Boundary Algebra: A Simple Notation for Boolean Algebra and the Truth Functors

Boundary algebra [BA] is a simpler notation for Spencer-Brown’s (1969) primary algebra [pa], the Boolean algebra 2, and the truth functors. The primary arithmetic [PA] consists of the atoms ‘()’ and the blank page, concatenation, and enclosure between ‘(‘ and ‘)’, denoting the primitive notion of distinction. Inserting letters denoting the presence or absence of () into a PA formula yields a BA formula. The BA axioms are "()()=()" (A1), and "(()) [=?] may be written or erased at will” (A2). Repeated application of these axioms to a PA formula yields a member of B= {(),?} called its simplification. (a) has two intended interpretations: (a) ? a? (Boolean algebra 2), and (a) ? ~a (sentential logic). BA is self-dual: () ? 1 [dually 0] so that B is the carrier for 2, ab ? a?b [a?b], and (a)b [(a(b))] ? a=b, so that ?=() [()=?] follows trivially and B is a poset. The BA basis abc= bca (Dilworth 1938), a(ab)= a(b), and a()=() (Bricken 2002) facilitates clausal reasoning and proof by calculation. BA also simplifies normal forms and Quine’s (1982) truth value analysis. () ? true [false] yields boundary logic.G. Spencer Brown; boundary algebra; boundary logic; primary algebra; primary arithmetic; Boolean algebra; calculation proof; C.S. Peirce; existential graphs.

Preemption Operators (NMR 2012)

International audienceWe introduce a family of operators for belief change that aim at making a new piece of information to be preemptive so that any former belief subsuming it is given up. That is, the current belief base is to be altered even in the case that it is logically consistent with the new piece of information. Existing operators for belief revision are inadequate for this purpose because they amount to settheoretic union in a contradiction-free case.We propose a series of postulates for such preemption operators.We show that a preemption operator can be defined as a multiple contraction followed by an expansion, drawing on operators from belief revision

Form and Content: An Introduction to Formal Logic

Derek Turner, Professor of Philosophy, has written an introductory logic textbook that students at Connecticut College, or anywhere, can access for free. The book differs from other standard logic textbooks in its reliance on fun, low-stakes examples involving dinosaurs, a dog and his friends, etc. This work is published in 2020 under a Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International License. You may share this text in any format or medium. You may not use it for commercial purposes. If you share it, you must give appropriate credit. If you remix, transform, add to, or modify the text in any way, you may not then redistribute the modified text.https://digitalcommons.conncoll.edu/oer/1000/thumbnail.jp

AGM 25 years: twenty-five years of research in belief change

The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model.info:eu-repo/semantics/publishedVersio

Faculty Senate Chronicle November 2, 2000

Minutes for the regular meeting of The University of Akron Faculty Senate on November 2, 2000

Faculty Senate Chronicle February 6, 2003

Minutes for the regular meeting of The University of Akron Faculty Senate on February 6, 2003

Modern Technology and an Aging Population: Can the Use of the Wii Fit Gaming System Improve Functional Balance in Community Dwelling Seniors?

Seniors are a growing segment of the population of the United States. By 2030 they will make up nearly 20% of the general population. Senior citizens face many health challenges as they age. Injury due to falling is a major concern for many in this age group. Research shows that approximately one third of seniors will fall each year. Injuries that result from falls have been identified as the number one cause of accidental death in this age group each year. While falls have been studied by researchers for a number of years, and some progress has been made in finding ways to improve balance in seniors, the high incidence of falls continues to plague this demographic. Many of the current treatments to improve balance are too expensive, not accessible, or not motivating for seniors. This research project explored the effect of using a readily available video-game system to address these barriers. The Wii Fit gaming system was used with participants three times each week for 30 minutes and the resulting changes were documented. The Berg Balance Scale and Timed Up and Go test, both frequently used by professionals to assess balance in seniors, were used to document balance change. Every participant showed improvement. The Activities-specific Balance Confidence scale, which is used to measure a person\u27s fear of falling, was also used to assess the participant\u27s confidence in their balance as well as the level of fear associated with falling. The results of this test were positive but not to the extent of the balance tests. Finally, each participant was interviewed to assess how easy to use the participants felt the Wii Fit was as well as the motivational qualities of the Wii Fit as a balance tool. Answers given by the participants in the interview were generally positive. These results indicate that the Wii Fit gaming system may be beneficial for improving balance in seniors

