Related papers: From Liar Paradox to Incongruent Sets: A Normal Fo…

Factual consistency is one of the most important requirements when editing high quality documents. It is extremely important for automatic text generation systems like summarization, question answering, dialog modeling, and language…

Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses…

The form and justification of inductive inference rules depend strongly on the representation of uncertainty. This paper examines one generic representation, namely, incomplete information. The notion can be formalized by presuming that the…

Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…

Missing sentence generation (or sentence infilling) fosters a wide range of applications in natural language generation, such as document auto-completion and meeting note expansion. This task asks the model to generate intermediate missing…

Linear sequences of words are implicitly represented in our brains by hierarchical structures that organize the composition of words in sentences. Linguists formalize different frameworks to model this hierarchy; two of the most common…

Human explanations of natural language, rationales, form a tool to assess whether models learn a label for the right reasons or rely on dataset-specific shortcuts. Sufficiency is a common metric for estimating the informativeness of…

It is claimed that a variety of facts concerning ellipsis, event reference, and interclausal coherence can be explained by two features of the linguistic form in question: (1) whether the form leaves behind an empty constituent in the…

In this paper we propose an interpretation for self-referential propositions in a "meta-model" N* of ZF. This meta-model N* is considered as an informal model of arithmetic that mathematicians often use when working with number theory.…

Referring is one of the most basic and prevalent uses of language. How do speakers choose from the wealth of referring expressions at their disposal? Rational theories of language use have come under attack for decades for not being able to…

F-systems are digraphs that enable to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and Yablo's can be analyzed with that tool to find graph-theoretic patterns. In this paper we present the F-systems…

Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…

Compositional generalization benchmarks for semantic parsing seek to assess whether models can accurately compute meanings for novel sentences, but operationalize this in terms of logical form (LF) prediction. This raises the concern that…

Do state-of-the-art models for language understanding already have, or can they easily learn, abilities such as boolean coordination, quantification, conditionals, comparatives, and monotonicity reasoning (i.e., reasoning about word…

The aim of this article is to generalize logics of formal inconsistency ($\textbf{LFI}$s) to systems dealing with the concept of incompatibility, expressed by means of a binary connective. The basic idea is that having two incompatible…

We show that self-reference can be formalized in Basic logic by means of the new connective @, called "entanglement". In fact, the property of non-idempotence of the connective @ is a metatheorem, which states that a self-entangled sentence…

This paper presents a formal approach to explaining change of inference in Quantitative Bipolar Argumentation Frameworks (QBAFs). When drawing conclusions from a QBAF and updating the QBAF to then again draw conclusions (and so on), our…

Lack of factual correctness is an issue that still plagues state-of-the-art summarization systems despite their impressive progress on generating seemingly fluent summaries. In this paper, we show that factual inconsistency can be caused by…

We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b)…

Large Language Models (LLMs) have transformed natural language processing and hold growing promise for advancing science, healthcare, and decision-making. Yet their training paradigms remain dominated by affirmation-based inference, akin to…