Partial Boolean algebras in a broader sense and Boolean embeddings
Partially additive states on orthomodular posets
We fix a Boolean subalgebra B of an orthomodular poset P and study the mappings s:P → [0,1] which respect the ordering and the orthocomplementation in P and which are additive on B. We call such functions B-states on P. We first show that every P possesses "enough" two-valued B-states. This improves the main result in [13], where B is the centre of P. Moreover, it allows us to construct a closure-space representation of orthomodular lattices. We do this in the third section. This result may also...
Perspectivity and congruence in partial abelian semigroups
Polarity compatible with a closure system
Polarized category theory, modules, and game semantics.
Polyadic algebras over nonclassical logics
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 Łukasiewicz, modal logics that admit the rule of necessitation, BCK logic, etc.
Poset-valued preference relations
In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives...
Pre-adjunctions and lambda-algebraic theories
Preboolean MV-algebras as bipartite MV-algebras.
In this note we characterize bipartite MV-algebras by introducing the notion of preboolean MV-algebras.
Precomplete classes of operations on an uncountable set
Predicates and measures on Boolean σ-algebras
Predicative algebraic set theory.
Preface to the special volume: “Chu spaces: theory and applications".
Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras
In this work we give a duality for many classes of lattice ordered algebras, as Integral Commutative Distributive Residuated Lattices MTL-algebras, IMTL-algebras and MV-algebras (see page 604). These dualities are obtained by restricting the duality given by the second author for DLFI-algebras by means of Priestley spaces with ternary relations (see [2]). We translate the equations that define some known subvarieties of DLFI-algebras to relational conditions in the associated DLFI-space.
Prime ideal theorem for double Boolean algebras
Double Boolean algebras are algebras (D,⊓,⊔,⊲,⊳,⊥,⊤) of type (2,2,1,1,0,0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under ⊓ (resp. ⊔). A filter F is called primary if F ≠ ∅ and for all x ∈ D we have x ∈ F or . In this note we prove that if F is a filter and I an ideal such that F ∩ I = ∅ then there is a primary filter G containing F such that G...
Prime ideals yield almost maximal ideals
Problems in Boolean algebras
Projection postulate and superposition principle in non-lattice quantum logics
Proof theory for full intuitionistic linear logic, bilinear logic, and MIX categories.
Propositional dynamic logic with recursive programs