Binary relation mining has been extensively studied. Nevertheless,many interesting 0/1 data naturally appear as n-ary relations withn > 2. A timely challenge is to extend local patternextraction, \eg, closed pattern mining, to such contexts. Whenconsidering higher arities, faint noise affects more and more thequality of the extracted patterns. We study a declarativespecification of error-tolerant patterns by means of new primitiveconstraints and the design of an efficient algorithm to extractevery solution pattern. It exploits the enumeration principles ofthe state-of-the-art \textsc{Data-Peeler} algorithm for $n$-aryrelation mining. Efficiently enforcing error-tolerance cruciallydepends on innovative strategies to incrementally compute partialinformation on the data. Our prototype is tested on both syntheticand real datasets. It returns relevant collections of patterns evenin the case of very noisy ternary or $4$-ary relations, \eg, in thecontext of pattern discovery from dynamic networks.