Related papers: Improvements for Free
This is a survey and research note on the modified Orlik conjecture derived from the division theorem introduced in [2]. The division theorem is a generalization of classical addition-deletion theorems for free arrangements. The division…
Cut-elimination is the bedrock of proof theory with a multitude of applications from computational interpretations to proof analysis. It is also the starting point for important meta-theoretical investigations including decidability,…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…
This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized…
Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
Large language models have the potential to generate explanations for their own predictions in a variety of styles based on user instructions. Recent research has examined whether these self-explanations faithfully reflect the models'…
In Knowledge Management, variations in information expressions have proven a real challenge. In particular, classical semantic relations (e.g. synonymy) do not connect words with different parts-of-speech. The method proposed tries to…
Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training…
Starting from a small number of well-motivated axioms, we derive a unique definition of sums with a noninteger number of addends. These "fractional sums" have properties that generalize well-known classical sum identities in a natural way.…
Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…
We present a~novel approach to the problem of automated theorem proving. Polynomial cost procedures that recognise sentences belonging to a theory are generated on a basis of a set of axioms of the so-called Truncated Predicate Calculus…
Paraphrasing is rooted in semantics. We show the effectiveness of transformers (Vaswani et al. 2017) for paraphrase generation and further improvements by incorporating PropBank labels via a multi-encoder. Evaluating on MSCOCO and…
Tree ensembles, including boosting methods, are highly effective and widely used for tabular data. However, large ensembles lack interpretability and require longer inference times. We introduce a method to prune a tree ensemble into a…
Classifier-Free Guidance (CFG) has recently emerged in text-to-image generation as a lightweight technique to encourage prompt-adherence in generations. In this work, we demonstrate that CFG can be used broadly as an inference-time…
While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…
We present Decalf, a directed, effectful cost-aware logical framework for studying quantitative aspects of functional programs with effects. Like Calf, the language is based on an internal phase distinction between the behavior of a program…
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…
Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…
We present an impossibility result, called a theorem about facts and words, which pertains to a general communication system. The theorem states that the number of distinct words used in a finite text is roughly greater than the number of…