Ciao - The Ciao programming language
Ciao is a programming language that builds up from a logic-based simple kernel, and is designed to be extensible and modular.
s(CASP) - The main contribution of s(CASP) is its ability to evaluate Constraint Answer Set Programs without a grounding phase, either before or during execution.
So ASP in s(CASP) is Answer Set Programming
CASP is ASP with constraints (ref)
For how s(CASP) came into SWI-Prolog see Initial port for sCASP, a top-down interpreter for ASP programs with constraints
s(ASP) - The s(ASP) Predicate Answer Set Programming System (ref)
The s() part is a play on Peano axioms. s() being the successor function. Make sense?
“A Short Tutorial on s(CASP), a Goal-directed Execution of Constraint Answer Set Programs” by Joaquín Arias, Gopal Gupta and Manuel Carro (pdf)
HTH