scholarly journals Sequent-Type Calculi for Three-Valued and Disjunctive Default Logic

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 84 ◽  
Author(s):  
Sopo Pkhakadze ◽  
Hans Tompits
Keyword(s):  
Proof Theory ◽  
Consistency Condition ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Inference Process ◽  
Default Theory ◽  
Valid Inference ◽  
The One ◽  
Base Logic ◽  
Selection Of

Default logic is one of the basic formalisms for nonmonotonic reasoning, a well-established area from logic-based artificial intelligence dealing with the representation of rational conclusions, which are characterised by the feature that the inference process may require to retract prior conclusions given additional premisses. This nonmonotonic aspect is in contrast to valid inference relations, which are monotonic. Although nonmonotonic reasoning has been extensively studied in the literature, only few works exist dealing with a proper proof theory for specific logics. In this paper, we introduce sequent-type calculi for two variants of default logic, viz., on the one hand, for three-valued default logic due to Radzikowska, and on the other hand, for disjunctive default logic, due to Gelfond, Lifschitz, Przymusinska, and Truszczyński. The first variant of default logic employs Łukasiewicz’s three-valued logic as the underlying base logic and the second variant generalises defaults by allowing a selection of consequents in defaults. Both versions have been introduced to address certain representational shortcomings of standard default logic. The calculi we introduce axiomatise brave reasoning for these versions of default logic, which is the task of determining whether a given formula is contained in some extension of a given default theory. Our approach follows the sequent method first introduced in the context of nonmonotonic reasoning by Bonatti, which employs a rejection calculus for axiomatising invalid formulas, taking care of expressing the consistency condition of defaults.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Costumes and Choreography from Bodenwieser's Trunk: The Coat as Affective Memory

2019 ◽  
Vol 37 (1) ◽  
pp. 89-110
Author(s):  
Rachel Fensham
Keyword(s):  
Modern Dance ◽  
Human Condition ◽  
Personal Life ◽  
Creative Thought ◽  
Cain And Abel ◽  
Embodied Research ◽  
The Many ◽  
The One ◽  
Material Evidence ◽  
Selection Of

The Viennese modern choreographer Gertrud Bodenwieser's black coat leads to an analysis of her choreography in four main phases – the early European career; the rise of Nazism; war's brutality; and postwar attempts at reconciliation. Utilising archival and embodied research, the article focuses on a selection of Bodenwieser costumes that survived her journey from Vienna, or were remade in Australia, and their role in the dramaturgy of works such as Swinging Bells (1926), The Masks of Lucifer (1936, 1944), Cain and Abel (1940) and The One and the Many (1946). In addition to dance history, costume studies provides a distinctive way to engage with the question of what remains of performance, and what survives of the historical conditions and experience of modern dance-drama. Throughout, Hannah Arendt's book The Human Condition (1958) provides a critical guide to the acts of reconstruction undertaken by Bodenwieser as an émigré choreographer in the practice of her craft, and its ‘materializing reification’ of creative thought. As a study in affective memory, information regarding Bodenwieser's personal life becomes interwoven with the author's response to the material evidence of costumes, oral histories and documents located in various Australian archives. By resurrecting the ‘dead letters’ of this choreography, the article therefore considers how dance costumes offer the trace of an artistic resistance to totalitarianism.

Proof Theory of the Cut Rule

2018 ◽  
Author(s):  
J. R. B. Cockett ◽  
R. A. G. Seely
Keyword(s):  
Proof Theory ◽  
Graphical Representation ◽  
Basic Component ◽  
Graphical Representations ◽  
Mathematical Language ◽  
Basic Logic ◽  
Cut Rule ◽  
Structural Rules ◽  
The One ◽  
Categorical Semantics

This chapter describes the categorical proof theory of the cut rule, a very basic component of any sequent-style presentation of a logic, assuming a minimum of structural rules and connectives, in fact, starting with none. It is shown how logical features can be added to this basic logic in a modular fashion, at each stage showing the appropriate corresponding categorical semantics of the proof theory, starting with multicategories, and moving to linearly distributive categories and *-autonomous categories. A key tool is the use of graphical representations of proofs (“proof circuits”) to represent formal derivations in these logics. This is a powerful symbolism, which on the one hand is a formal mathematical language, but crucially, at the same time, has an intuitive graphical representation.

