Related papers: Structural Complexity of Rational Interactive Proo…
Let L be some extension of classical propositional logic. The non-iterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a…
We show how to extract a monotonic learning algorithm from a classical proof of a geometric statement by interpreting the proof by means of interactive realizability, a realizability sematics for classical logic. The statement is about the…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Transformer language models are state of the art in a multitude of NLP tasks. Despite these successes, their opaqueness remains problematic. Recent methods aiming to provide interpretability and explainability to black-box models primarily…
Recently, researchers have been working toward the development of practical general-purpose protocols for verifiable computation. These protocols enable a computationally weak verifier to offload computations to a powerful but untrusted…
Information retrieval models have witnessed a paradigm shift from unsupervised statistical approaches to feature-based supervised approaches to completely data-driven ones that make use of the pre-training of large language models. While…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
The communication complexity of many fundamental problems reduces greatly when the communicating parties share randomness that is independent of the inputs to the communication task. Natural communication processes (say between humans)…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
Selective rationalization explains the prediction of complex neural networks by finding a small subset of the input that is sufficient to predict the neural model output. The selection mechanism is commonly integrated into the model itself…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
Multimodal document question answering requires retrieving dispersed evidence from visually rich long documents and performing reliable reasoning over heterogeneous information. Existing multimodal RAG systems remain limited by two…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
To comprehensively evaluate the mathematical reasoning capabilities of Large Language Models (LLMs), researchers have introduced abundant mathematical reasoning datasets. However, most existing datasets primarily focus on linear reasoning,…
We consider the problem of how a trusted, but computationally bounded agent (a 'verifier') can learn to interact with one or more powerful but untrusted agents ('provers') in order to solve a given task. More specifically, we study the case…
The application of automatic theorem provers to discharge proof obligations is necessary to apply formal methods in an efficient manner. Tools supporting formal methods, such as Atelier~B, generate proof obligations fully automatically.…
Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on…
Motivated by certain applications from physics, biochemistry, economics, and computer science, in which the objects under investigation are not accessible because of various limitations, we propose a trial-and-error model to examine…
Neural networks have shown substantial promise at automatic theorem-proving in interactive proof assistants (ITPs) like Lean and Coq. However, most neural theorem-proving models are restricted to specific ITPs, leaving out opportunities for…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…