Software applications in Artificial Intelligence, particularly Natural Language Processing, often need to decide how far two given strings differ from each other in their content. To this day edit distance remains to be widely used for measuring the difference. Symbols in strings are compared, but the meanings of strings are not considered in almost all algorithms based on edit distance. This paper aims to define a logical formalism for comparing strings. Thus the comparisons are enhanced with computer-comprehensible semantics. More precisely, we propose SMAT, a String Matching Action Theory, written in the language of Situation Calculus. We show that SMAT can be used to flexibly represent various string operators. Damerau-Levenshtein edit operators are specifically used as an illustration example. We remark that 1) SMAT is, in addition, a software program implementation for string matching; 2) Knowledge-based heuristics in support of string-matching strategies can be easily incorporated into SMAT, and 3) SMAT provides new opportunities for string matching through automated planning in Artificial Intelligence.