Related papers: Improvements for Free
Functional Distributional Semantics provides a computationally tractable framework for learning truth-conditional semantics from a corpus. Previous work in this framework has provided a probabilistic version of first-order logic, recasting…
We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as…
Speculative decoding aims to speed up autoregressive generation of a language model by verifying in parallel the tokens generated by a smaller draft model.In this work, we explore the effectiveness of learning-free, negligible-cost draft…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Word frequency-based methods for extractive summarization are easy to implement and yield reasonable results across languages. However, they have significant limitations - they ignore the role of context, they offer uneven coverage of…
Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of providing a system with explicit, general knowledge and having the system reason over that knowledge. However, expressing the knowledge in a formal (logical or…
We show that strategies implemented in automatic theorem proving involve an interesting tradeoff between execution speed, proving speedup/computational time and usefulness of information. We advance formal definitions for these concepts by…
We present a novel formal system for proving quantitative-leakage properties of programs. Based on a theory of Quantitative Information Flow (QIF) that models information leakage as a noisy communication channel, it uses "gain-functions"…
The free metaplectic transformation (FMT) is widely used in many fields such as filter design, pattern recognition, image processing and optics. In order to obtain a more concise and intuitive convolution form, this paper studies two kinds…
We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
With one exception, our previous work on recurrence extraction and denotational semantics has focused on a source language that supports inductive types and structural recursion. The exception handles general recursion via an initial…
The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.
Expressions are not functions. Confusing the two concepts or failing to define the function that is computed by an expression weakens the rigour of interval arithmetic. We give such a definition and continue with the required re-statements…
Significant work has been done on learning regular expressions from a set of data values. Depending on the domain, this approach can be very successful. However, significant time is required to learn these expressions and the resulting…
Automating the formalization of mathematical statements for theorem proving remains a major challenge for Large Language Models (LLMs). LLMs struggle to identify and utilize the prerequisite mathematical knowledge and its corresponding…
The high cost of agentic workflows in formal mathematics hinders large-scale data synthesis, exacerbating the scarcity of open-source corpora. To address this, we introduce \textbf{TheoremForge}, a cost-effective formal data synthesis…
Scientific press briefings are a valuable information source. They consist of alternating expert speeches, questions from the audience and their answers. Therefore, they can contribute to scientific and fact-based media coverage. Even…
In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…
Dictionary example sentences play an important role in illustrating word definitions and usage, but manually creating quality sentences is challenging. Prior works have demonstrated that language models can be trained to generate example…