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

Changes in the nutrient content of agricultural soil on conversion to organic farming, in relation to farm level nutrient balances and soil contents of clay and organic matter.

Agricultural soil on 12 farms converting to organic farming was sampled in 1989 and 1995 at the same sample points. Concentrations of plant-available (-AL) P, K, Ca and Mg, HNO3-soluble K, tot- N, tot-C and pH were measured in two layers. The average K-AL concentration and pH were reduced in both layers. The average P-AL concentration was reduced in the topsoil. K-AL and P-AL increased in samples with low concentrations and decreased in samples with high and very high concentrations in 1989. The total N concentration increased in the subsoil. Tot-N and tot-C increased in top- and subsoil with a low organic matter content. The net import of P, calculated by farm level nutrient balances, was negatively correlated to the change in kg P-AL per hectare in the topsoil. No such correlation was found for K

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

Simplified Semantics for Further Relevant Logics I: Unreduced Semantics for E and Π′

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E the rule of restricted assertion or equivalently Ackermann’s δ-rule is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of the ternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction ◦ – as well as the converse conditional ←

Simplified Semantics for Further Relevant Logics II: Propositional Constants

It is shown how to model propositional constants within the simplified Routley-Meyer semantics. Various axioms and rules allowing the definition of modal operators, implicative negations, enthymematical conditionals, and propositions expressing various infinite conjunctions and disjunctions are set forth and shown to correspond to specific frame conditions. Two propositional constants which are both often designated as “the Ackermann constant” are shown to capture two such “infinite” propositions: The conjunction of every logical law and the conjunction of every truth –what Anderson and Belnap called the “world” constant.publishedVersio

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