We introduce a framework within which reasoning according to à Lukasiewicz logic can be represented. We consider a separable Boolean algebra B endowed with a (certain type of) group G of automorphisms; the pair (B, G) will be called a Boolean ambiguity algebra. B is meant to model a system of crisp properties; G is meant to express uncertainty about these properties. We define fuzzy proposition...

Prolog is a programming language based on a restricted subset of classical rst order predicate logic. In order to overcome some problems of classical logic to handle imperfect human knowledge, we provide a formal framework for a Lukasiewicz logic based Prolog system. The use of Lukasiewicz logic with its connection to Ulam games enables us to deal with partial inconsistencies by interpreting th...

We explore different ways to generalize Hintikka’s classic game theoretic semantic to a many-valued setting, where the unit interval is taken as the set of truth values. In this manner a plethora of characterizations of Lukasiewicz logic arise. Among the described semantic games is Giles’s dialogue and betting game, presented in a manner that makes the relation to Hintikka’s game more transpare...

A fuzzy control system based on a new method called maximal fuzzy similarity in fact the equivalence relation of Lukasiewicz logic is introduced to control an isolated pedestrian crossing signals The main goal in this multi objective optimization problem is to minimize both pedestrians and vehi cles delay and make the tra c ow as u ent and safe as possible Lukasiewicz many valued logic in known...

In his foundation of probability theory, Bruno de Finetti devised a betting scheme where a bookmaker offers bets on the outcome of events φ occurring in the future. He introduced a criterion for coherent bookmaking, and showed that coherent betting odds are given by some probability distribution. While de Finetti dealt with yes-no events and boolean propositional logic, Mundici generalized the ...

We present some model theoretic results for Lukasiewicz predicate logic by using the methods of continuous model theory developed by Chang and Keisler. We prove compactness theorem with respect to the class of all structures taking values in the Lukasiewicz BL-algebra. We also prove some appropriate preservation theorems concerning universal and inductive theories. Finally, Skolemization and Mo...

In fuzzy logic in wider sense t norms got a prominent r ole in recent times In many valued logic the Lukasiewicz systems the G odel sytems and also the product logic are t norm based The present paper discusses the more general problem of the adequate axiomatizability for such t norm based logical systems in general survey ing results of the last years

The polyadic algebras that arise from the algebraization of the first-order extensions of a SIC are characterized and a representation theorem is proved. Standard implicational calculi (SIC)’s were considered by H. Rasiowa [19] and include classical and intuitionistic logic and their various weakenings and fragments, the many-valued logics of Post and Lukasiewicz, modal logics that admit the ru...

We explore some links between abstract argumentation, logic and kernels in digraphs. Viewing argumentation frameworks as propositional theories in graph normal form, we observe that the stable semantics for argumentation can be given equivalently in terms of satisfaction and logical consequence in classical logic. We go on to show that the complete semantics can be formulated using Lukasiewicz ...