scholarly journals Non-well-founded Deduction for Induction and Coinduction

Author(s):  
Liron Cohen

AbstractInduction and coinduction are both used extensively within mathematics and computer science. Algebraic formulations of these principles make the duality between them apparent, but do not account well for the way they are commonly used in deduction. Generally, the formalization of these reasoning methods employs inference rules that express a general explicit (co)induction scheme. Non-well-founded proof theory provides an alternative, more robust approach for formalizing implicit (co)inductive reasoning. This approach has been extremely successful in recent years in supporting implicit inductive reasoning, but is not as well-developed in the context of coinductive reasoning. This paper reviews the general method of non-well-founded proofs, and puts forward a concrete natural framework for (co)inductive reasoning, based on (co)closure operators, that offers a concise framework in which inductive and coinductive reasoning are captured as we intuitively understand and use them. Through this framework we demonstrate the enormous potential of non-well-founded deduction, both in the foundational theoretical exploration of (co)inductive reasoning and in the provision of proof support for (co)inductive reasoning within (semi-)automated proof tools.

1987 ◽  
Vol 10 (4) ◽  
pp. 387-413
Author(s):  
Irène Guessarian

This paper recalls some fixpoint theorems in ordered algebraic structures and surveys some ways in which these theorems are applied in computer science. We describe via examples three main types of applications: in semantics and proof theory, in logic programming and in deductive data bases.


Author(s):  
Alistair Irons ◽  
Roger Boyle

Many more computer systems do not work in the way they are intended (Sommerville, 2004; Pressman, 2004). Computer systems are also increasingly vulnerable to misuse (Edgar, 1997; Rowe & Thompson, 1996) and crime (Barrett, 1997; NHTCU, 2003; Casey, 2004). The concerns ascribed to the development of computer systems can also be attributed to the development of computer artifacts in undergraduate and postgraduate projects; poor software practice can often be traced back to the education of the practitioner. The main issue addressed here is the steps academics, computing schools, and departments and universities should take in order to address the potential harm that could result from inappropriate projects, and the potential benefits of introducing an ethical approval phase.


Author(s):  
Rafael Moreno-Sanchez

The Semantic Web (SW) and Geospatial Semantic Web (GSW) are considered the next step in the evolution of the Web. For most non-Web specialists, geospatial information professionals, and non-computer-science students these concepts and their impacts on the way we use the Web are not clearly understood. The purpose of this chapter is to provide this broad audience of non-specialists with a basic understanding of: the needs and visions driving the evolution toward the SW and GSW; the principles and technologies involved in their implementation; the state of the art in the efforts to create the GSW; the impacts of the GSW on the way we use the Web to discover, evaluate, and integrate geospatial data and services; and the needs for future research and development to make the GSW a reality. A background on the SW is first presented to serve as a basis for more specific discussions on the GSW.


Author(s):  
Jennifer (Jenny) L. Penland ◽  
Kennard Laviers

Of all the technologies emerging today, augmented reality (AR) stands to be one of, if not the, most transformational in the way we teach our students across the spectrum of age groups and subject matter. The authors propose “best practices” that allow the educator to use AR as a tool that will not only teach the processes of a skill but will also encourage students to use AR as a motivational tool that allows them to discover, explore, and perform work beyond what is capable with this revolutionary device. Finally, the authors provide and explore the artificial intelligence (AI) processors behind the technologies driving down cost while driving up the quality of AR and how this new field of computer science is transforming all facets of society and may end up changing pedagogy more profoundly than anything before it.


