Generic substitutions

2005 ◽  
Vol 70 (1) ◽  
pp. 61-83 ◽  
Author(s):  
Giovanni Panti
Keyword(s):  
Continuous Function ◽  
Free Algebra ◽  
Classical Logic ◽  
Propositional Logic ◽  
Dual Space ◽  
Extensive Literature ◽  
Cantor Space ◽  
Natural Measure ◽  
The Subject ◽  
Stochastic Properties

AbstractUp to equivalence, a substitution in propositional logic is an endomorphism of its free algebra. On the dual space, this results in a continuous function, and whenever the space carries a natural measure one may ask about the stochastic properties of the action. In classical logic there is a strong dichotomy: while over finitely many propositional variables everything is trivial, the study of the continuous transformations of the Cantor space is the subject of an extensive literature, and is far from being a completed task. In many-valued logic this dichotomy disappears: already in the finite-variable case many interesting phenomena occur, and the present paper aims at displaying some of these.

The History and Future of Logic Puzzles

2017 ◽  
Author(s):  
Jason Rosenhouse
Keyword(s):  
Future Development ◽  
Classical Logic ◽  
Propositional Logic ◽  
Lewis Carroll ◽  
History Of Logic ◽  
Nonclassical Logics ◽  
History Of ◽  
The Subject

This chapter first considers the history of logic puzzles through the contributions of Lewis Carroll and Raymond Smullyan. These two figures are united not only by their love of logic, but also by their conviction that puzzles provide an accessible gateway into the deep ideas of the subject. Their puzzles depend on what philosophers typically refer to as “classical logic.” Although mathematical historians generally credit Aristotle with being the first to undertake the study of logic in a systematic manner, the first to present logic explicitly for recreational purposes was Carroll. Smullyan is the most significant among the authors who have explored the recreational possibilities of propositional logic. The remainder of the chapter considers a possible future development of logic puzzles by investigating puzzles based on nonclassical logics.

scholarly journals On density of truth of the intuitionistic logic in one variable

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Zofia Kostrzycka
Keyword(s):  
Intuitionistic Logic ◽  
Classical Logic ◽  
Propositional Logic ◽  
Propositional Variable ◽  
Intuitionistic Propositional Logic ◽  
International Audience

International audience In this paper we focus on the intuitionistic propositional logic with one propositional variable. More precisely we consider the standard fragment $\{ \to ,\vee ,\bot \}$ of this logic and compute the proportion of tautologies among all formulas. It turns out that this proportion is different from the analog one in the classical logic case.

The weak König lemma and uniform continuity

2008 ◽  
Vol 73 (3) ◽  
pp. 933-939 ◽  
Author(s):  
Josef Berger
Keyword(s):  
Continuous Function ◽  
Uniform Continuity ◽  
Baire Space ◽  
Cantor Space

AbstractWe prove constructively that the weak König lemma and quantifier-free number–number choice imply that every pointwise continuous function from Cantor space into Baire space has a modulus of uniform continuity.

scholarly journals A Roadmap to the Development of Key Competencies of Engineering and Technology Graduates

2019 ◽  
Vol 9 (5) ◽  
pp. 75
Author(s):  
Arwa Y. Aleryani ◽  
Abdullatif A. AlMunifi
Keyword(s):  
Learning Strategies ◽  
Paradigm Shift ◽  
Teaching And Learning ◽  
Extensive Literature ◽  
College Administration ◽  
Engineering And Technology ◽  
Teaching And Learning Strategies ◽  
Key Competencies ◽  
The Subject ◽  
Support Students

The world of employment is impacted by major trends that are imposed by the on-going industrial advances. The changing labor market and the future of work calls for a paradigm shift in teaching and learning to equip graduates with compe-tencies they need for current and future jobs, and in particular, those of the engi-neering and technology programs. The purpose of this study is to discuss previ-ous work in the subject matter, to outline a set of teaching and learning strategies, and to create a roadmap for main players to work through to arm graduates with the intended competencies skills. To achieve this objective an extensive literature review was carried out to identify what teaching and learning strategies are cur-rently in-place, and what skills are anticipated. However, still, the education insti-tutions not been able to provide the workplace with competent graduates. A pro-posed set of intended competencies skills along with teaching and learning strate-gies for properly preparing future engineering and technology graduates was de-veloped; and a roadmap was built to show the roles of college administration, professors and students to ensure an effective way to support students gaining these skills. It is recommended that these sets of strategies including the facilita-tion of the roles of the main players to be incorporated in the educational pro-grams learning outcomes.

scholarly journals Therapeutic potential of intermittent hypoxia: a matter of dose

