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In this work, we leverage the linear algebraic structure of distributed word representations to automatically extend knowledge bases and allow a machine to learn new facts about the world. Our goal is to extract structured facts from…
We lay out an infinity categorical interpretation of reconstruction theorems which are germane to the symmetric monoidal perspective of noncommutative algebraic geometry, present sufficient conditions which allow for the factorization of…
Distributional semantic models learn vector representations of words through the contexts they occur in. Although the choice of context (which often takes the form of a sliding window) has a direct influence on the resulting embeddings, the…
Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small…
Different from previous surveys in semantic parsing (Kamath and Das, 2018) and knowledge base question answering(KBQA)(Chakraborty et al., 2019; Zhu et al., 2019; Hoffner et al., 2017) we try to takes a different perspective on the study of…
We consider the equivalence between the two main categorical models for the type-theoretical operation of context comprehension, namely P. Dybjer's categories with families and B. Jacobs' comprehension categories, and generalise it to the…
Categorial type logics, pioneered by Lambek, seek a proof-theoretic understanding of natural language syntax by identifying categories with formulas and derivations with proofs. We typically observe an intuitionistic bias: a structural…
Generating paraphrases that are lexically similar but semantically different is a challenging task. Paraphrases of this form can be used to augment data sets for various NLP tasks such as machine reading comprehension and question answering…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…
Formal concept analysis has grown from a new branch of the mathematical field of lattice theory to a widely recognized tool in Computer Science and elsewhere. In order to fully benefit from this theory, we believe that it can be enriched…
We prove strong completeness of a range of substructural logics with respect to a natural poset-based relational semantics using a coalgebraic version of completeness-via-canonicity. By formalizing the problem in the language of coalgebraic…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
We present a factorized compositional distributional semantics model for the representation of transitive verb constructions. Our model first produces (subject, verb) and (verb, object) vector representations based on the similarity of the…
In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic…
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
Latent Semantic Analysis is a method of matrix decomposition used for discovering topics and topic weights in natural language documents. This study uses Latent Semantic Analysis to analyze the composition of binaries of malicious programs.…