This work extends the game-based framework of μ-calculus model checking to the multi-valued setting. In multi-valued model checking a formula is interpreted over a Kripke structure defined over a lattice. The value of the formula is also an element of the lattice. This problem has many applications in verification, such as handling abstract or partial models, analyzing systems in the presence o...

We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabili...

The paper investigates the characterisation of vague concepts within the framework of modal logic. This work builds on the su-pervaluation approach of Fine and exploits the idea of a precisiication space. A simple language is presented with two modalities: a necessity operator and an operatorìt is unequivocal that' which is used to articulate the logic of vagueness. Both these operators obey th...

Abstract This paper collects and presents unpublished notes of Kurt Gödel concerning the field many-valued logic. In order to get a picture as complete possible, both formal philosophical notes, transcribed from Gabelsberger shorthand system, are included.

Linear constraints occur naturally in many reasoning problems and the information that they represent is often uncertain. There is a difficulty in applying AI uncertainty formalisms to this situation, as their representation of the underlying logic, either as a mutually exclusive and exhaustive set of possibilities, or with a propositional or a predicate logic, is inappropriate (or at least unh...