Neural logic programs and neural nets
Christian Antić
TL;DR
This paper addresses neural-symbolic integration by providing a formal semantics for boolean neural nets and a principled construction of neural logic programs from first principles. It defines a least-model semantics for positive nets via the monotone operator $T_N$ and extends to non-monotonic settings with Approximation Fixed Point Theory (AFT) using the 3-valued Fitting operator $\Phi_N$, leading to an answer-set semantics for arbitrary nets. It then defines neural logic programs and their semantics, and proves that nets and programs are equivalent under minimalist transformations. The work offers a foundational bridge between connectionist models and symbolic reasoning, enabling clearer semantics, potential learning integration, and future extensions toward first-order, HEX, and sequential compositions.
Abstract
Neural-symbolic integration aims to combine the connectionist subsymbolic with the logical symbolic approach to artificial intelligence. In this paper, we first define the answer set semantics of (boolean) neural nets and then introduce from first principles a class of neural logic programs and show that nets and programs are equivalent.