Knjiga apstrakata - Mathematical Institute of the Serbian Academy of ...

On Archimedean inference ruleAleksandar PerovićFaculty of transportation and traffic engineeringUniversity of Belgrade,pera@sf.bg.ac.rsThe Archimedean inference rule is an infinitary inference rule designed to overcome the compactness issue in non restrictedreal valued probability logics. The key reason behind incompleteness lies in possibility to construct finitely satisfiabletheories that express something like “the probability of α is infinitely close but different from s”, where s is some rationalnumber from the real unit interval [0, 1]. Since 〈R, 〉 omits the type of the infinitely small element, any such theory isunsatisfiable - hence we get both incompleteness and non-compactness.Intuitively, the Archimedean rule works as follows: if probability of α is infinitely close to a, than it must be equal to a.The exact formulation will be presented at the talk. I will also discuss the application of Archimedean-like inference rulesin real valued formalization of other types of many valued logics such as possibility and fuzzy logic.32