Related papers: The exponential logic of sequentialization
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…
Hierarchical graph rewriting is a highly expressive computational formalism that manipulates graphs enhanced with box structures for representing hierarchies. It has provided the foundations of various graph-based modeling tools, but the…
Large Language Models (LLMs) have showcased impressive reasoning capabilities, particularly when guided by specifically designed prompts in complex reasoning tasks such as math word problems. These models typically solve tasks using a…
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be…
Large Language Models (LLMs) excel at linear reasoning tasks but remain underexplored on non-linear structures such as those found in natural debates, which are best expressed as argument graphs. We evaluate whether LLMs can approximate…
Large language models have evolved to process multiple modalities beyond text, such as images and audio, which motivates us to explore how to effectively leverage them for graph reasoning tasks. The key question, therefore, is how to…
Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…
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…
The exponential modalities of linear logic have been used by various authors to model infinite-dimensional quantum systems. This paper explains how these modalities can also give rise to the complementarity principle of quantum mechanics.…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Table-based reasoning with large language models (LLMs) is a promising direction to tackle many table understanding tasks, such as table-based question answering and fact verification. Compared with generic reasoning, table-based reasoning…
We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the…
Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies…
Effectively combining logic reasoning and probabilistic inference has been a long-standing goal of machine learning: the former has the ability to generalize with small training data, while the latter provides a principled framework for…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
Markov logic networks (MLNs) reconcile two opposing schools in machine learning and artificial intelligence: causal networks, which account for uncertainty extremely well, and first-order logic, which allows for formal deduction. An MLN is…
We offer a simple graphical representation for proofs of intuitionistic logic, which is inspired by proof nets and interaction nets (two formalisms originating in linear logic). This graphical calculus of proofs inherits good features from…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…