2014 ◽  
Vol 307 (10) ◽  
pp. R1181-R1197 ◽  
Author(s):  
Angela Navarrete-Opazo ◽  
Gordon S. Mitchell
Keyword(s):  
Intermittent Hypoxia ◽  
Therapeutic Potential ◽  
Therapeutic Effects ◽  
Extensive Literature ◽  
Beneficial Effects ◽  
Metabolic Bone ◽  
Clinical Disorders ◽  
The Subject ◽  
Critical Characteristics ◽  
The Impact

Intermittent hypoxia (IH) has been the subject of considerable research in recent years, and triggers a bewildering array of both detrimental and beneficial effects in multiple physiological systems. Here, we review the extensive literature concerning IH and its impact on the respiratory, cardiovascular, immune, metabolic, bone, and nervous systems. One major goal is to define relevant IH characteristics leading to safe, protective, and/or therapeutic effects vs. pathogenesis. To understand the impact of IH, it is essential to define critical characteristics of the IH protocol under investigation, including potentially the severity of hypoxia within episodes, the duration of hypoxic episodes, the number of hypoxic episodes per day, the pattern of presentation across time (e.g., within vs. consecutive vs. alternating days), and the cumulative time of exposure. Not surprisingly, severe/chronic IH protocols tend to be pathogenic, whereas any beneficial effects are more likely to arise from modest/acute IH exposures. Features of the IH protocol most highly associated with beneficial vs. pathogenic outcomes include the level of hypoxemia within episodes and the number of episodes per day. Modest hypoxia (9–16% inspired O2) and low cycle numbers (3–15 episodes per day) most often lead to beneficial effects without pathology, whereas severe hypoxia (2–8% inspired O2) and more episodes per day (48–2,400 episodes/day) elicit progressively greater pathology. Accumulating evidence suggests that “low dose” IH (modest hypoxia, few episodes) may be a simple, safe, and effective treatment with considerable therapeutic potential for multiple clinical disorders.

A ‘Hyaline’ Layer in the Skin of Squids

1997 ◽  
Vol 77 (4) ◽  
pp. 1247-1250 ◽  
Author(s):  
J.J. Madan ◽  
M.J. Wells
Keyword(s):  
Oxygen Uptake ◽  
Blood Vessels ◽  
Amorphous Material ◽  
Thick Layer ◽  
Extensive Literature ◽  
Potential Importance ◽  
Nervous Control ◽  
The Subject ◽  
The Brain

The skin of Loligo vulgaris and Illex illecebrosus contains a thick layer of amorphous material. In Loligo it lies above and in Illex below the chromatophore layer. We can find no mention of this layer in the considerable literature on squid skins despite its potential importance as a protection to underlying tissues and as a possible barrier to cutaneous oxygen uptake.Cephalopods have soft complicated skins. Embedded in the skin, most species have chromatophores, small bags of pigment that can be expanded by muscles that are under direct nervous control from the brain. There is an extensive literature on the physiology of chromatophores (Packard, 1988) and on their function in the behaviour of the animals (Hanlon & Messenger, 1996; Packard & Hochberg, 1977). Further cutaneous structures concerned in the determination of the colour of living cephalopods, the reflecting iridophores and leucophores (Cloney & Brocco, 1983), and the light generating photophores (Herring, 1988), have been the subject of a number of reports but other skin features such as the distribution of blood vessels have attracted little attention.

The Roman Military Occupation of North-West Spain

1976 ◽  
Vol 66 ◽  
pp. 45-66 ◽  
Author(s):  
R. F. J. Jones
Keyword(s):  
Archaeological Site ◽  
Second Century ◽  
Military Force ◽  
Extensive Literature ◽  
Main Text ◽  
Gold Mines ◽  
North West ◽  
The North ◽  
History Of ◽  
The Subject

The north-west corner of Spain was long neglected by Roman archaeologists, who have tended to concentrate on the more spectacular remains to be found in the south and east. However, recently more attention has been directed there by workers of several nationalities, who have now produced a quite extensive literature on the gold mines, as well as on wider aspects, chiefly in connection with the activities of the legion VII Gemina. Yet there has been little attempt in all this to examine why a substantial military force was maintained in the region for so long. This paper aims to review that problem to about the end of the second century A.D. The evidence available is almost entirely epigraphic, chiefly consisting of epitaphs and religious dedications. Building inscriptions are scarce. For convenience all the epigraphic material from the north-west of Spain that is relevant to the disposition of the army is collected in the appendix, and in the main text reference will be made to the numbers given there. In addition a few historical passages are of importance, but the archaeological site evidence is very slight. The nature of the evidence is such that most attention must be devoted to the units attested in the region and their deployment, with little to be said about their actual bases. Previous work on the subject has been dominated by the late Antonio García y Bellido in several masterly papers. However it has tended to concentrate more on the history of the units themselves than on questions of topography and the reasons behind their presence.

