An algebra A is said to be congruence coherent if every subalgebra of A that contains a class of some congruence θ on A is a union of θ-classes. This property has been investigated in several varieties of lattice-based algebras. These include, for example, de Morgan algebras, p-algebras, double p-algebras, and double MS-algebras. Here we determine precisely when the property holds in the class ...

A simplified proof of Thorp and Walden’s fundamental theorem of card counting is presented, and a corresponding central limit theorem is established. Results are applied to the casino game of trente et quarante, a game studied by Poisson and De Morgan.

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 ...

Different languages that are offered to model vague preferences are reviewed and an interval-valued language is proposed to resolve a particular difficulty encountered with other languages. It is shown that interval-valued languagesare well definedfor De Morgan triples constructedby continuoustriangular norms, conorms and a strong negation function. A new transitivity condition for vague prefer...

Logical connectives on fuzzy sets arise from those on the unit interval. The basic theory of these connectives is cast in an algebraic spirit with an emphasis on equivalence between the various systems that arise. Special attention is given to De Morgan systems with strict Archimedean t-norms and strong negations. A typical result is that any De Morgan system with strict t-norm and strong negat...

Resume One of the characteristics of Indigenous writing around the world may be the use of oral features as deliberate techniques in literary production. The author considers the work of Patricia Grace (of New Zealand), Sally Morgan (Australia) and Marie Annharte Baker (from Canada) in these terms. Une des caractéristiques des oeuvres indigènes autour du monde peut être l'usage des traits oraux...

In the context of natural deduction for propositional classical logic, with classicality given by the inference rule reductio ad absurdum, we investigate the De Morgan translation of disjunction in terms of negation and conjunction. Once the translation is extended to proofs, it obtains a reduction of provability to provability in the disjunction-free subsystem. It is natural to ask whether a r...