Aspects of this topic are discussed in the following places at Britannica.
...second area is model theory, which investigates the various structures about which formal theories can be constructed. Here the emphasis is on what cannot be validly deduced from a set of material hypotheses. One attempts to find structures about which the hypotheses are true and yet for which a particular statement is false. Third is recursion theory, which deals with questions involving the...
PC is often presented by what is known as the method of natural deduction. Essentially this consists of a set of rules for drawing conclusions from hypotheses (assumptions, premises) represented by wffs of PC and thus for constructing valid inference forms. It also provides a method of deriving from these inference forms valid proposition forms, and in this way it is analogous to the derivation...
...much to ask for. Following Hans Reichenbach (1891–1953), philosophers often distinguished between the “context of discovery” and the “context of justification.” Once a hypothesis has been proposed, there are canons of logic that determine whether or not it should be accepted—that is, there are rules of method that hold in the context of justification. There...
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