A General Proof Method for Modal Predicate Logic without the Barcan Formula

Peter Jackson, Han Reichgelt

We present a general proof method for normal systems of modal predicate logic with identical inference rules for each such logic. Different systems are obtained by changing the conditions under which two formulas are considered complementary. The paper extends previous work in that we are no longer confined. to models in which the Barcan formula and its converse hold. This allows the domain of individuals to vary from world to world. Modifications to the original inference rules are given, and a semantic justification is provided.

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