Constraint logic programming is logic programming extended with constraints, and a constraint solver is an engine for checking and resolving such constraints. I guess that's not very useful if you don't know what constraints are but a full explanation can get very involved very quickly, so check out the wikipedia page for a brief (ish) intro.
From personal experience, if you're used to programming in a logic programming language, trying CLP out is like being in declarative heaven. Swi Prolog, as I think all the full Prolog implementations, has a few CLP libraries, frex see:
Minikanren is a relational language that's introduced in the Reasoned Schemer as an example of a relational language. I don't think it's fully a logic programming language (ie, no theorem proving) but I might be wrong. Check out the book for more.
Inductive Logic Programming is a machine learning technique for learning Prolog programs from data. More to the point, you declare knowledge about the world as positive and negative examples given as Prolog unit clauses (facts). An inductive Logic Programming algorithm then will learn a full Prolog program for you, including definite clauses (rules).
ILP is closely er, related to Relational Learning a.k.a. Statistical and Relational Learning and a number of probabilistic logic programming languages like Problog
(no typo).
You can find a lot of information about ILP in the textbook Logical and Relational Learning by Luc de Raedt [http://www.springer.com/us/book/9783540200406], which I recommend (not related to the author) (but I am a logic programming looney so).
- minikanren
- constraint logic prog
- constraint solving
- inductive logic
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