In this talk, I will present the propositional fragment of the logic LA, a logic that aims to formalize the notion of CL-analysis. When goal directed proofs are constructed with the prospective dynamics (as defined in [1]), no constructive steps are needed (formulas are only broken down into less complex formulas). Analyzing the candidate consequence (the goal) and the premises suffices to find out whether the candidate consequence is indeed a consequence of the premises. Precisely this analyzing process is captured with the consequence relation LA. In LA neither addition nor introduction of the conjunction are valid (they create more complex formulas), but simplification, modus ponens, modus tollens and disjunctive syllogism are valid rules. Thanks to the addition of a classical implication to the object language, LA is a “usual” logic, i.e. it is monotonic, reflexive and transitive and it has a deterministic two valued semantics and a regular axiomatization. Of course LA in itself is a very weak paraconsistent logic. Nevertheless the standard goal directed proofs can be translated into proofs of this logic, as long as they do not rely on the rule “ex falso quodlibet”. As a consequence, also the non-transitive logic $CL^{-}$ (CL-min), which is CL without explosion (but with all primitive CL-rules), can be easily translated into LA. So, the axiomatization of LA can be used as a straight forward rule system for $CL^{-}$ and its semantics can also function as a (deterministic) semantics for $CL^{-}$. [1] Diderik Batens and Dagmar Provijn. Pushing the Search Paths in the Proofs. A Study in Proof Heuristics. [Logique et Analyse, 173-174-175, 2001, pp. 113-134 (Appeared 2003)]