The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Finally, (...) we investigate the relationship between unsharp orthoalgebras, generalized MV algebras, and orthomodular lattices. (shrink)
Fuzzy intuitionistic quantum logics (called also Brouwer-Zadeh logics) represent to non standard version of quantum logic where the connective not is split into two different negation: a fuzzy-like negation that gives rise to a paraconsistent behavior and an intuitionistic-like negation. A completeness theorem for a particular form of Brouwer-Zadeh logic (BZL 3) is proved. A phisical interpretation of these logics can be constructed in the framework of the unsharp approach to quantum theory.
The term “law” appears in different contexts with different meanings. We are used to speaking of natural laws, legal laws, moral laws, aesthetic laws, historical laws. Such a linguistic convention has represented a constant phenomenon through the history of civilization. Is there any deep common root among all these different uses and meanings?
Medium- and high-spin states of Pr-134 were populated using the Cd-116(Na-23, 5n) reaction and studied with the GAMMASPHERE spectrometer. Several new bands have been found in this nucleus, one of them being linked to the previously observed chiral-candidate twin-band structure. The ground state of Pr-134 could be determined through establishing a level structure that connects the two previously known long-lived isomeric states. Unambiguous spin-parity assignments for the excited states could be performed based on the known 2(-) spin-parity of the ground (...) state combined with the present experimental data. Intrinsic single-particle configurations have been assigned to the newly observed bands on the basis of the measured B(M1)/B(E2) ratios, alignments, band-crossing frequencies, bandhead spins, the observed single-particle configurations in the neighboring nuclei, and taking into account the predictions of total Routhian surface and tilted-axis cranking calculations. (shrink)
In 1920 Łukasiewicz published a two-page article whose title was “On Three-valued Logic”. The paper proposes a semantic characterization for the logic that has been later called Ł3 . In spite of the shortness of the paper, all the important points concerning the semantics of Ł3 are already there and can be naturally generalized to the case of a generic number n of truth-values . The conclusion of the article is quite interesting:The present author is of the opinion that three-valued (...) logic has above all theoretical importance as an endeavour to construct a system of non-aristotelian logic. Whether the new system of logic has any practical importance will be seen only when the logical phenomena, especially those in the deductive sciences, are thoroughly examined, and when the consequences of the indeterministic philosophy, which is the metaphysical substratum of the new logic, can be compared with empirical data. (shrink)
High-spin states have been studied in Pr-135(59), populated through the Cd-116(Na-23,4n) reaction at 115 MeV, using the Gammasphere gamma-ray spectrometer. The negative-parity yrast band has been significantly extended to spin similar to 45 (h) over bar and excitation energy 21.5 MeV, showing evidence for several rotational alignments. The positive-parity yrast band of Ce-135(58), populated through the p4n channel of this reaction, was also populated to spin similar to 38 (h) over bar and excitation energy 18 MeV. Cranking calculations indicate that (...) these nuclei are soft with respect to the triaxiality parameter gamma and that several competing nuclear shapes occur at high spin. (shrink)
How does a Muslim jurist think the law and how, accordingly, he judges a fact? Using Alice in Wonderland as hermeneutical device to explore the logic of fiqh, this article identifies a divergence between Western and Islamic legal thinking in the application of abduction as key form of inference in the law of Islam. In particular, looking at the fact/law relation in symbolic terms, the article highlights how, while a dichotomy between fact and law characterizes Western legal thinking, fiqh upholds (...) a connection between the “real” and the “right”, where the effort in understanding sharī‘ah postulates the actualization of the “rule” in God’s creation. Thus, if sharī‘ahpre-scribes the Law, not only is the rule discovered through the sources, but the right has to be justified through a verdict de-scribing the fact, for the law to be validly stated for the given situation. In this sense, abduction as explanatory “hypothesis” and “inference to the best explanation” of sharī‘ah provides an account for the probabilistic nature of fiqh, its ramification through verdicts, as well as for the epistemic and narrative function of the tradition as core aspects of the logic of Islamic law. At the same time, doubts can be raised about the compatibility between this logic and the deductive logic of modern state law, as a sub-product of Western legal thinking. (shrink)
The debate about constructivism in physics has led to different kinds of questions that can be conventionally framed in two classes. One concerns the mathematics that is considered for the theoretical development of physics. The other is concerned with the experimental parts of physical theories. It is unnecessary to observe that the intersection between our two classes of problems is far from being empty. In this paper we will mainly deal with topics belonging to the second class. However, let us (...) briefly mention some important problems that have been debated in the framework of our first class. For instance, the following: to what extent do the undecidability and incompleteness results of classical mathematics affect fragments of physical theories, in such way as to have a “real physical meaning”? are the mathematical arguments that seem to be essential for physics justifiable in the framework of traditional mathematical constructivism?The first question has recently been investigated by Pitowski, Penrose, da Costa, Doria, Mundici, Svozil and others. As expected by most logicians, one can construct undecidable sentences whose physical meaning seems to be hardly questionable. This happens both in classical and in quantum mechanics. (shrink)