Related papers: Introducing Quantified Cuts in Logic with Equality

Recent advances in large language models (LLMs) have popularized the chain-of-thought (CoT) paradigm, in which models produce explicit reasoning steps in natural language. Although this approach improves interpretability and facilitates…

Nowadays there is a large number of non-classical logics, each one best suited for reasoning about some issues in abstract fields, such as linguistics or epistemology, among others. Proving interesting properties for each one of them…

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical…

The emphasis is made on the juxtaposition of (quantum~theorem) proving versus quantum (theorem~proving). The logical contents of verification of the statements concerning quantum systems is outlined. The Zittereingang (trembling input)…

We investigate the task of inserting new concepts extracted from texts into an ontology using language models. We explore an approach with three steps: edge search which is to find a set of candidate locations to insert (i.e., subsumptions…

We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing. In this work we take a coarser (and…

Pruning has emerged as a promising direction for accelerating large language model (LLM) inference, yet existing approaches often suffer from instability because they rely on offline calibration data that may not generalize across inputs.…

We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming…

We study the notion of stratification, as used in subsystems of linear logic with low complexity bounds on the cut-elimination procedure (the so-called light logics), from an abstract point of view, introducing a logical system in which…

Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…

Viewing formal mathematical proofs as logical terms provides a powerful and elegant basis for analyzing how human experts tend to structure proofs and how proofs can be structured by automated methods. We pursue this approach by (1)…

Formal reasoning about finite sets and cardinality is an important tool for many applications, including software verification, where very often one needs to reason about the size of a given data structure and not only about what its…

Large Language Models (LLMs) have been achieving competent performance on a wide range of downstream tasks, yet existing work shows that inference on structured data is challenging for LLMs. This is because LLMs need to either understand…

The rise of large language models (LLMs) has significantly advanced various natural language processing (NLP) tasks. However, the resource demands of these models pose substantial challenges. Structured pruning is an effective approach to…

Computability logic (CL) (see http://www.cis.upenn.edu/~giorgi/cl.html) is a recently launched program for redeveloping logic as a formal theory of computability, as opposed to the formal theory of truth that logic has more traditionally…

The zero-shot chain of thought (CoT) approach is often used in question answering (QA) by language models (LMs) for tasks that require multiple reasoning steps. However, some QA tasks hinge more on accessing relevant knowledge than on…

<p>We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted…

In this paper, we develop a novel verification technique to reason about programs featuring concurrency, pointers and randomization. While the integration of concurrency and pointers is well studied, little is known about the combination of…

Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…