On Categorical Equivalences of Commutative BCK-algebras

A commutative BCK-algebra with the relative cancellation property is a commutative BCK-algebra (X;*,0) which satisfies the condition: if a ≤ x, a ≤ y and x * a = y * a, then x = y. Such BCK-algebras form a variety, and the category of these BCK-algebras is categorically equivalent to the category of Abelian ℓ-groups whose objects are pairs (G, G ₀), where G is an Abelian ℓ-group, G ₀ is a subset of the positive cone generating G ⁺ such that if u, v ∈ G ₀, then 0 ∨ (u - v) ∈ G ₀, and morphisms are ℓ-group homomorphisms h: (G, G ₀) → (G′,G′₀) with f(G ₀) ⫅ G′₀. Our methods in particular cases give known categorical equivalences of Cornish for conical BCK-algebras and of Mundici for bounded commutative BCK-algebras (= MV-algebras). This revised version was published online in June 2006 with corrections to the Cover Date.     

The Classification of Propositional Calculi

We discuss Smirnovs problem of finding a common background for classifying implicational logics. We formulate and solve the problem of extending, in an appropriate way, an implicational fragment H of the intuitionistic propositional logic to an implicational fragment TV of the classical propositional logic. As a result we obtain logical constructions having the form of Boolean lattices whose elements are implicational logics. In this way, whole classes of new logics can be obtained. We also consider the transition from implicational logics to full logics. On the base of the lattices constructed, we formulate the main classification principles for propositional logics.     

Die Rechtsansichten der Eurasier -- Rechtsordnung oder Wertordnung?

In their juridical doctrines, the members of the Evrazijstvo movement advocated the idea of a Russian special path criticizing at the same time the formalism and coldness of the western conception of law, based principally on Roman law. Their views are characterized by an evident priority accorded to justice over law, to the order of values over legal order.     

Preembryo Personhood: An Assessment of the President’s Council Arguments

The President’s Council on Bioethics has addressed the moral status of human preembryos in its reports on stem cell research and human therapeutic cloning. Although the Council has been criticized for being hand-picked to favor the right-to-life viewpoint concerning human preembryos, it has embraced the idea that the right-to-life position should be defended in secular terms. This is an important feature of the Council’s work, and it demonstrates a recognition of the need for genuine engagement between opposing sides in the debate over stem cell research. To promote this engagement, the Council has stated in secular terms several arguments for the personhood of human preembryos. This essay presents and critiques those arguments, and it concludes that they are unsuccessful. If the best arguments in support of the personhood of human preembryos have been presented by the Council, then there are no reasonable secular arguments in support of that view.     

On Finite Models of the Lambek Calculus

We study a class of finite models for the Lambek Calculus with additive conjunction and with and without empty antecedents. The class of models enables us to prove the finite model property for each of the above systems, and for some axiomatic extensions of them. This work strengthens the results of [3] where only product-free fragments of these systems are considered. A characteristic feature of this approach is that we do not rely on cut elimination in opposition to e.g. [5], [9].     

Algebraic Kripke Sheaf Semantics for Non-Classical Predicate Logics

In so-called Kripke-type models, each sentence is assigned either to true or to false at each possible world. In this setting, every possible world has the two-valued Boolean algebra as the set of truth values. Instead, we take a collection of algebras each of which is attached to a world as the set of truth values at the world, and obtain an extended semantics based on the traditional Kripke-type semantics, which we call here the algebraic Kripke semantics. We introduce algebraic Kripke sheaf semantics for super-intuitionistic and modal predicate logics, and discuss some basic properties. We can state the Gödel-McKinsey-Tarski translation theorem within this semantics. Further, we show new results on super-intuitionistic predicate logics. We prove that there exists a continuum of super-intuitionistic predicate logics each of which has both of the disjunction and existence properties and moreover the same propositional fragment as the intuitionistic logic.     

The authorship list in science: Junior physicists’ perceptions of who appears and why

A questionnaire probing the distribution of authorship credit was given to postdoctoral associates (“postdocs”) in order to determine their awareness of the professional society’s ethical statement on authorship, the extent of communication with their supervisors about authorship criteria, and the appropriateness of authorship assignments on submitted papers. Results indicate a low awareness of the professional society’s ethical statement and that little communication takes place between postdocs and supervisors about authorship criteria. A substantial amount of authorship credit given to supervisors and other workers is perceived by the postdocs to violate the professional society’s ethical statement.