–
Room P3.10, Mathematics Building
The World of Possible Logics and Universal Kripke Structures
Given a specific language $L$ and the corresponding set of formulas $F$, we consider the class of all sets of formulas (the power set of $F$). Each such a set can be viewed as a logic taken as a set of tautologies. Relations such as inclusion can be used to compare these logics and this leads to a structure that we call the world of possible logics of type $L$. Elements of such a structure can be considered in fact as bivalutions (taking the characteristic functions) and relations between elements as accessibility relations. This leads to the concept of UKS: Universal Kripke Structure. We will show how such general concepts can be used to develop universal logic, i.e., a general theory of logics, and applied to develop specific constructions such as a logic of imagination.