ON CONTRA-CLASSICAL VARIANTS OF NELSON LOGIC N4 AND ITS CLASSICAL EXTENSION

In two recent articles, Norihiro Kamide introduces unusual variants of Nelson’s paraconsistent logic and its classical extension. Kamide’s systems, IP and CP, are unusual insofar as double negations in these logics behave as intuitionistic and classical negations, respectively. In this article we present Hilbert-style axiomatizations of both IP and CP. The axiom system for IP is shown to be sound and complete with respect to a four-valued Kripke semantics, and the axiom system for CP is characterized by four-valued truth tables. Moreover, we note some properties of IP and CP, and emphasize that these logics are unusual also because they are contra-classical and inconsistent but nontrivial. We point out that Kamide’s approach exemplifies a general method for obtaining contra-classical logics, and we briefly speculate about a linguistic application of Kamide’s logics.

PENGARUH STRATEGI PENYULUHANDAN TINGKAT STATUS SOSIAL EKONOMITERHADAP PENGETAHUAN NELAYANTENTANG KOSERVASI PESISIR PANTAI (Sebuah Eksperimen di Kecamatan Telukbetung Barat, Kota Bandar Lampung)

This study aims to determine the effect of counseling strategies and levels of socio economic status of knowledge about the conservation of coastal fishermen. The method used in this study is an experiment with 2 x 2 factorial design. The study population was fishing in the District of West Telukbetung, Bandar Lampung numbered 32 people. Data analysis technique used is the Two-Way Analysis of Variance followed by Tukkey test. The findings of this study include: 1) Knowledge of the conservation of coastal areas that follow the strategy of grouping extension is higher than that following the classical extension strategy.; 2) For the fisherman with high level of social economic status with knowledge about coastal conservation among groups of fishermen who follow counseling strategies and follow the strategy of grouping classical education. Where the higher is the group of fishermen that high social economic status following the strategy of grouping extension; 3) For the fisherman with a low level of socio-economic status with knowledge about coastal conservation among groups of fishermen who follow the strategy of grouping extension and follow the classical extension strategy. Where the higher is the group of fishermen that low social economic status following the strategy of classical education, and 4) There is interaction effect between education strategy and the level of socio economic status of knowledge on coastal conservation. Based on these findings we can conclude that there is no extension strategies are most effective, depending on background characteristic fishermen and their socio economic status. Therefore, if the selected grouping strategy is appropriate only to fishermen who have a high socioeconomic status, education classical conversely, if the strategy is dominated by the lecture method is chosen, then it is just right for the fishermen who have low socioe conomic status.

THE RELEVANCE OF PREMISES TO CONCLUSIONS OF CORE PROOFS

The rules for Core Logic are stated, and various important results about the system are summarized. We describe its relationship to other systems, such as Classical Logic, Intuitionistic Logic, Minimal Logic, and the Anderson–Belnap relevance logic R. A precise, positive explication is offered of what it is for the premises of a proof to connect relevantly with its conclusion. This characterization exploits the notion of positive and negative occurrences of atoms in sentences. It is shown that all Core proofs are relevant in this precisely defined sense. We survey extant results about variable-sharing in rival systems of relevance logic, and find that the variable-sharing conditions established for them are weaker than the one established here for Core Logic (and for its classical extension). Proponents of other systems of relevance logic (such as R and its subsystems) are challenged to formulate a stronger variable-sharing condition, and to prove that R or any of its subsystems satisfies it, but that Core Logic does not. We give reasons for pessimism about the prospects for meeting this challenge.

Classical extension of quantum-correlated separable states

Li and Luo [Phys. Rev. A 78 (2008) 024303] discovered a remarkable relation between discord and entanglement. It establishes that all separable states can be obtained via reduction of a classically-correlated state "living" in a space of larger dimension. Starting from this result, we discuss here an optimal classical extension of separable states and explore this notion for low-dimensional systems. We find that the larger the dimension of the classical extension, the larger the discord in the original separable state. Further, we analyze separable states of maximum discord in ℂ2 ⊗ ℂ2 and their associated classical extensions showing that, from the reduction of a classical state in (ℂ2 ⊗ ℂ3) ⊗ ℂ2, one can obtain a separable state of maximum discord in ℂ2 ⊗ ℂ2.

Homogenization of a class of quasilinear elliptic equations with non-standard growth in high-contrast media

We study the asymptotic behaviour of solutions to a quasilinear equation with high-contrast coefficients. The energy formulation of the problem leads to work with variable exponent Lebesgue spaces Lpε (·) in a domain Ω with a complex microstructure depending on a small parameter ε. Assuming only that the functions pε converge uniformly to a limit function p0 and that p0 satisfy certain logarithmic uniform continuity conditions, we rigorously derive the corresponding homogenized problem which is completely described in terms of local energy characteristics of the original domain. In the framework of our method we do not have to specify the geometrical structure Ω. We illustrate our result with periodical examples, extending, in particular, the classical extension results to variable exponent Sobolev spaces.

Melanocortin Receptor 1 (MC1R) Mutations and Coat Color in Pigs

The melanocortin receptor 1 (MC1R) plays a central role in regulation of eumelanin (black/brown) and phaeomelanin (red/yellow) synthesis within the mammalian melanocyte and is encoded by the classical Extension (E) coat color locus. Sequence analysis of MC1R from seven porcine breeds revealed a total of four allelic variants corresponding to five different E alleles. The European wild boar possessed a unique MC1R allele that we believe is required for the expression of a wild-type coat color. Two different MC1R alleles were associated with the dominant black color in pigs. MC1R*2 was found in European Large Black and Chinese Meishan pigs and exhibited two missense mutations compared with the wild-type sequence. Comparative data strongly suggest that one of these, L99P, may form a constitutively active receptor. MC1R*3 was associated with the black color in the Hampshire breed and involved a single missense mutation D121N. This same MC1R variant was also associated with EP, which results in black spots on a white or red background. Two different missense mutations were identified in recessive red (e/e) animals. One of these, A240T, occurs at a highly conserved position, making it a strong candidate for disruption of receptor function.

Elementary intuitionistic theories

The present paper concerns itself primarily with the decision problem for formal elementary intuitionistic theories and the method is primarily model-theoretic. The chief tool is the Kripke model for which the reader may find sufficient background in Fitting's book Intuitionistic logic model theory and forcing (North-Holland, Amsterdam, 1969). Our notation is basically that of Fitting, the differences being to favor more standard notations in various places.The author owes a great debt to many people and would particularly like to thank S. Feferman, D. Gabbay, W. Howard, G. Kreisel, G. Mints, and R. Statman for their valuable assistance.The method of elimination of quantifiers, which has long since proven its use in classical logic, has also been applied to intuitionistic theories (i) to demonstrate decidability ([9], [15], [17]), (ii) to prove the coincidence of an intuitionistic theory with its classical extension ([9], [17]), and (iii), as we will see below, to establish relations between an intuitionistic theory and its classical extension. The most general of these results is to be obtained from the method of Lifshits' quantifier elimination for the intuitionistic theory of decidable equality.Since the details of Lifshits' proof have not been published, and since the proof yields a more general result than that stated in his abstract [15], we include the proof and several corollaries.