Several new higher-order spatial symbol recognition methods for optical symbolic substitution-based calculations are presented. In the case of logic processing, higher-order symbolic substitution (SS) rules can implement multivariable logic functions. For binary arithmetic calculations requiring carry propagation by simultaneously processing a number of bits, the computational speed increases. Finally, in image processing, the higher-order SS rules allow the use of larger local windows. For a higher-order spatial symbol recognition, both multiplicative and additive logic techniques are discussed. Four different higher-order SS recognition optical architectures are suggested: a multireflecting technique using an optical cavity, a lenslet array, an optical phase conjugation, and a content-addressable memory. Either dual-rail or triple-rail optical spatial intensity encoding is employed. Some preliminary experimental results are also presented.