PROMETHEE-based ranking of project managers based on the five personality traits

Kybernetes ◽  
2019 ◽  
Vol 49 (4) ◽  
pp. 1083-1102
Author(s):  
Georgios N. Aretoulis ◽  
Jason Papathanasiou ◽  
Fani Antoniou
Keyword(s):  
Personality Traits ◽  
Questionnaire Survey ◽  
Multicriteria Decision Making ◽  
Project Managers ◽  
Preference Ranking ◽  
Infrastructure Projects ◽  
Public Infrastructure ◽  
Content Type ◽  
The One ◽  
Selection Of

Purpose This paper aims to rank and identify the most efficient project managers (PMs) based on personality traits, using Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) methodology. Design/methodology/approach The proposed methodology relies on the five personality traits. These were used as the selection criteria. A questionnaire survey among 82 experienced engineers was used to estimate the required weights per personality trait. A second two-part questionnaire survey aimed at recording the PMs profile and assess the performance of personality traits per PM. PMs with the most years of experience are selected to be ranked through Visual PROMETHEE. Findings The findings suggest that a competent PM is the one that scores low on the “Neuroticism” trait and high especially on the “Conscientiousness” trait. Research limitations/implications The research applied a psychometric test specifically designed for Greek people. Furthermore, the proposed methodology is based on the personality characteristics to rank the PMs and does not consider the technical skills. Furthermore, the type of project is not considered in the process of ranking PMs. Practical implications The findings could contribute in the selection of the best PM that maximizes the project team’s performance. Social implications Improved project team communication and collaboration leading to improved project performance through better communication and collaboration. This is an additional benefit for the society, especially in the delivery of public infrastructure projects. A lot of public infrastructure projects deviate largely as far as cost and schedule is concerned and this is an additional burden for public and society. Proper project management through efficient PMs would save people’s money and time. Originality/value Identification of the best PMbased on a combination of multicriteria decision-making and psychometric tests, which focus on personality traits.

scholarly journals More on Modal Aspects of Default Logic1

1992 ◽  
Vol 17 (1-2) ◽  
pp. 99-116
Author(s):  
V. Wiktor Marek ◽  
Miroslaw Truszczynski
Keyword(s):  
Modal Logic ◽  
Default Logic ◽  
Nonmonotonic Logic ◽  
Default Reasoning ◽  
Default Theory ◽  
Autoepistemic Logic ◽  
The Relationship ◽  
Natural Classes ◽  
Weak Extension

Investigations of default logic have been so far mostly concerned with the notion of an extension of a default theory. It turns out, however, that default logic is much richer. Namely, there are other natural classes of objects that might be associated with default reasoning. We study two such classes of objects with emphasis on their relations with modal nonmonotonic formalisms. First, we introduce the concept of a weak extension and study its properties. It has long been suspected that there are close connections between default and autoepistemic logics. The notion of weak extension allows us to precisely describe the relationship between these two formalisms. In particular, we show that default logic with weak extensions is essentially equivalent to autoepistemic logic, that is, nonmonotonic logic KD45. In the paper we also study the notion of a set of formulas closed under a default theory. These objects are shown to correspond to stable theories and to modal logic S5. In particular, we show that skeptical reasoning with sets closed under default theories is closely related with provability in S5. As an application of our results we determine the complexity of reasoning with weak extensions and sets closed under default theories.

Default Logic Models of Certain Inheritance Systems with Exceptions

1993 ◽  
Vol 18 (2-4) ◽  
pp. 129-149
Author(s):  
Serge Garlatti
Keyword(s):  
Hierarchical Structure ◽  
Formal Semantics ◽  
Sufficient Conditions ◽  
Nonmonotonic Reasoning ◽  
Default Logic ◽  
Representation Systems ◽  
The Hierarchical Structure ◽  
Necessary And Sufficient ◽  
Structure Of Knowledge ◽  
Made In

Representation systems based on inheritance networks are founded on the hierarchical structure of knowledge. Such representation is composed of a set of objects and a set of is-a links between nodes. Objects are generally defined by means of a set of properties. An inheritance mechanism enables us to share properties across the hierarchy, called an inheritance graph. It is often difficult, even impossible to define classes by means of a set of necessary and sufficient conditions. For this reason, exceptions must be allowed and they induce nonmonotonic reasoning. Many researchers have used default logic to give them formal semantics and to define sound inferences. In this paper, we propose a survey of the different models of nonmonotonic inheritance systems by means of default logic. A comparison between default theories and inheritance mechanisms is made. In conclusion, the ability of default logic to take some inheritance mechanisms into account is discussed.

scholarly journals Gradient boosting for linear mixed models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Colin Griesbach ◽  
Benjamin Säfken ◽  
Elisabeth Waldmann
Keyword(s):  
Random Effects ◽  
Mixed Models ◽  
Selection Procedure ◽  
Classification Theory ◽  
Gradient Boosting ◽  
Random Structure ◽  
Boosting Algorithm ◽  
The One ◽  
Biased Estimates ◽  
Selection Of

Abstract Gradient boosting from the field of statistical learning is widely known as a powerful framework for estimation and selection of predictor effects in various regression models by adapting concepts from classification theory. Current boosting approaches also offer methods accounting for random effects and thus enable prediction of mixed models for longitudinal and clustered data. However, these approaches include several flaws resulting in unbalanced effect selection with falsely induced shrinkage and a low convergence rate on the one hand and biased estimates of the random effects on the other hand. We therefore propose a new boosting algorithm which explicitly accounts for the random structure by excluding it from the selection procedure, properly correcting the random effects estimates and in addition providing likelihood-based estimation of the random effects variance structure. The new algorithm offers an organic and unbiased fitting approach, which is shown via simulations and data examples.

