Related papers: Scavenger 0.1: A Theorem Prover Based on Conflict …
Retrieval-Augmented Generation (RAG) systems implicitly assume mutual consistency among retrieved documents -- an assumption that frequently fails in practice. We present ConflictRAG, a conflict-aware RAG framework that detects, classifies,…
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…
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…
I build a canonical model for constant domain basic first-order logic (BQLCD), the constant domain first-order extension of Visser's basic propositional logic, and use the canonical model to verify that BQLCD satisfies the disjunction and…
Large language models (LLMs) have achieved impressive advancements across numerous disciplines, yet the critical issue of knowledge conflicts, a major source of hallucinations, has rarely been studied. Only a few research explored the…
The formal semantics of an interpreted first-order logic (FOL) statement can be given in Tarskian Semantics or a basically equivalent Game Semantics. The latter maps the statement and the interpretation into a two-player semantic game. Many…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
We introduce a new data structure for answering connectivity queries in undirected graphs subject to batched vertex failures. Precisely, given any graph G and integer k, we can in fixed-parameter time construct a data structure that can…
In this paper, our aim is to analyse the generalization capabilities of first-order methods for statistical learning in multiple, different yet related, scenarios including supervised learning, transfer learning, robust learning and…
The use of symbolic knowledge representation and reasoning as a way to resolve the lack of transparency of machine learning classifiers is a research area that lately attracts many researchers. In this work, we use knowledge graphs as the…
Large Language Models (LLMs) often exhibit limited logical coherence, mapping premises to conclusions without adherence to explicit inference rules. We propose Proof-Carrying Reasoning with LLMs (PCRLLM), a framework that constrains…
Classification is the basis of cognition. Unlike other solutions, this study approaches it from the view of outliers. We present an expanding algorithm to detect outliers in univariate datasets, together with the underlying foundation. The…
We consider the problem of sequential decision making under uncertainty in which the loss caused by a decision depends on the following binary observation. In competitive on-line learning, the goal is to design decision algorithms that are…
We propose a new approach to promote safety in classification tasks with established concepts. Our approach -- called a conceptual safeguard -- acts as a verification layer for models that predict a target outcome by first predicting the…
A set of Maple V R.3/4 computer algebra routines for the analytical solving of 1st. order ODEs, using Lie group symmetry methods, is presented. The set of commands includes a 1st. order ODE-solver and routines for, among other things: the…
We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic. Higher-order interactive theorem provers enable the formalization of arbitrary mathematical theories and thereby present an…
Complex reasoning problems are most clearly and easily specified using logical rules, but require recursive rules with aggregation such as count and sum for practical applications. Unfortunately, the meaning of such rules has been a…
An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…
PIE is a Prolog-embedded environment for automated reasoning on the basis of first-order logic. It includes a versatile formula macro system and supports the creation of documents that intersperse macro definitions, reasoner invocations and…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…