Syntactic Refutations against Finite Models in Modal Logic

Modal Logic over Finite Structures

Modal Logic over Finite Structures

In this paper, we develop various aspects of the finite model theory of propositional modal logic. In particular, we show that certain results about the expressive power of modal logic over the class of all structures, due to van Benthem and his collaborators, remain true over the class of finite structures. We establish that a firstorder definable class of finite models is closed under bisimul...

A Logic of Finite Syntactic Epistemic States

The thesis presents a logic of the explicit knowledge of deliberative agents who represent their knowledge symbolically as sets of formulae – agents with finite syntactic epistemic states. It is well known that modal epistemic logic either describes implicit knowledge, including all logical consequences of the explicit knowledge, or describes the explicit knowledge of unrealistically intelligen...

Finite Model Property of Pretransitive Modal Logic

The finite model property of the quasi-transitive modal logic K32 = K ⊕ ✷✷p → ✷✷✷p is proved. This modal logic is conservatively extended to the tense logic Kt32. We present a Gentzen sequent calculus Gt32 for Kt 3 2 which admits cut elimination. The sequent calculus Gt 3 2 is shown to have the finite model property by a construction of finite syntactic model. It follows that Kt32 has the finit...

Coalgebraic modal logic of finite rank