Related papers: Modelling Multiplicative Linear Logic via Deep Inf…

Large language models (LLMs) often struggle with complex mathematical tasks, prone to "hallucinating" incorrect answers due to their reliance on statistical patterns. This limitation is further amplified in average Small LangSLMs with…

In this paper we discuss the relationships between conditional and preferential logics and neural network models, based on a multi-preferential semantics. We propose a concept-wise multipreference semantics, recently introduced for…

Selective inference aims at providing valid inference after a data-driven selection of models or hypotheses. It is essential to avoid overconfident results and replicability issues. While significant advances have been made in this area for…

This paper gives a broad account of the various sequent-based proof formalisms in the proof-theoretic literature. We consider formalisms for various modal and tense logics, intuitionistic logic, conditional logics, and bunched logics. After…

Linear logic is a substructural logic proposed as a refinement of classical and intuitionistic logics, with applications in programming languages, game semantics, and quantum physics. We present a template for Gentzen-style linear logic…

Deep learning models are widely used for various industrial and scientific applications. Even though these models have achieved considerable success in recent years, there exists a lack of understanding of the rationale behind decisions…

Substitutions play a crucial role in a wide range of contexts, from analyzing the dynamics of social opinions and conducting mathematical computations to engaging in game-theoretical analysis. For many situations, considering one-step…

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…

Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain…

We show that for Multiplicative Exponential Linear Logic (without weakenings) the syntactical equivalence relation on proofs induced by cut-elimination coincides with the semantic equivalence relation on proofs induced by the multiset based…

We introduce DeepProbLog, a probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques can be adapted for the new language. Our experiments…

The process of translation is ambiguous, in that there are typically many valid trans- lations for a given sentence. This gives rise to significant variation in parallel cor- pora, however, most current models of machine translation do not…

We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…

With the increasing capabilities of Large Language Models (LLMs), parallel reasoning has emerged as a new inference paradigm that enhances reasoning robustness by concurrently exploring multiple lines of thought before converging on a final…

Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…

Several recent works have developed a new, probabilistic interpretation for numerical algorithms solving linear systems in which the solution is inferred in a Bayesian framework, either directly or by inferring the unknown action of the…

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…

In this work we explore the connections between (linear) nested sequent calculi and ordinary sequent calculi for normal and non-normal modal logics. By proposing local versions to ordinary sequent rules we obtain linear nested sequent…

Reasoning encompasses two typical types: deductive reasoning and inductive reasoning. Despite extensive research into the reasoning capabilities of Large Language Models (LLMs), most studies have failed to rigorously differentiate between…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…