Language, logic and ontology: uncovering the structure of commonsense knowledge

The purpose of this paper is twofold: (i) we argue that the structure of commonsense knowledge must be discovered, rather than invented; and (ii) we argue that natural language, which is the best known theory of our (shared) commonsense knowledge, should itself be used as a guide to discovering the structure of commonsense knowledge. In addition to suggesting a systematic method to the discovery of the structure of commonsense knowledge, the method we propose seems to also provide an explanation for a number of phenomena in natural language, such as metaphor, intensionality, and the semantics of nominal compounds. Admittedly, our ultimate goal is quite ambitious, and it is no less than the systematic ‘discovery’ of a well-typed ontology of commonsense knowledge, and the subsequent formulation of the longawaited goal of a meaning algebra

Supervised Typing of Big Graphs using Semantic Embeddings

We propose a supervised algorithm for generating type embeddings in the same semantic vector space as a given set of entity embeddings. The algorithm is agnostic to the derivation of the underlying entity embeddings. It does not require any manual feature engineering, generalizes well to hundreds of types and achieves near-linear scaling on Big Graphs containing many millions of triples and instances by virtue of an incremental execution. We demonstrate the utility of the embeddings on a type recommendation task, outperforming a non-parametric feature-agnostic baseline while achieving 15x speedup and near-constant memory usage on a full partition of DBpedia. Using state-of-the-art visualization, we illustrate the agreement of our extensionally derived DBpedia type embeddings with the manually curated domain ontology. Finally, we use the embeddings to probabilistically cluster about 4 million DBpedia instances into 415 types in the DBpedia ontology.Comment: 6 pages, to be published in Semantic Big Data Workshop at ACM, SIGMOD 2017; extended version in preparation for Open Journal of Semantic Web (OJSW

Sequent and Hypersequent Calculi for Abelian and Lukasiewicz Logics

We present two embeddings of infinite-valued Lukasiewicz logic L into Meyer and Slaney's abelian logic A, the logic of lattice-ordered abelian groups. We give new analytic proof systems for A and use the embeddings to derive corresponding systems for L. These include: hypersequent calculi for A and L and terminating versions of these calculi; labelled single sequent calculi for A and L of complexity co-NP; unlabelled single sequent calculi for A and L.Comment: 35 pages, 1 figur