2018 ◽  
Vol 2 (S1) ◽  
pp. 5-5
Author(s):  
Christine M. Weston ◽  
Mia S. Terkowitz ◽  
Daniel E. Ford

OBJECTIVES/SPECIFIC AIMS: The objectives of this study were to compare different methods for determining the disciplines involved in a research article. We sought to address the following questions: To what extent does the number of disciplines reported by an article’s corresponding author agree with their description of the article as unidisciplinary or interdisciplinary? (Q1) and To what extent does the corresponding author’s description of the research as unidisciplinary or interdisciplinary agree with its classification as unidisciplinary or interdisciplinary based on the affiliation of its co-authors? (Q2). METHODS/STUDY POPULATION: Using Scopus, we randomly selected 100 articles from 2010 and 2015 from science teams that had at least 1 author affiliated with Johns Hopkins. Author affiliations were grouped into common academic disciplines: Basic Science, Medicine (and all clinical specialties), Public Health, Engineering, Social Science, Computer Science, Pharmacy, Nursing, and Other. Articles with more than 1 discipline were considered, interdisciplinary. We then sent an online Qualtrics survey to the corresponding author of each article and asked them to indicate (1) all of the disciplines that contributed to the research article at hand, and (2) to indicate whether they considered the research to be “unidisciplinary” or “interdisciplinary” based on definitions that we provided. RESULTS/ANTICIPATED RESULTS: For Q1, we asked corresponding authors to indicate the number of disciplines involved in their research and then to choose the definition that best described their research. Among 76 respondents, 42 indicated that their research consisted of 1 discipline, and 34 indicated that their research consisted of more than 1 discipline. Of the 42 respondents who indicated that their research consisted of one discipline, 21 (50%) respondents described their research as “unidisciplinary” and 21 (50%) described their research as “interdisciplinary.” However, of the 34 respondents who indicated that their research consisted of more than 1 discipline, all but 1 (97%) described their research as “interdisciplinary.” For Q2, we assigned a discipline to each co-author based on his/her affiliation and counted the number of disciplines involved. Among 76 respondents, of the 22 who described their research as “unidisciplinary,” 16 (73%) were categorized as “unidisciplinary” and 6 (27%) were categorized as “interdisciplinary,” using this method. Of the 54 respondents who described their research as “interdisciplinary,” 30 (56%) were categorized as “interdisciplinary” and 24 (44%) as “unidisciplinary.” DISCUSSION/SIGNIFICANCE OF IMPACT: Our results highlight that different methods for determining whether a given research article is interdisciplinary are likely to yield different results. Even when researchers indicate that their research is based within one major discipline, they may still consider it interdisciplinary. Likewise, classifying an article as either unidisciplinary or interdisciplinary based on the affiliations of its co-authors, may not be consistent with the way it is viewed by its authors. It is important to acknowledge that assessing the interdisciplinarity of research is complex and that objective and subjective views may differ.


2009 ◽  
Vol 23 (30) ◽  
pp. 5705-5714
Author(s):  
VOJKAN M. ZORIĆ ◽  
VJEKOSLAV SAJFERT ◽  
LJILJANA MAŠKOVIĆ ◽  
JELENA ZORIĆ

In this work the mechanism of resonance is proposed as the way for determining of wall paint age. The method consists in accelerated growing old of wall paint on the basis of resonance. Measuring is concerned with the humidity of wall paint and it is a general method since water molecules are present in every material. Besides, the water molecules are dipoles so that the resonance with them can be achieved by the mechanical as well as the electrical way.


1999 ◽  
Vol 64 (4) ◽  
pp. 1601-1627 ◽  
Author(s):  
Kai Hauser

AbstractFor a canonical model of set theory whose projective theory of the real numbers is stable under set forcing extensions, a set of reals of minimal complexity is constructed which fails to be universally Baire. The construction uses a general method for generating non-universally Baire sets via the Levy collapse of a cardinal, as well as core model techniques. Along the way it is shown (extending previous results of Steel) how sufficiently iterable fine structure models recognize themselves as global core models.


Author(s):  
Nigel Ward ◽  

Potential applicants to graduate school find it difficult to predict, even approximately, which schools will accept them. We have created a predictive model of admissions decision-making, packaged in the form of a web page that allows students to enter their information and see a list of schools where they are likely to be accepted. This paper explains the rationale for the model’s design and parameter values. Interesting issues include the way that evidence is combined, the estimation of parameters, and the modeling of uncertainty.


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