General normal forms for any additive logic

Abstract

In this article, we define general normal forms for any logic that has propositional part and whose non-propositional connectives distribute over the finite disjunctions. We do not require the non-propositional connectives to be closed on the set of formulas, so our normal forms cover logics with partial connectives too. We also show that most of the known normal forms in the literature are in fact particular cases of our general forms. These general normal forms are natural improvement of the distributive normal forms of J. Hintikka [2] and their modal analogues, e.g. [1] and [3].

First order logic without equality on relativized semantics

“…To prove the above theorems, we use the normal forms defined in [44], these are generalizations of the normal forms introduced by J. Hintikka [3]. We show that, for each satisfiable normal form in Drs α , there is an algebra in Drs α , whose base is finite, that witnesses the satisfiability of this form.…”