Modal Logic and Model Theory

نویسنده

  • Giangiacomo Gerla
چکیده

We propose a first order modal logic, the QS?E-logic, obtained by adding to the well-known first order modal logic QS4 a rigidity axiom sch?mas : A -> O A, where A denotes a basic formula. In this logic, the possibility entails the possibility of extending a given classical first order model. This allows us to express some impor? tant concepts of classical model theory, such as existential completeness and the state of being infinitely generic, that are not expressibile in classical first order logic. Since they can be expressed in I/^-logic, we are also induced to compare the expressive powers of QS4?E and Lm ?,. Some questions concerning the power of rigidity axiom are also examined.

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تاریخ انتشار 2008