Related papers: The relational model is injective for Multiplicati…
We present a proof-theoretical study of the interpretability logic IL, providing a wellfounded and a non-wellfounded sequent calculus for IL. The non-wellfounded calculus is used to establish a cut elimination argument for both calculi. In…
We present a polymorphic linear lambda-calculus as a proof language for second-order intuitionistic linear logic. The calculus includes addition and scalar multiplication, enabling the proof of a linearity result at the syntactic level.
We introduce the two substructural propositional logics KL, KL+, which use disjunction, fusion and a unary, (quasi-)exponential connective. For both we prove strong completeness with respect to the interpretation in Kleene algebras and a…
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…
We introduce RelNet: a new model for relational reasoning. RelNet is a memory augmented neural network which models entities as abstract memory slots and is equipped with an additional relational memory which models relations between all…
Word embeddings have been found to capture a surprisingly rich amount of syntactic and semantic knowledge. However, it is not yet sufficiently well-understood how the relational knowledge that is implicitly encoded in word embeddings can be…
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which…
Full Intuitionistic Linear Logic (FILL) is multiplicative intuitionistic linear logic extended with par. Its proof theory has been notoriously difficult to get right, and existing sequent calculi all involve inference rules with complex…
A new and rapidly growing econometric literature is making advances in the problem of using machine learning methods for causal inference questions. Yet, the empirical economics literature has not started to fully exploit the strengths of…
The database community lacks a unified relational query language for subset selection and optimisation queries, limiting both user expression and query optimiser reasoning about such problems. Decades of research (latterly under the rubric…
The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be…
There has been increasing interest in evaluations of language models for a variety of risks and characteristics. Evaluations relying on natural language understanding for grading can often be performed at scale by using other language…
In this paper, we present MELT-ML, a machine learning extension to the Matching and EvaLuation Toolkit (MELT) which facilitates the application of supervised learning for ontology and instance matching. Our contributions are twofold: We…
Large-scale multi-relational embedding refers to the task of learning the latent representations for entities and relations in large knowledge graphs. An effective and scalable solution for this problem is crucial for the true success of…
We prove several representation theorems for infinitary predicate modal logic
This paper presents proof nets for multiplicative-additive linear logic (MALL), called conflict nets. They are efficient, since both correctness and translation from a proof are p-time (polynomial time), and abstract, since they are…
In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…
The paper considers general multiplicative models for complete and incomplete contingency tables that generalize log-linear and several other models and are entirely coordinate free. Sufficient conditions of the existence of maximum…
This paper introduces a logic with a class of social network models that is based on standard Linear Temporal Logic (LTL), leveraging the power of existing model checkers for the analysis of social networks. We provide a short literature…
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…