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

PERCUTANEOUS RENAL BIOPSY IN CHILDREN

PEDIATRICS ◽  
1962 ◽  
Vol 30 (2) ◽  
pp. 287-296
Author(s):  
W. F. Dodge ◽  
C. W. Daeschner ◽  
J. C. Brennan ◽  
H. S. Rosenberg ◽  
L. B. Travis ◽  
...  
Keyword(s):  
Renal Disease ◽  
Renal Biopsy ◽  
Clinical Importance ◽  
Renal Diseases ◽  
Renal Lesion ◽  
Bleeding Tendency ◽  
Percutaneous Renal Biopsy ◽  
The One ◽  
Selection Of

Since 1951, when the percutaneous renal biopsy was introduced as an adjunctive method for study of patients with renal disease, reports of some 4,000 kidney biopsies have appeared in the literature. Only about 250 of these, however, have been performed in children. A biopsy specimen containing 5 to 10 glomeruli has been reported to be adequate for interpretation and to be representative of the total renal parenchyma in 84% of the cases with diffuse renal disease. Using a biopsy technique similar to that described by Kark, we have obtained an adequate specimen in 92% of 205 kidney biopsies performed in 168 children with diffuse renal diseases. Seven deaths have been previously reported in the literature. The circumstances surrounding the death of these seven patients and of the one death that occurred in our series are described. Perirenal hematoma has had a reported incidence of 0.4%. It has been our experience, as well as that of the other investigators, that if blood boss is replaced, the patient has an otherwise uneventful course and the mass subsequently disappears. Gross hematuria has had a reported incidence of 5.2%. Microscopic hematuria, lasting for 6 to 12 hours after biopsy, has been found to be the rule rather than the exception. The complications which have occurred have been associated with bleeding, and therefore a careful history concerning bleeding tendency and a study of the clotting mechanism is essential if the risk of needle renal biopsy is to be minimized. In addition to a bleeding tendency or defect in clotting mechanism, most investigators are agreed that the presence of only one kidney or an uncooperative patient are absolute contraindications to renal biopsy. The renal biopsy is primarily, at present, an additional and most useful investigative tool in the elucidation of the pathogenesis, natural history (by serial studies) and effectiveness of specific therapy upon the various renal diseases. It is of practical clinical importance in the selection of those patients with the nephrotic syndrome in whom glucocorticoid therapy is likely to be beneficial or the patient with anuria whose renal lesion is probably reversible with time; and, as a guide to the effectiveness of therapy in patients with pyelonephritis or lupus nephritis. It is not a technique that can be recommended for general or casual use. A classification of the pathohistobogic findings of diffuse glomerulonephritis, patterned after Ellis, is presented and discussed. This classification will be used in the description and discussion of various renal diseases and systemic diseases with associated nephritis in the three subsequent papers.

A distributional theory for asymptotic expansions

1990 ◽  
Vol 428 (1875) ◽  
pp. 399-430 ◽  
Keyword(s):  
Asymptotic Expansions ◽  
Asymptotic Series ◽  
Generalized Functions ◽  
The Moment ◽  
The One ◽  
Topological Tensor Products ◽  
Multidimensional Integrals ◽  
Vector Valued ◽  
Selection Of ◽  
Mathematics And Physics

We present various techniques for the asymptotic expansions of generalized functions. We show that the moment asymptotic expansions hold for a very wide variety of kernels such as generalized functions of rapid decay and rapid oscillations. We do not use Mellin transform techniques as done by previous authors in the field. Instead, we introduce a direct approach that not only solves the one-dimensional problems but also applies to various multidimensional integrals and oscillatory kernels as well. This approach also helps in the development of various asymptotic series arising in diverse fields of mathematics and physics. We find that the asymptotic expansions of generalized functions depend on the selection of suitable spaces of test functions. Accordingly, we have exercised special care in classifying the spaces and the distributions defined on them. Furthermore, we use the theory of topological tensor products to obtain the expansions of vector-valued distributions. We present several examples to illustrate that many classical results follow in a simple manner. For instance, we derive from our results the asymptotic expansions of certain series considered by Ramanujan.

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