Resolution in Linguistic Propositional Logic based on Linear Symmetrical Hedge Algebra

The paper introduces a propositional linguistic logic that serves as the basis for automated uncertain reasoning with linguistic information. First, we build a linguistic logic system with truth value domain based on a linear symmetrical hedge algebra. Then, we consider G\"{o}del's t-norm and t-conorm to define the logical connectives for our logic. Next, we present a resolution inference rule, in which two clauses having contradictory linguistic truth values can be resolved. We also give the concept of reliability in order to capture the approximative nature of the resolution inference rule. Finally, we propose a resolution procedure with the maximal reliability.Comment: KSE 2013 conferenc

Ordering based decision making: a survey

Decision making is the crucial step in many real applications such as organization management, financial planning, products evaluation and recommendation. Rational decision making is to select an alternative from a set of different ones which has the best utility (i.e., maximally satisfies given criteria, objectives, or preferences). In many cases, decision making is to order alternatives and select one or a few among the top of the ranking. Orderings provide a natural and effective way for representing indeterminate situations which are pervasive in commonsense reasoning. Ordering based decision making is then to find the suitable method for evaluating candidates or ranking alternatives based on provided ordinal information and criteria, and this in many cases is to rank alternatives based on qualitative ordering information. In this paper, we discuss the importance and research aspects of ordering based decision making, and review the existing ordering based decision making theories and methods along with some future research directions

Vagueness in mathematics talk

The Cockcroft Report claimed that "mathematics provides a means of communication which is powerful, concise and unambiguous". Such precision in language may be a conventional aim of mathematics, particularly when communicated in writing. Nonetheless, as this thesis demonstrates, vagueness is commonplace when people talk about mathematics. In this thesis, I examine the circumstances in which vagueness arises in mathematics talk, and consider the practical purposes which speakers achieve by means of vague utterances in this context. The empirical database, which is considered in Chapters 4 to 7, consists almost entirely of transcripts of mathematical conversations between adult interviewers (including myself) and one or two children. The data were collected from clinical interviews focused on a small number of tasks, and from fragments of teaching. For the most part, the pupils involved in the study were aged between 9 and 12, although the age-range in Chapter 7 extends from 4 to 25. I draw on a number of approaches to discourse associated with 'pragmatics' -a field of linguistics - to analyse the motives and communicative effectiveness of speakers who deploy vagueness in mathematics talk. I claim that, for these speakers, vagueness fulfills a number of purposes, especially 'shielding', i. e. self-protection against accusation of being wrong. Another purpose is to give approximate information; sometimes to achieve shielding, but also to provide the level of detail that is deemed to be appropriate in a given situation. A different purpose, associated with a particular form of vagueness (of reference), is to compensate for lexical gaps in pursuit of effective communication of concepts and ideas. I show, in particular, how speakers use the pronouns 'it' and 'you' in mathematics talk to communicate concepts and generalisations. Some consideration is given to the intentions of 'expert speakers of mathematics when they deploy vague language. Their purposes include some of those identified for novices. Teachers also use vagueness as a means of indirectness in addressing pupils; this strategy is associated with the redress of 'face threatening acts'. My thesis is that vagueness can be viewed and presented, not as a disabling feature of language, but as a subtle and versatile device which speakers can and do deploy to make mathematical assertions with as much precision, accuracy or as much confidence as they judge is warranted by both the content and the circumstances of their utterances. I report on the validation and generalisation of my findings by an Informal Research Group of school teachers, who transcribed and analysed their own classroom interactions using the methods I had developed

Non-verbal IQ Gains from Relational Operant Training Explain Variance in Educational Attainment: An Active-Controlled Feasibility Study

Research suggests that training relational operant patterns of behavior can lead to increases in general cognitive ability and educational outcomes. Most studies to date have been under-powered and included proxy measures of educational attainment. We attempted to extend previous findings with increased experimental control in younger children (aged 6.9–10.1 years). Participants (N = 49) were assigned to either a relational training or chess control group. Over 5 months, teachers assigned class time to complete either relational training or play chess. Those who were assigned relational training gained 8.9 non-verbal IQ (NVIQ) points, while those in the control condition recorded no gains (dppc2 = .99). Regression analyses revealed that post-training NVIQ predicted reading test scores (conducted approximately 1 month later) over and above baseline NVIQ in the experimental condition only, consistent with what we might expect in a full test of far transfer towards educational outcomes

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc

Non-Verbal IQ gains from relational operant training explain variance in educational attainment: An active-controlled feasibility study

Research suggests that training relational operant patterns of behavior can lead to increases in general cognitive ability and educational outcomes. Most studies to date have been under powered and included proxy measures of educational attainment. We attempted to extend previous findings with increased experimental control in younger children (aged 6.9-10.1 yrs.). Participants (N = 49) were assigned to either a relational training or chess control group. Over five months, teachers assigned class-time to complete either relational training or play chess. Those who were assigned relational training gained 8.9 Non-Verbal IQ (NVIQ) points, while those in the control condition recorded no gains (dppc2 = .99). Regression analyses revealed that post-training NVIQ predicted reading test scores (conducted approximately one month later) over and above baseline NVIQ in the experimental condition only, consistent with what we might expect in a full test of far transfer towards educational outcomes

Chi-Thinking: Chiasmus and Cognition

The treatise proposes chiasmus is a dominant instrument that conducts processes and products of human thought. The proposition grows out of work in cognitive semantics and cognitive rhetoric. These disciplines establish that conceptualization traces to embodied image schematic knowledge. The Introduction sets out how this knowledge gathers from perceptions, experiences, and memories of the body's commonplace engagements in space. With these ideas as suppositional foundation, the treatise contends that chiastic instrumentation is a function of a corporeal mind steeped in elementary, nonverbal spatial forms or gestalts. It shows that chiasmus is a space shape that lends itself to cognition via its simple, but unique architecture and critically that architecture's particular meaning affordances. We profile some chiastic meanings over others based on local conditions. Chiastic iconicity ('lending') devolves from LINE CROSSING in 2-D and PATH CROSSING in 3-D space and from other image schemas (e.g., BALANCE, PART-TO-WHOLE) that naturally syndicate with CROSSING. Profiling and iconicity are cognitive activities. The spatio-physical and the visual aspects of cross diagonalization are discussed under the Chapter Two heading 'X-ness.' Prior to this technical discussion, Chapter One surveys the exceptional versatility and universality of chiasmus across verbal spectra, from radio and television advertisements to the literary arts. The purposes of this opening section are to establish that chiasticity merits more that its customary status as mere rhetorical figure or dispensable stylistic device and to give a foretaste of the complexity, yet automaticity of chi-thinking. The treatise's first half describes the complexity, diversity, and structural inheritance of chiasmus. The second half treats individual chiasma, everything from the most mundane instantiations to the sublime and virtuosic. Chapter Three details the cognitive dimensions of the macro chiasm, which are appreciable in the micro. It builds on the argument that chiasmus secures two cognitive essentials: association and dissociation. Chapter Four, advantaged by Kenneth Burke's "psychology of form," elects chiasmus an instrument of inordinate form and then explores the issue of Betweenity, i.e., how chiasma, like crisscrosses, direct notice to an intermediate region. The study ends on the premise that chiasmus executes form-meaning pairings with which humans are highly fluent