3,594 research outputs found
A generalization of analytic deduction via labelled deductive systems. Part 1: basic substructural logics
No full textIn this series of papers we set out to generalize the notion of classical analytic deduction (i.e., deduction via elimination rules) by combining the methodology of labelled deductive systems (LDS) with the classical systemKE. LDS is a unifying framework for the study of logics and of their interactions. In the LDS approach the basic units of logical derivation are not just formulae butlabelled formulae, where the labels belong to a given labelling algebra. The derivation rules act on the labels as well as on the formulae, according to certain fixed rules of propagation. By virtue of the extra power of the labelling algebras, standard (classical or intuitionistic) proof systems can be extended to cover a much wider territory without modifying their structure. The systemKE is a new tree method for classical analytic deduction based on analytic cut.KE is a refutation system, like analytic tableaux and resolution, but it is essentially more efficient than tableaux and, unlike resolution, does not require any reduction to normal form.
We start our investigation with the family of substructural logics. These are logical systems (such as Lambek''s calculus, Anderson and Belnap''s relevance logic, and Girard''s linear logic) which arise from disallowing some or all of the usual structural properties of the notion of logical consequence. This extension of traditional logic yields a subtle analysis of the logical operators which is more in tune with the needs of applications. In this paper we generalize the classicalKE system via the LDS methodology to provide a uniform refutation system for the family of substructural logics.
The main features of this generalized method are the following: (a) each logic in the family is associated with a labelling algebra; (b) the tree-expansion rules (for labelled formulae) are the same for all the logics in the family; (c) the difference between one logic and the other is captured by the conditions under which a branch is declared closed; (d) such conditions depend only on the labelling algebra associated with each logic; and (e) classical and intuitionistic negations are characterized uniformly, by means of the same tree-expansion rules, and their difference is reduced to a difference in the labelling algebra used in closing a branch. In this first part we lay the theoretical foundations of our method. In the second part we shall continue our investigation of substructural logics and discuss the algorithmic aspects of our approach
On constructive models of theories with linear Rudin-Keisler ordering
No full textIt is known that the class of Ehrenfeucht theories admits a syntactical characterization and that a finite (Rudin-Keisler) pre- ordering and a function mapping this pre-ordering to naturals play the role of parameters in this characterization. In the article, we construct for any finite linear ordering L, a hereditary decidable Ehrenfeucht theory T possessing L as its Rudin-Keisler pre-ordering. Also, we discuss decidable and computable models of such theories
Paraconsistent Logic
No full textB1 - Research Book ChaptersParaconsistent logics are those which permit inference from inconsistent information in a non-trivial fashion. Their articulation and investigation is a relatively recent phenomenon, even by the standards of modern logic. (For example, there was no article on them in the first edition of the Handbook.) The area has grown so rapidly, though, that a comprehensive survey is already impossible. The aim of this article is to spell out the basic ideas and some applications. Paraconsist logic has interest for philosophers, mathematicians and computer scientists. As befits the Handbook, I will concentrate on those aspects of the subject that are likely to be of more interest to philosopher-logicians. The subject also raises many important philosophical issues. However, here I shall tread over these very lightly—except in the last section, where I shall tread over them lightly
Paraconsistency and dialetheism
No full textB1 - Research Book ChaptersPublisher This chapter discusses paraconsistent logic, in which contradictions do not entail everything. However, the roots of paraconsistency lie deep in the history of logic, its modern developments date to just before the middle of the 20th century. Since then, the paraconsistent logic have been proposed and constructed for many and for different reasons. The most philosophically challenging of these reasons is dialetheism, the view that some contradictions are true. The chapter discusses the history of paraconsistency and the history of dialetheism. The chapter also discusses the modern developments of paraconsistency and dialetheism, those since about 1950. Some important issues that bear on paraconsistency, or on which paraconsistency bears the foundations of mathematics, the notion of negation, and rationality are discussed in the chapter
Relevant and substructural logics
No full textB1 - Research Book ChaptersPublisher This chapter discusses proof theory of relevant and substructural logics, and the model theory of these logics. The discipline of relevant logic grew out of an attempt to understand notions of consequence and conditionality where the conclusion of a valid argument is relevant to the premises, and where the consequent of a true conditional is relevant to the antecedent. The structural rules dictate admissible forms of transformations of premises contained in proofs. The chapter discusses how relevant logics are naturally counted as substructural logics, as certain commonly admitted structural rules are responsible for introducing irrelevant consequences into proofs
Entanglement and quantity in quantum space - About quantum measurement (II)
No full textAs a continuation and extension of "quantity in phase space" "quantity in quantum space" is introduced. With that, the disappearing of quantum interference discussed in a previous paper [S. Durr, et al., Nature 395 (1998) 33] is explained in the same spirit as our recent papers [Ren De-Ming, Commun. Theor. Phys. (Beijing, China) 41 (2004) 685, 833].Physics, MultidisciplinarySCI(E)中国科学引文数据库(CSCD)1ARTICLE133-364
Sneutrino DM in the NMSSM with inverse seesaw mechanism
No full textIn supersymmetric theories like the Next-to-Minimal Supersymmetric Standard Model (NMSSM), the lightest neutralino with bino or singlino as its dominant component is customarily taken as dark matter (DM) candidate. Since light Higgsinos favored by naturalness can strength the couplings of the DM and thus enhance the DM-nucleon scattering rate, the tension between naturalness and DM direct detection results becomes more and more acute with the improved experimental sensitivity. In this work, we extend the NMSSM by inverse seesaw mechanism to generate neutrino mass, and show that in certain parameter space the lightest sneutrino may act as a viable DM candidate, i.e. it can annihilate by multi-channels to get correct relic density and meanwhile satisfy all experimental constraints. The most striking feature of the extension is that the DM-nucleon scattering rate can be naturally below its current experimental bounds regardless of the higgsino mass, and hence it alleviates the tension between naturalness and DM experiments. Other interesting features include that the Higgs phenomenology becomes much richer than that of the original NMSSM due to the relaxed constraints from DM physics and also due to the presence of extra neutrinos, and that the signatures of sparticles at colliders are quite different from those with neutralino as DM candidate.National Natural Science Foundation of China (NNSFC) [11575053]SCI(E)ARTICLE1
Classical mechanics and quantum mechanics
No full textThe Newton equation of motion is derived from quantum mechanics.Physics, MultidisciplinarySCI(E)中国科学引文数据库(CSCD)2ARTICLE5685-6884
- …
