This article investigates the weak distributivity of Boolean ó-algebras satisfying the countable chain condition. It addresses primarily the question when such algebras carry a ó-additive measure. We use as a starting point the problem of John von Neumann stated in 1937 in the Scottish Book. He asked if the countable chain condition and weak distributivity are sufficient for the existence of su...

We characterize those formulas of MSO monadic second order logic that are safe for bisim ulation formulas de ning binary relations such that any bisimulation is also a bisimulation with respect to these de ned relations Every such formula is equivalent to one constructed from calculus tests atomic actions and the regular operations The proof uses a characterization of completely additive calcul...

A repeated bijection in an isotopism of quasigroups is called a companion of the third component. The last is called a pseudoisomorphism with the companion. Isotopy coincides with pseudoisomorphy∗ in the class of inverse property loops and with isomorphy in the class of commutative inverse property loops. This result is a generalization of the corresponding theorem for commutative Moufang loops...

Binary and unary operation preserving binary relations and quotients of those operations modulo equivalence relations are introduced. It is shown that the quotients inherit some important properties (commutativity, associativity, distributivity, ect.). Based on it the quotient (also called factor) lattice modulo filter (ie. modulo the equivalence relation w.r.t the filter) is introduced. Simila...

Symmetric generalized Galois logics (i.e., symmetric gGls) are distributive gGls that include weak distributivity laws between some operations such as fusion and fission. Motivations for considering distribution between such operations include the provability of cut for binary consequence relations, abstract algebraic considerations and modeling linguistic phenomena in categorial grammars. We r...

The Lambek-Grishin calculus is a symmetric extension of the Lambek calculus: in addition to the residuated family of product, left and right division operations of Lambek's original calculus, one also considers a family of coproduct, right and left difference operations, related to the former by an arrow-reversing duality. Communication between the two families is implemented in terms of linear...

We introduce a controlled form of recursion in XQuery, inflationary fixed points, familiar in the context of relational databases. This imposes restrictions on the expressible types of recursion, but we show that inflationary fixed points nevertheless are sufficiently versatile to capture a wide range of interesting use cases, including the semantics of Regular XPath and its core transitive clo...

This paper discusses various reciprocalization strategies in Turkish, including lexical, pronominal, and verbal reciprocals, as well the collective discontinuous constructions that appear with symmetric predicates. We propose there are two distinct sources of reciprocity Turkish: symmetry distributivity–reciprocity. Lexical reciprocals established via symmetry, whereas pronominal formed distrib...