Reservoir computing (RC) offers a computationally cheap alternative to backpropagationthrough-time for temporal modeling: a fixed, randomly initialized recurrent substrate (the reservoir) projects an input stream into a high-dimensional state space, and only a lightweight readout is trained. This efficiency comes at the cost of a readout that is typically a plain linear or ridge regression model, with no mechanism for incorporating domain knowledge expressed as logical rules. We introduce EchoLogic Networks (ELN), a neurosymbolic architecture that augments the readout's training objective with differentiable fuzzy-logic penalties derived from symbolic constraints-a product t-norm for mutual exclusion and a Łukasiewicz-style implication for temporal precedence rules-while leaving the reservoir untouched. We identify and address an optimization pathology in the naive formulation: without an asymmetric-gradient correction, the model satisfies an implication rule "A ⇒ C" by suppressing the antecedent A rather than raising the consequent C. We further distill the trained readout into a shallow, human-auditable decision tree over reservoir states. On a controlled synthetic benchmark, EchoLogic improves F1 on the rule-implied event from 0.504 ± 0.043 to 0.621 ± 0.030 across 20 independent seeds (Wilcoxon signed-rank p = 1.9 × 10-6 , paired Cohen's d = 3.94), with no measurable cost to unrelated event classes. A controlled ablation isolates the asymmetric-gradient correction as necessary, not cosmetic: removing it lets accuracy on the antecedent class collapse from 0.506 to 0.257. The distilled surrogate reaches 0.982 ± 0.003 held-out fidelity to the full model. We report the method's benefit as a function of reservoir size, spectral radius, and rule reliability, and we present an honest compute-accuracy comparison against a fully backpropagation-trained LSTM: EchoLogic reaches its accuracy plateau roughly an order of magnitude faster, but the LSTM's final ceiling is substantially higher given sufficient training time. We argue this is the correct scientific framing-a speed/ceiling trade-off, not a contest EchoLogic needs to win-and we discuss the central open threat to validity: all experiments here are generated from the same rules injected into the training objective, and validation on an independently-sourced real-world rule set remains the necessary next step.