  In this paper we present the initial development of a general theory for
mapping inference in predicate logic to computation over Tensor Product
Representations (TPRs; Smolensky (1990), Smolensky & Legendre (2006)). After an
initial brief synopsis of TPRs (Section 0), we begin with particular examples
of inference with TPRs in the 'bAbI' question-answering task of Weston et al.
(2015) (Section 1). We then present a simplification of the general analysis
that suffices for the bAbI task (Section 2). Finally, we lay out the general
treatment of inference over TPRs (Section 3). We also show the simplification
in Section 2 derives the inference methods described in Lee et al. (2016); this
shows how the simple methods of Lee et al. (2016) can be formally extended to
more general reasoning tasks.
