairs their effective applicability in…