Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANs

arXiv cs.AIAugust 25, 2026en

arXiv:2608.21605v1 Announce Type: new Abstract: Logic Tensor Network-Enhanced Generative Adversarial Networks (LTN-GANs) inject background knowledge by grounding each logical axiom as a predicate and training the generator to raise its satisfaction, a fuzzy truth value in $[0,1]$. Previous LTN-GAN work grounded every constraint this way, at the predicate level, and improved constraint satisfaction. A predicate, however, only scores a sample, so it cannot embed hard structural constraints, rules such as orderings, positivity, and definitional identities that must hold in every generated sample. In this work, we investigate grounding each axiom as a function symbol inside the LTN framework. We

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