Minimal Varieties of Involutive Residuated Lattices

We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices. The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated lattice. Dedicated to the memory of Willem Johannes Blok     

Constructive Logic with Strong Negation is a Substructural Logic. I

The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL _ew of the substructural logic FL _ew . In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL _ew (namely, a certain variety of FL _ew -algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated theorem-prover Prover9 in order to establish the result. The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL _ew are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL _ew . Presented by Heinrich Wansing     

Adding Involution to Residuated Structures

Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x ²x but fails to preserve the contraction property xx ². The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) is decidable, settling a question implicitly posed by P. Jipsen and C. Tsinakis. The corresponding logical result is the (theorem-) decidability of the negation-free axioms and rules of the logic RW, formulated with fusion and the Ackermann constant t. This completes a result of S. Giambrone whose proof relied on the absence of t.     

On Some Categories of Involutive Centered Residuated Lattices

Motivated by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras we define the functor K ^• relating integral residuated lattices with 0 (IRL₀) with certain involutive residuated lattices. Our work is also based on the results obtained by Cignoli about an adjunction between Heyting and Nelson algebras, which is an enrichment of the basic adjunction between lattices and Kleene algebras. The lifting of the functor to the category of residuated lattices leads us to study other adjunctions and equivalences. For example, we treat the functor C whose domain is cuRL, the category of involutive residuated lattices M whose unit is fixed by the involution and has a Boolean complement c (the underlying set of C M is the set of elements greater or equal than c). If we restrict to the full subcategory NRL of cuRL of those objects that have a nilpotent c, then C is an equivalence. In fact, C M is isomorphic to C _e M, and C _e is adjoint to , where assigns to an object A of IRL₀ the product A × A ⁰ which is an object of NRL.     

Closure Operators and Complete Embeddings of Residuated Lattices

In this paper, a theorem on the existence of complete embedding of partially ordered monoids into complete residuated lattices is shown. From this, many interesting results on residuated lattices and substructural logics follow, including various types of completeness theorems of substructural logics.     

Products of Classes of Residuated Structures

The central result of this paper provides a simple equational basis for the join, IRLLG, of the variety LG of lattice-ordered groups (-groups) and the variety IRL of integral residuated lattices. It follows from known facts in universal algebra that IRLLG=IRL×LG. In the process of deriving our result, we will obtain simple axiomatic bases for other products of classes of residuated structures, including the class IRL×_s LG, consisting of all semi-direct products of members of IRL by members of LG. We conclude the paper by presenting a general method for constructing such semi-direct products, including wreath products.     

On Varieties of Biresiduation Algebras

A biresiduation algebra is a 〈/,\,1〉-subreduct of an integral residuated lattice. These algebras arise as algebraic models of the implicational fragment of the Full Lambek Calculus with weakening. We axiomatize the quasi-variety B of biresiduation algebras using a construction for integral residuated lattices. We define a filter of a biresiduation algebra and show that the lattice of filters is isomorphic to the lattice of B-congruences and that these lattices are distributive. We give a finite basis of terms for generating filters and use this to characterize the subvarieties of B with EDPC and also the discriminator varieties. A variety generated by a finite biresiduation algebra is shown to be a subvariety of B. The lattice of subvarieties of B is investigated; we show that there are precisely three finitely generated covers of the atom. Mathematics Subject Classification (2000): 03G25, 06F35, 06B10, 06B20 Dedicated to the memory of Willem Johannes Blok     

-autonomous Lattices

-autonomous lattices are the algebraic exponentials and without additive constants. In this paper, we investigate the structure theory of this variety and some of its subvarieties, as well as its relationships with other classes of algebras.     

Marriage,Morality, and Institutional Value

This paper develops a Kantian account of the moral assessment of institutions. The problem I address is this: while a deontological theory may find that some legal institutions are required by justice, it is not obvious how such a theory can assess institutions not strictly required (or prohibited) by justice. As a starting-point, I consider intuitions that in some cases it is desirable to attribute non-consequentialist moral value to institutions not required by justice. I will argue that neither consequentialist nor virtue-ethical accounts account for these intuitions, suggesting that a distinctive deontological account is needed. The account I give is drawn from Kant’s Metaphysics of Morals; I distinguish it from Kantian views of institutions developed by Barbara Herman and Onora O’Neill. Throughout, I use marriage as an example.

Relations Among Milk and Non-Milk Beverage Consumption, Calcium, and Relative Weight in High-Weight Status Children

Relations among weight, calcium, and milk have received considerable attention, but inconsistencies remain regarding strength and direction of associations. Calcium, milk, other beverages, and weight status associations were examined among children >75th BMI percentile from three studies. Results indicated negative relations between z-BMI and non-whole milk and calcium in one sample, with lower z-BMI and percent body fat among older children drinking any non-whole milk. In one older child sample, z-BMI and percent body fat were higher for whole milk consumers. The only significant relation observed for other beverages was the negative association between juice and percent body fat in younger children. Milk, calcium, and child weight status associations are inconsistent, and appear dependent on milk type and child age.     

Pluralism,Postmodernism and Interreligious Dialogue

Interreligious dialogue does not take place in a vacuum, nor is it a matter of casual conversation. Dialogue is a contested phenomenon, advocated and embraced on one hand, eschewed and discarded on the other. By way of an exploration of the fact of plurality, the notions of modernism and postmodernism, and a brief discussion of select pertinent issues (unity, truth, and the very idea of theology), the paradigmatic context of pluralism will be critically discussed. Contemporary engagement in interreligious dialogue and interfaith relations requires to be underpinned by a carefully thought-out conceptualising of the context in which it can authentically occur. This paper seeks to contribute to the understanding of the context of and for interreligious dialogue.

