Publicado originalmente em 1974, este breve artigo de John Corcoran analisa algumas passagens da obra Jan Lukasiewicz dedicada à silogística Aristóteles, refutando a tese do lógico polonês que os silogismos aristotélicos seriam condicionais universalizados.

The paper deals with Lukasiewicz filters. It analyzes some of their possible constructions and their basic properties. The Cartesian product of Lukasiewicz filters is introduced.

The multi-valued logic of Lukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation elimination, [DNE]. However, our understanding of Lukasiewicz logic can be improved by separating its classical and intuitionistic aspects. The intuitionistic aspect of Lukasiewicz logic ...

In this paper we give a characterization of all the interpretations of the varieties of bounded distributive lattices, De Morgan algebras and Lukasiewicz algebras of order m in the variety of Lukasiewicz algebras of order n. In the case of distributive lattices we give a structure theorem that is generalized to De Morgan algebras and to Lukasiewicz algebras of order m. In the last two cases we ...

Moisil logic, having as algebraic counterpart Lukasiewicz-Moisil algebras, provides an alternative way to reason about vague information based on the following principle: a many-valued event is characterized by a family of Boolean events. However, using the original definition of Lukasiewicz-Moisil algebra, the principle does not apply for subalgebras. In this paper we identify an alternative a...

We investigate admissible rules of Lukasiewicz multi-valued propositional logic. We show that admissibility of multiple-conclusion rules in Lukasiewicz logic, as well as validity of universal sentences in free MV -algebras, is decidable (in PSPACE ).

In the framework of propositional Lukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly defining each of the rational elements in the standard semantics are explored, and based on that, a faithful interpretation of theories in Rational Pavelka logic ...