Related papers: Unification nets: canonical proof net quantifiers

Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…

Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…

We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern…

A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…

Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…

Markov Logic Networks (MLNs), which elegantly combine logic rules and probabilistic graphical models, can be used to address many knowledge graph problems. However, inference in MLN is computationally intensive, making the industrial-scale…

Linearizability is a standard correctness criterion for concurrent algorithms, typically proved by establishing the algorithms' linearization points (LP). However, LPs often hinder abstraction, and for some algorithms such as the…

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…

Visual reasoning is challenging, requiring both precise object grounding and understanding complex spatial relationships. Existing methods fall into two camps: language-only chain-of-thought approaches, which demand large-scale (image,…

The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations…

Learning-based systems are increasingly deployed across various domains, yet the complexity of traditional neural networks poses significant challenges for formal verification. Unlike conventional neural networks, learned Logic Gate…

We extend the constructive dependent type theory of the Logical Framework $\mathsf{LF}$ with monadic, dependent type constructors indexed with predicates over judgements, called Locks. These monads capture various possible proof attitudes…

A novel model-based approach to verify dynamic networks is proposed; the approach consists in formally describing the network topology and dynamic link parameters. A many sorted first order logic formula is constructed to check the model…

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the…

In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…

Cut-elimination is the bedrock of proof theory. It is the algorithm that eliminates cuts from a sequent calculus proof that leads to cut-free calculi and applications. Cut-elimination applies to many logics irrespective of their semantics.…

In this paper we investigate two logics from an algebraic point of view. The two logics are: MALL (multiplicative-additive Linear Logic) and LL (classical Linear Logic). Both logics turn out to be strongly algebraizable in the sense of Blok…

QNNVerifier is the first open-source tool for verifying implementations of neural networks that takes into account the finite word-length (i.e. quantization) of their operands. The novel support for quantization is achieved by employing…

Modern neural networks demonstrate state-of-the-art performance on numerous existing benchmarks; however, their high computational requirements and energy consumption prompt researchers to seek more efficient solutions for real-world…

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…