Is there a tool for analyzing soundness in philosophical arguments?

Logic as a discipline and a tool is fantastic for philosophy. It allows to precisely determine the validity of arguments.

However, contemporary standard logic works generally in formal languages(propositional, first order, etc..) and, as such, it’s possible to construct arguments that are valid though completely weird and unsound on natural language(if 2+2=4, then the sky is blue, 2+2=4, therefore, the sky is blue - a common modus ponens).

Considering that, is there a tool/discipline, similar to logic, in which, it analyzes arguments by their soundness(how probable/true are the premisses)? It seems, when it comes to analyzing how true the premisses are, things get a bit contextual