Related papers: Introducing Quantified Cuts in Logic with Equality

We provide a new sequent calculus that enjoys syntactic cut-elimination and strongly terminating backward proof search for the intuitionistic Strong L\"ob logic $\sf{iSL}$, an intuitionistic modal logic with a provability interpretation. A…

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a…

This paper presents a simple notion of proof net for multiplicative linear logic with units. Cut elimination is direct and strongly normalising, in contrast to previous approaches which resorted to moving jumps (attachments) of par units…

The demonstrated code-understanding capability of LLMs raises the question of whether they can be used for automated program verification, a task that demands high-level abstract reasoning about program properties that is challenging for…

In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP…

Whether QML can offer a transformative advantage remains an open question. The severe constraints of NISQ hardware, particularly in circuit depth and connectivity, hinder both the validation of quantum advantage and the empirical…

Measurable cones, with linear and measurable functions as morphisms, are a model of intuitionistic linear logic and of call-by-name probabilistic PCF which accommodates "continuous data types" such as the real line. So far however, they…

This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with Both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short).…

Tuning pre-trained language models (PLMs) with task-specific prompts has been a promising approach for text classification. Particularly, previous studies suggest that prompt-tuning has remarkable superiority in the low-data scenario over…

Previous works by Gor\'e, Postniece and Tiu have provided sound and cut-free complete proof systems for modal logics extended with path axioms using the formalism of nested sequent. Our aim is to provide (i) a constructive cut-elimination…

Large language models (LLMs) can effectively handle outdated information through knowledge editing. However, current approaches face two key limitations: (I) Poor generalization: Most approaches rigidly inject new knowledge without ensuring…

This paper introduces ThoughtProbe, a novel inference time framework that leverages the hidden reasoning features of Large Language Models (LLMs) to improve their reasoning performance. Unlike previous works that manipulate the hidden…

Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…

Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…

We investigate the satisfaction of specifications in Prompt Linear Temporal Logic (Prompt-LTL) by concurrent systems. Prompt-LTL is an extension of LTL that allows to specify parametric bounds on the satisfaction of eventualities, thus…

Reinforcement Learning (RL) enhances LLM reasoning, yet a paradox emerges as models scale: strong base models saturate standard benchmarks (e.g., MATH), yielding correct but homogeneous solutions. In such environments, the lack of failure…

This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…

Any set of truth-functional connectives has sequent calculus rules that can be generated systematically from the truth tables of the connectives. Such a sequent calculus gives rise to a multi-conclusion natural deduction system and to a…

In large-scale industrial LLM systems, prompt templates often expand to thousands of tokens as teams iteratively incorporate sections such as task instructions, few-shot examples, and heuristic rules to enhance robustness and coverage. This…

We consider modal logic extended with the well-known temporal operator 'eventually' and provide a cut-elimination procedure for a cyclic sequent calculus that captures this fragment. The work showcases an adaptation of the reductive…