A Formal Anaylysis Of Hohfeldian Relations

It is the goal of this article to provide a formal system in which all the Hohfeldian terms are formalized and in which all the relations Hohfeld requires among his concepts may be proved to hold. The effort will commence with a brief look at Professor Hohfeld\u27s work. The development of the formal system will then begin with a reformulization of Professor Allen\u27s work.\u27 It will be a reformulation in that there will be a change in notation and his inference rules will be changed to an equivalent set of rules. The system must then also be extended to provide the logical machinery necessary to allow for changes in legal relations

Multimodal Smoking Cessation in a Real-Life Setting: Combining Motivational Interviewing With Official Therapy and Reduced Risk Products

Background: Tobacco use is a global pandemic, affecting an estimated 1.2 billion people and resulting in substantial health burdens and associated costs. Objectives: The aim of this study was to estimate the efficacy of several treatments for smoking cessation in a real-life setting and to evaluate predictors of smoking abstinence. Methods: This research was designed with a sample of 593 cases recorded over the period between 2015 and 2016. Six treatment groups were included: (1) bupropion and motivational interviewing (MI); (2) bupropion, nicotine replacement therapy (NRT), and MI; (3) NRT and MI; (4) varenicline and MI; (5) personal vaporizer electronic cigarette and MI; and (6) electronic cigarette, cigarette like “cigalike,” and MI. Results: Results support the efficacy of all treatment groups when used in a real-life setting. The predictors of smoking abstinence were sex, partner smoking status, previous quit attempts, daily consumption, self-efficacy, and level of nicotine dependence. Conclusions: The use of different therapeutic strategies in clinical practice, including pharmacotherapy and nonstandard electronic nicotine delivery systems, such as an electronic cigarette, ensures a greater chance of cessation success and the possibility of tailoring interventions according to patients’ resources

Tobacco dependence treatment education for dental students using standardized patients.

Dentists can play a key role in helping patients quit tobacco use by providing tobacco cessation treatment (TCT) in their practice. Although the majority of dentists receive training in TCT, most do not provide adequate intervention. Many feel they are not adequately trained. Using standardized patients (SPs) shows promise in TCT training by providing a simulated clinical environment for students to practice counseling skills with individuals trained to portray patients. Standardized patients evaluate students\u27 skills and provide immediate feedback. The purpose of this study is to determine if there is a difference in dental students\u27 attitudes, perceived barriers, subjective norms, perceived skills, self-efficacy, intentions to provide TCT, and cessation knowledge between those students who receive a lecture along with practice sessions using SPs and those students who receive a lecture only. Variables were selected to coincide with the constructs of the theory of planned behavior. Freshman dental students in an introductory clinical course were invited to participate in the study by completing a pre- and post-questionnaire. The prequestionnaire was administered to all students in the course prior to a two hour tobacco cessation lecture. The intervention group of students (n = 42) completed the second questionnaire after the lecture, practice sessions with SPs and a debriefing session. The control group (n = 52) completed the second questionnaire after the lecture. The training using SPs increased dental students\u27 perceived barriers, subjective norms, perceived skills, self-efficacy, and intentions to provide TCT (p \u3c .05) more than lecture only; however, it did not significantly increase attitude and knowledge. Dental students\u27 attitude, perceived barriers, subjective norms, perceived skills and knowledge significantly impacted intent to provide TCT (p \u3c .005), while training type, tobacco status and use did not. The time between the groups receiving the lecture and practice sessions with SPs did not significantly affect the variables. The findings suggest that using SPs is a valuable educational method that increases dental students\u27 social pressures, skills, confidence and intentions to provide TCT. The training using SPs did increase students\u27 awareness of barriers in providing TCT. Additional research is needed to reduce barriers in providing TCT