This allows us to formulate a notion of linear validity: Linear validity: A formula A is linearly valid iff there is a closed dialogue for P- -A such that the P- -Asitional content of any move has been used (and therefore is bracketed).
Thus the dialogues that do characterize a definite notion of validity can be seen as an abstraction from concrete, empirical dialogue games.
Kanger (1957), Montague (1960, but originally presented in 1955), Hintikka (1961), and Prior (1957) were all thinking of a relation between worlds, and Hintikka (1961) like Kripke (1959) adopted a new notion of validity that required truth in all arbitrary sets of worlds.
The proof however effectively employs a schematic notion of validity.
Moreover, we prove that this system is complete for a reasonable notion of validity for Hoare judgments.
In a manner analogous to Boolean-valued validity, one can introduce an appropriate notion of validity in E of a sentence σ of its internal language.
It is equally obvious that if one has at hand a notion of model-theoretic validity for a formalized language which is based on a minimally reasonable notion of structure, then all logical truths (of that language) will be model-theoretically valid.
The notion of validity of a formula \(A\) with respect to an algebraic structure from \ \bK\) is defined as if this structure would form a logical matrix.
So far, we have a very useful consequence of the classical notion of validity.
