In addition to jsprolog, there are several JavaScript libraries for logic programming:
chr.js is a constraint logic programming library for JavaScript. It is an implementation of the Constraint Handling Rules programming language.
There are several JavaScript implementations of Datalog such as DataScript.
Yield Prolog allows Prolog programs to be embedded directly in JavaScript. This is especially useful because it allows JavaScript functions to be used in Prolog predicates, and vice-versa.
LogicJS is a JavaScript library that is based on MiniKanRen, which has been implemented in many programming languages, including JavaScript.
JavaScript-Logic-Programming-System is another logic programming system for JavaScript.
There is another Prolog implementation that was written in less than 200 lines of JavaScript code.
Of course, there are also several C++ libraries for logic programming that could be automatically ported into JavaScript using Emscripten.