scholarly journals Humanistic training in Medicine through dancing in the hospital: students’ perceptions

2021 ◽  
Vol 45 (1) ◽  
Author(s):  
Amanda Barbosa Lisboa ◽  
Marcela Rodrigues Ciccone ◽  
Marina Kadekaru ◽  
Izabel Cristina Rios
Keyword(s):  
Medical Students ◽  
Medical Training ◽  
The Other ◽  
Male Students ◽  
Extensive Literature ◽  
The Arts ◽  
Data Production ◽  
The Subject ◽  
Self Knowledge ◽  
The Look

Abstract: Introduction: The humanization of assistance is associated to empathy, embracing, and effective communication, being part of the medical training. According to its nature, humanization requires methods that involve affections and stimulates critical thinking. Objective: Extensive literature shows the benefits of the arts in medical education; however, there are still few studies on dancing, the subject of this study, which was carried out by medical students and whose aim was to investigate hospital dancing in the teaching of humanization, from the perspective of medical students. Method: A qualitative action research study was designed, in which medical students performed choreographies for patients, companions and employees in three different wards of the teaching hospital. The action consisted of continuous cycles in the planning of interventions, performance, observing, reflection, and re-planning of subsequent actions, in a systematic manner and controlled by the researchers. Data production took place by direct observation, narratives and focal group. The data were analyzed using the content and thematic analysis methods. Results: For three months, 17 female and 7 male students between 18 and 24 years of age performed the action, producing data that was subsequently classified into 3 thematic categories: 1. Dimension of affection: contents of the student’s emotional character; 2. Care dimension: contents about caring for the patient; 3. Dance dimension: contents on dance in the humanistic training in Medicine. In the triangulation of the techniques, it was observed that joy, anxiety, and the perception of dance as an instrument of bonding were significant. The experience of changing socially-marked places for the student and the patient made the student face and overcome different feelings. The dance allowed the refinement of the look and the capacity to understand the other, taking into account perspectives that converge to or diverge from their own convictions. On the other hand, the students experienced the anxiety and joy of an encounter with themselves, perceiving dance as a pleasurable and humanizing activity. Conclusion: The dance in the hospital lead to experiences and reflections that stimulated the students’ self-knowledge, favored the student-patient relationship, and brought elements to understand the use of dancing in medicine, mainly for the teaching of empathy and humanized care.

scholarly journals An Holistic Extension for Classical Logic via Quantum Fredkin Gate

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1178
Author(s):  
Hector Freytes ◽  
Giuseppe Sergioli
Keyword(s):  
Quantum Computation ◽  
Classical Logic ◽  
Propositional Logic ◽  
Classical Propositional Logic ◽  
Mixed States ◽  
Fredkin Gate ◽  
Bipartite States ◽  
Extended Notion

An holistic extension for classical propositional logic is introduced in the framework of quantum computation with mixed states. The mentioned extension is obtained by applying the quantum Fredkin gate to non-factorizable bipartite states. In particular, an extended notion of classical contradiction is studied in this holistic framework.

scholarly journals Recovery operators, paraconsistency and duality

2019 ◽  
Vol 28 (5) ◽  
pp. 624-656 ◽  
Author(s):  
Walter Carnielli ◽  
Marcelo E Coniglio ◽  
Abilio Rodrigues
Keyword(s):  
Common Core ◽  
Classical Logic ◽  
Propositional Logic ◽  
Inference Rules ◽  
Object Language ◽  
Logical Operators ◽  
Formal Systems ◽  
Excluded Middle

Abstract There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express metalogical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the logics of formal inconsistency (LFIs) and by the logics of formal undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent scenario, while LFUs recover the validity of the principle of excluded middle in a paracomplete scenario. We introduce definitions of duality between inference rules and connectives that allow comparing rules and connectives that belong to different logics. Two formal systems are studied, the logics mbC and mbD, that display the duality between paraconsistency and paracompleteness as a duality between inference rules added to a common core—in the case studied here, this common core is classical positive propositional logic. The logics mbC and mbD are equipped with recovery operators that restore classical logic for, respectively, consistent and determined propositions. These two logics are then combined obtaining a pair of LFI and undeterminedness, namely, mbCD and mbCDE. The logic mbCDE exhibits some nice duality properties. Besides, it is simultaneously paraconsistent and paracomplete, and able to recover the principles of excluded middle and explosion one at a time. The last sections offer an algebraic account for such logics by adapting the swap structures semantics framework of the LFIs the LFUs. This semantics highlights some subtle aspects of these logics, and allows us to prove decidability by means of finite nondeterministic matrices.

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