Concentrations of soil potassium after long-term organic dairy production

On five long-term organic dairy farms aiming at self-sufficiency with nutrients, soil concentrations of ammonium-acetate lactate extractable potassium (K-AL) and acid-soluble K was measured twice in topsoil (0-20 cm) and subsoil (20-40 cm) over periods of 6-14 years. Organic management had occurred for >9 years at the second sampling. On average there were most probably field level K-deficits. Even so, topsoil K-AL concentrations were medium high (65-155 mg K kg–1 soil), and did not decrease during the study period. However, for three farms, topsoil K-AL was approaching a minimum level determined by soil texture, where further decrease is slow. Subsoil K-AL concentrations were generally low (<65). The soils were mostly light-textured, and reserves of K-releasing soil minerals (illite) were low, never exceeding 6% of the mineral particles <2 mm diameter. Topsoil acid-soluble K concentrations were low (<300 mg K kg–1 soil) on two farms, medium (300–800) on three farms and decreased significantly on one farm. Cation-exchange capacity increased on two farms. This may indicate increased amount of expanded clay minerals caused by K-depletion. On self-sufficient organic dairy farms, purchased nutrients will be required by low soil nutrient reserves to avoid seriously decreased yields and quality of crops

Skolem Functions in Non-Classical Logics

This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A(x,y) determines the extension of a function and f is a Skolem function for A

Relevance through topical unconnectedness: Ackermann and Plumwood’s motivational ideas on entailment

Ackermann’s motivational spin on his theory of rigorous implication is analyzed and it is shown to contain en equivalent idea to Plumwood’s notion of suppression freedom. The formal properties these ideas back turn out to be properly weaker than Belnap’s variable sharing property, but it is shown that they can be strengthen in various ways. Some such strengthenings, it is shown, yield properties which are equivalent to Belnap’s, and thus provide for new ways of motivating Belnap’s fundamental relevance principle

Farewell to Suppression-Freedom

Val Plumwood and Richard Sylvan argued from their joint paper The Semantics of First Degree Entailment (Routley and Routley in Noûs 6(4):335–359, 1972, https://doi.org/10.2307/2214309) and onward that the variable sharing property is but a mere consequence of a good entailment relation, indeed they viewed it as a mere negative test of adequacy of such a relation, the property itself being a rather philosophically barren concept. Such a relation is rather to be analyzed as a sufficiency relation free of any form of premise suppression. Suppression of premises, therefore, gained center stage. Despite this, however, no serious attempt was ever made at analyzing the concept. This paper shows that their suggestions for how to understand it, either as the Anti-Suppression Principle or as the Joint Force Principle, turn out to yield properties strictly weaker than that of variable sharing. A suggestion for how to understand some of their use of the notion of suppression which clearly is not in line with these two mentioned principles is given, and their arguments to the effect that the Anderson and Belnap logics T, E and R are suppressive are shown to be both technically and philosophically wanting. Suppression-freedom, it is argued, cannot do the job Plumwood and Sylvan intended it to do.publishedVersio

Confused Entailment

Under embargo until: 2022-09-22Priest argued in his paper Fusion and Confusion (Priest, 2015a) for a new concept of logical consequence over the relevant logic B, one where premises my be “confused” together. This paper develops Priest’s idea. Whereas Priest uses a substructural proof calculus, this paper provides a Hilbert proof calculus for it. Using this it is shown that Priest’s consequence relation is weaker than the standard Hilbert consequence relation for B, but strictly stronger than Anderson and Belnap’s original relevant notion of consequence. Unlike the latter, however, Priest’s consequence relation does not satisfy a variant of the variable sharing property. This paper shows that how it can be modified so as to do so. Priest’s consequence relation turns out to be surprisingly weak in some respects. The prospects of strengthening it is raised and discussed in a broader philosophical context.acceptedVersio

Non-Boolean classical relevant logics I

Under embargo until: 2020-12-13Relevant logics have traditionally been viewed as paraconsistent. This paper shows that this view of relevant logics is wrong. It does so by showing forth a logic which extends classical logic, yet satisfies the Entailment Theorem as well as the variable sharing property. In addition it has the same S4-type modal feature as the original relevant logic E as well as the same enthymematical deduction theorem. The variable sharing property was only ever regarded as a necessary property for a logic to have in order for it to not validate the so-called paradoxes of implication. The Entailment Theorem on the other hand was regarded as both necessary and sufficient. This paper shows that the latter theorem also holds for classical logic, and so cannot be regarded as a sufficient property for blocking the paradoxes. The concept of suppression is taken up, but shown to be properly weaker than that of variable sharing.acceptedVersio

From Hilbert proofs to consecutions and back

Restall set forth a "consecution" calculus in his An Introduction to Substructural Logics. This is a natural deduction type sequent calculus where the structural rules play an important role.&nbsp; This paper looks at different ways of extending Restall's calculus. It is shown that Restall's weak soundness and completeness result with regards to a Hilbert calculus can be extended to a strong one so as to encompass what Restall calls proofs from assumptions. It is also shown how to extend the calculus so as to validate the metainferential rule of reasoning by cases, as well as certain theory-dependent rules

Boolean negation and non-conservativity I: Relevant modal logics

Under embargo until: 2021-07-15Many relevant logics are conservatively extended by Boolean negation. Not all, however. This paper shows an acute form of non-conservativeness, namely that the Boolean-free fragment of the Boolean extension of a relevant logic need not always satisfy the variable-sharing property. In fact, it is shown that such an extension can in fact yield classical logic. For a vast range of relevant logic, however, it is shown that the variable-sharing property, restricted to the Boolean-free fragment, still holds for the Boolean extended logic.acceptedVersio