Les algèbres de Heyting-Brouwer : point de rencontre de plusieurs structures
Löb operators and interior operators
Logical Aggregation Based on Interpolative Boolean Algebra.
Logique, catégories et faisceaux
Lògiques distributives i booleanes.
Continuing the study of different types of Abstract Logics [5], and following works by Brown-Bloom [1] and Brown-Suszko [2], we analyze in this paper some logics in which, if we identify equivalent formulae by means of the consequence operator, we obtain distributive lattices or Boolean algebras.
Many-sorted coalgebraic modal logic : a model-theoretic study
This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...
Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study
This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...
Matrix representation of homomorphic mappings of finite Boolean algebras
Modus ponens on Boolean algebras revisited.
In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.
Monadic epimorphisms and applications
Note über den Operationskreis des Logikcalculs
Observation Space And Observables In Classical Mechanics
Observation space and observables in classical mechanics.
On a characterization of probability measures on Boolean algebras and some orthomodular lattices
On A Class Of Sentential Functions
On a class of sentential functions.
On automorphism groups of boolean algebras
On Boolean modus ponens.
An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].
On BPI Restricted to Boolean Algebras of Size Continuum
(i) The statement P(ω) = “every partition of ℝ has size ≤ |ℝ|” is equivalent to the proposition R(ω) = “for every subspace Y of the Tychonoff product the restriction |Y = Y ∩ B: B ∈ of the standard clopen base of to Y has size ≤ |(ω)|”. (ii) In ZF, P(ω) does not imply “every partition of (ω) has a choice set”. (iii) Under P(ω) the following two statements are equivalent: (a) For every Boolean algebra of size ≤ |ℝ| every filter can be extended to an ultrafilter. (b) Every Boolean algebra of...
On collections of almost disjoint families