Related papers: Introducing Quantified Cuts in Logic with Equality
We extend the theoretical framework of proof mining by establishing general logical metatheorems that allow for the extraction of the computational content of theorems with prima facie "non-computational" proofs from probability theory,…
When proving the correctness of a method for slicing probabilistic programs, it was previously discovered by the authors that for a fixed point iteration to work one needs a non-standard starting point for the iteration. This paper presents…
We apply an idea originated in the theory of programming languages - monadic meta-language with a distinction between values and computations - in the design of a calculus of cut-elimination for classical logic. The cut-elimination calculus…
Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…
Approximate computing is an attractive paradigm for reducing the design complexity of error-resilient systems, therefore improving performance and saving power consumption. In this work, we propose a new two-level approximate logic…
One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…
Large language models (LLMs) sometimes demonstrate poor performance on knowledge-intensive tasks, commonsense reasoning is one of them. Researchers typically address these issues by retrieving related knowledge from knowledge graphs or…
We present cut-free labelled sequent calculi for a central formalism in logics of agency: STIT logics with temporal operators. These include sequent systems for Ldm, Tstit and Xstit. All calculi presented possess essential structural…
Thematic analysis and other variants of inductive coding are widely used qualitative analytic methods within empirical legal studies (ELS). We propose a novel framework facilitating effective collaboration of a legal expert with a large…
For performance and verification in machine learning, new methods have recently been proposed that optimise learning systems to satisfy formally expressed logical properties. Among these methods, differentiable logics (DLs) are used to…
Recent advancements in large language models (LLMs) are propelling us toward artificial general intelligence with their remarkable emergent abilities and reasoning capabilities. However, the substantial computational and memory requirements…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
A common strategy for fact-checking long-form content generated by Large Language Models (LLMs) is extracting simple claims that can be verified independently. Since inaccurate or incomplete claims compromise fact-checking results, ensuring…
In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time. In this paper, we introduce INT, an INequality Theorem proving benchmark, specifically designed to…
First-order logic has been established as an important tool for modeling and verifying intricate systems such as distributed protocols and concurrent systems. These systems are parametric in the number of nodes in the network or the number…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
We introduce a proof language for Intuitionistic Multiplicative Additive Linear Logic (IMALL), extended with a modality B to capture mixed-state quantum computation. The language supports algebraic constructs such as linear combinations,…
As large language models (LLMs) have become the norm in NLP, demonstrating good performance in generation and reasoning tasks, one of its most fatal disadvantages is the lack of factual correctness. Generating unfactual texts not only leads…
Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…
The rise of Large Language Models (LLMs) has had a profoundly transformative effect on a number of fields and domains. However, their uptake in Law has proven more challenging due to the important issues of reliability and transparency. In…