Handbook of the World Congress and School on Universal Logic III April 18 - 25 Lisbon - Portugal Edited by Jean-Yves B ́eziau, Carlos Caleiro, Jo ̃ao Rasga e Alexandre Costa-Leite
In the same way that universal algebra is a general theory of algebraic structures, universal logic is a general theory of logical structures. During the 20th century, numerous logics have been created: intuitionistic logic, deontic logic, many- valued logic, relevant logic, linear logic, non monotonic logic, etc. Universal logic is not a new logic, it is a way of unifying this multiplic ity of logics by developing general tools and concepts that can be applied to all logics. One aim of universal logic is to determine the domain of valid ity of such and such metatheorem (e.g. the completeness theorem) and to give general formulations of metatheorems. This is very useful for appli cations and helps to make the distinction between what is really essential to a particular logic and what is not, and thus gives a better understanding of this particular logic. Universal logic can also be seen as a toolkit for producing a s pecific logic required for a given situation, e.g. a paraconsistent deontic temporal logic. This is the third edition of a world event dedicated to univer sal logic. This event is a combination of a school and a congress. The school offers 21 tutorials on a wide range of subjects. The congress will follow with invited talks and contributed talks organized in many sessions including 10 special sessions. There will also be a contest. This event is intended to be a major event in logic, providing a platform for future research guidelines. Such an event is of interest for all people dealing with logic in one way or another: pure logicians, mathematicians, computer scientists, AI researchers, linguists, psychologists, philosophers, etc
Some principles of demarcation of the bounds of logic as formal ontology are discussed. Although Tarski’s philosophical generalization of his permutation invariance criterion - our logic is logic of cardinality - appeared to be justified by the theory of monadic quantification (logic of properties of classes of individuals), it is not correct for the theory of binary quantification (logic of properties of classes of pairs of individuals). The point is that heterogeneous quantifier prefixes considered as binary quantifiers distinguish equicardinal relations. Thus not only cardinalities, but also patterns of ordering of the universe have to be taken into account by logic with binary quantifiers.