Modal Logic and Model Theory
نویسنده
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.
منابع مشابه
Suhrawardi's Modal Syllogisms
Suhrawardi’s logic of the Hikmat al-Ishraq is basically modal. So to understand his modal logic one first has to know the non-modal part upon which his modal logic is built. In my previous paper ‘Suhrawardi on Syllogisms’(3) I discussed the former in detail. The present paper is an exposition of his treatment of modal syllogisms. On the basis of some reasonable existential presuppositi...
متن کاملAbstract model theory for extensions of modal logic
model theory for extensions of modal logic
متن کاملA theoretical investigation into quantitative modal logic
Quantitative modal logic (QML) is a multi-modal formulation of possibilistic reasoning with the capacity of representing and reasoning about higher order uncertainty. In this paper, some results about QML and possibility theory are investigated. First, the concept of filtration in classical modal logic is introduced into QML and the fundamental filtration theorem is proved. Second, as a corolla...
متن کاملReportrapport Modal Model Theory Modal Model Theory
This paper contributes to the model theory of modal logic using bisimulations as the fundamental tool. A uniform presentation is given of modal analogues of well-known deenability and preservation results from rst-order logic. These results include algebraic characterizations of modal equivalence, and of the modally deenable classes of models; the preservation results concern preservation of mo...
متن کاملDoing Argumentation Theory in Modal Logic
The present paper applies well-investigated modal logics to provide formal foundations to specific fragments of argumentation theory. This logic-driven analysis of argumentation allows: first, to systematize several results of argumentation theory reformulating them within suitable formal languages; second, to import several techniques (calculi, model-checking, evaluation games, bisimulation ga...
متن کاملModal Logic As Dialogical Logic
The title reflects my conviction that, viewed semantically, modal logic is fundamentally dialogical; this conviction is based on the key role played by the notion of bisimulation in modal model theory. But this dialogical conception of modal logic does not seem to apply to modal proof theory, which is notoriously messy. Nonetheless, by making use of ideas which trace back to Arthur Prior (notab...
متن کامل