A modal analogue of Lindstrr om's characterization of rst-order logic is proved. Basic modal logics are characterized as the only modal logics that have a notion of nite rank, or, equivalently, as the strongest modal logic whose formulas are preserved under ultra-products over !. Also, basic modal logic is the strongest classical logic whose formulas are preserved under bisimulations and ultra-...

A general method of automated modal logic theorem proving is discussed and illustrated. This method is based on the sub-stitutional framework for the development of systems for hybrid reasoning. Sentences in modal logic are translated into a constraint logic in which the constraints represent the connections between worlds in the possible world semantics for modal logic. Deduction in the constr...

Jaśkowski’s logic D2 was formulated with the help of the modal logic S5, [8]–[10]. It was shown (see [12], [16]) that to define D2 one could use normal modal logics weaker than S5. In the present paper we indicate a certain regular modal logic which also defines D2. This logic is the weakest regular modal logic defining D2.

We introduce a new semantics for modal predicate logic, with respect to which a rich class of first-order modal logics is complete, namely all normal first-order modal logics that are extensions of free quantified K. This logic is defined by combining positive free logic with equality PFL . = and the propositional modal logic K. We then uniformly construct—for each modal predicate logic L—a can...