  Commonsense knowledge-graphs (CKGs) are important resources towards building
machines that can 'reason' on text or environmental inputs and make inferences
beyond perception. While current CKGs encode world knowledge for a large number
of concepts and have been effectively utilized for incorporating commonsense in
neural models, they primarily encode declarative or single-condition
inferential knowledge and assume all conceptual beliefs to have the same
likelihood. Further, these CKGs utilize a limited set of relations shared
across concepts and lack a coherent knowledge organization structure resulting
in redundancies as well as sparsity across the larger knowledge graph.
Consequently, today's CKGs, while useful for a first level of reasoning, do not
adequately capture deeper human-level commonsense inferences which can be more
nuanced and influenced by multiple contextual or situational factors.
  Accordingly, in this work, we study how commonsense knowledge can be better
represented by -- (i) utilizing a probabilistic logic representation scheme to
model composite inferential knowledge and represent conceptual beliefs with
varying likelihoods and (ii) incorporating a hierarchical conceptual ontology
to identify salient concept-relevant relations and organize beliefs at
different conceptual levels. Our resulting knowledge representation framework
can encode a wider variety of world knowledge and represent beliefs flexibly
using grounded concepts as well as free-text phrases. As a result, the
framework can be utilized as both a traditional free-text knowledge graph and a
grounded logic-based inference system more suitable for neuro-symbolic
applications. We describe how we extend the PrimeNet knowledge base with our
framework through crowd-sourcing and expert-annotation, and demonstrate its
application for more interpretable passage-based semantic parsing and question
answering.
