Parametric logic: Foundations (Q1902289)

We introduce a parametric operator. It is suitable for describing any objects which have a certain mathematical structure. It is formal enough to express various attitudes of natural language, ontologies of commonsense reasoning and general operations of propositions. In particular, it makes it possible to deal with qualifications with modalities in the same way. Also, it can be directly incorporated within the calculus. Various logics can be expressed as parametrized logic by parametric operators so that they can be studied in the same logical framework. We call the formalization of the parametric operator the parametric logic \({\mathcal P} {\mathcal L}\).