Related papers: Efficient Decision Procedures for RNmatrix Semanti…
In this paper, we study the nonnegative matrix factorization problem under the separability assumption (that is, there exists a cone spanned by a small subset of the columns of the input nonnegative data matrix containing all columns),…
Low dimensional nonlinear structure abounds in datasets across computer vision and machine learning. Kernelized matrix factorization techniques have recently been proposed to learn these nonlinear structures for denoising, classification,…
Large language models (LLMs) and theorem provers (TPs) can be effectively combined for verifiable natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and…
The notion of non-deterministic logical matrix (where connectives are interpreted as multi-functions) preserves many good properties of traditional semantics based on logical matrices (where connectives are interpreted as functions) whilst…
Neural Module Networks (NMNs) have been quite successful in incorporating explicit reasoning as learnable modules in various question answering tasks, including the most generic form of numerical reasoning over text in Machine Reading…
Matrix preconditioning is a critical technique to accelerate the solution of linear systems, where performance heavily depends on the selection of preconditioning parameters. Traditional parameter selection approaches often define fixed…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
The demand for formal verification tools for neural networks has increased as neural networks have been deployed in a growing number of safety-critical applications. Matrices are a data structure essential to formalising neural networks.…
In this paper, we propose a provably correct algorithm for convolutive nonnegative matrix factorization (CNMF) under separability assumptions. CNMF is a convolutive variant of nonnegative matrix factorization (NMF), which functions as an…
A grammar logic refers to an extension to the multi-modal logic K in which the modal axioms are generated from a formal grammar. We consider a proof theory, in nested sequent calculus, of grammar logics with converse, i.e., every modal…
Current large language models (LLMs) primarily rely on linear sequence generation and massive parameter counts, yet they severely struggle with complex algorithmic reasoning. While recent reasoning architectures, such as the Hierarchical…
The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…
Logic provides a controlled testbed for evaluating LLM-based reasoners, yet standard SAT-style benchmarks often conflate surface difficulty (length, wording, clause order) with the structural phenomena that actually determine…
Definite descriptions, such as 'the General Chair of KR 2024', are a semantically transparent device for object identification in knowledge representation. In first-order modal logic, definite descriptions have been widely investigated for…
Continuous-output neural machine translation (CoNMT) replaces the discrete next-word prediction problem with an embedding prediction. The semantic structure of the target embedding space (i.e., closeness of related words) is intuitively…
Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage…
In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally…
Natural language understanding requires interleaving textual and logical reasoning, yet large language models often fail to perform such reasoning reliably. Existing neurosymbolic systems combine LLMs with solvers but remain limited to…
While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…
Natural language questions are inherently compositional, and many are most easily answered by reasoning about their decomposition into modular sub-problems. For example, to answer "is there an equal number of balls and boxes?" we can look…