On se propose de donner une interprétation algébrique (en calcul des propositions classiques) des notions d'arbres, d'ensembles de Hintikka, de la méthode des tableaux de Beth-Hintikka Smullyan.
We set up axioms characterizing logical connective implication in a logic derived by an ortholattice. It is a natural generalization of an orthoimplication algebra given by J. C. Abbott for a logic derived by an orthomodular lattice.
Effect algebras are very natural logical structures as carriers of probabilities and states. They were introduced for modeling of sets of propositions, properties, questions, or events with fuzziness, uncertainty or unsharpness. Nevertheless, there are effect algebras without any state, and questions about the existence (for non-modular) are still unanswered. We show that every Archimedean atomic lattice effect algebra with at most five blocks (maximal MV-subalgebras) has at least one state, which...
In this paper we study the prime and maximal spectra of a BL-algebra, proving that the prime spectrum is a compact T 0 topological space and that the maximal spectrum is a compact Hausdorff topological space. We also define and study the reticulation of a BL-algebra.
We prove that a certain identity introduced by R. Halaš for classifying basic algebras can be used for characterizing orthomodular lattices in the class of ortholattices with antitone involutions on every principal filter.
In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
Nelson algebras were first studied by Rasiowa and Białynicki- Birula [1] under the name N-lattices or quasi-pseudo-Boolean algebras. Later, in investigations by Monteiro and Brignole [3, 4], and [2] the name “Nelson algebras” was adopted - which is now commonly used to show the correspondence with Nelson’s paper [14] on constructive logic with strong negation. By a Nelson algebra we mean an abstract algebra 〈L, T, -, ¬, →, ⇒, ⊔, ⊓〉 where L is the carrier, − is a quasi-complementation (Rasiowa used...