formal implication वाक्य

In the work of some composers, such as Paolo Quagliati, the terms seem to have had no formal implication at all.
In recognition of this problem, the sign ?! of formal implication in the propositional calculus is called material implication to distinguish it from the everyday, intuitive implication.
We shall find always, in all mathematical propositions, that the words " any " or " some " occur; and these words are the marks of a variable and a formal implication ".
The root of the paradoxes lies in a mismatch between the interpretation of the validity of logical implication in natural language, and its formal implication describes conditional if-then statements using a truth-functional interpretation, i . e . " p implies q " is "'defined "'to be " it is not the case that p is true and q false ".