Electrical conductivity of Nd and Ce co-doped Gd2Zr2O7 ceramics

In this study, (Gd_{1? x} Nd _x )₂(Zr_{1? x} Ce _x )₂O₇ (0 ≤ x ≤ 0.5) ceramics have been prepared by pressureless sintering at 1973 K to investigate the influence of Nd and Ce co-doping on their electrical conductivity. The electrical conductivity of the ceramics was investigated by impedance spectroscopy measurements from 723 to 1173 K over the frequency range of 20 Hz to 2 MHz in air. The measured values obey the Arrhenius relation. For each composition, the grain conductivity gradually increases with increasing temperature from 723 to 1173 K. At a given temperature, it gradually decreases with increasing neodymium and cerium contents from x = 0 to 0.3; thereafter, the grain conductivity exhibits a slight increase with further increasing neodymium and cerium contents up to x = 0.5.     

Compatibilism,Evil, and the Free-Will Defense

It is widely believed that (1) if theological determinism were true, in virtue of God’s role in determining created agents to perform evil actions, created agents would be neither free nor morally responsible for their evil actions and God would not be perfectly good; (2) if metaphysical compatibilism were true, the free-will defense against the deductive problem of evil would fail; and (3) on the assumption of metaphysical compatibilism, God could have actualized just any one of those myriad possible worlds that are populated only by compatibilist free creatures. The primary thesis of this essay is that none of these propositions is true. This thesis is defended by appealing to a recently proposed novel, acausal, composite, unified theory of free action – the Theory of Middle Freedom – that evades the central problems plaguing traditional theories of metaphysical compatibilism.

Supernatural Miracles and Religious Inclusiveness

In this paper I shall assess Clarke’s assertion that all definitions of miracles that purport to satisfy the criterion of religious inclusiveness should substitute the term ‘supernatural’ for ‘non-natural’. In addition, I shall attempt to strengthen Clarke’s conception of the supernatural by offering an analysis of what it means for something to be ‘above’ nature. Lastly, I shall offer a new argument as to why Clarke’s intention-based definition of miracles is necessarily less religiously inclusive than Mumford’s causation-based definition.

The Method of Socratic Proofs for Modal Propositional Logics: K5, S4.2, S4.3, S4F,S4R,S4M and G

The aim of this paper is to present the method of Socratic proofs for seven modal propositional logics: K5, S4.2, S4.3, S4M, S4F, S4R and G. This work is an extension of [10] where the method was presented for the most common modal propositional logics: K, D, T, KB, K4, S4 and S5. Presented by Jacek Malinowski     

Phonon densities of states of gamma-cerium and delta-cerium measured by time-of-flight inelastic neutron scattering

Time-of-flight inelastic neutron scattering spectra were measured on cerium metal at temperatures near the fcc (gamma)-to-bcc (delta) transition temperature. Phonon density-of-states (DOS) curves were extracted from data acquired over a wide range of momentum transfers. A large softening of the phonon DOS was found in going from gamma-cerium to delta-cerium, and this accounts for an increase in vibrational entropy of (0.71 +/- 0.05)k _B/atom. To be consistent with the latent heat of the gamma-delta transition, this increase in vibrational entropy must be accompanied by a large decrease in electronic entropy. The results not only confirm the recent discovery of a significant electronic contribution to the gamma-delta transition but also suggest that it may be twice that previously reported.     

Atomic geometry and energetics of carbon nanotube necking

Molecular mechanics simulations were performed to probe the incipient plastic deformation in carbon nanotubes (CNTs), which involves nucleation of Stone–Wales (SW) defects and spiral glide of 5/7 dislocation dipoles that lead to quantized necking through a stepwise reduction in tube diameter. Quantification of the strain-dependent energetics of dislocation glide reveals that such dislocation motions are energetically favoured at high tensile strain. Pre-existing dislocations critically affect subsequent nucleation and separation of SW defects, as manifested by the competing deformation modes of symmetric versus asymmetric necking. The results provide a quantitative basis for the dislocation dynamics simulations of superplastically deformed CNTs.     

Intentionalism and Change Blindness

According to reductive intentionalism, the phenomenal character of a conscious experience is constituted by the experience's intentional (or representational) content. In this article I attempt to show that a phenomenon in visual perception called change blindness poses a problem for this doctrine. Specifically, I argue that phenomenal character is not sensitive, as it should be if reductive intentionalism is correct, to fine-grained variations in content. The standard anti-intentionalist strategy is to adduce putative cases in which phenomenal character varies despite sameness of content. This paper explores an alternative antiintentionalist tack, arguing, by way of a specific example involving change blindness, that content can vary despite sameness of phenomenal character.

Theoretical explanation for Raman and ESR spectra of V3+ ions in salt guanidinium vanadium sulfate hexahydrate

The Raman spectra and electronic spin resonance (ESR) parameters (spin-Hamiltonian parameter g factors, zero-field splitting parameter D, and hyperfine structure constant A) for the trigonal V³⁺ centers in salt guanidinium vanadium sulfate hexahydrate (GVSH) are calculated from the complete diagonalization (of energy matrix) method. The theoretical results are in agreement with the experimental findings and the trigonal crystal-field parameters are determined. The difficulty in explaining ESR parameters of V³⁺ in GVSH is removed.