Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented in various ways can (...) be approximated by finite-valued logics. It is shown that the minimal m-valued logic for which a given calculus is strongly sound can be calculated. It is also investigated under which conditions propositional logics can be characterized as the intersection of (effectively given) sequences of finite-valued logics. (shrink)

We give a direct and elementary proof of the fact that every real-valued probability measure can be approximated—up to an infinitesimal—by a hyperreal-valued one which is regular and defined on the whole powerset of the sample space.

Software users have different sets of personal values, such as benevolence, self-direction, and tradition. Among other factors, these personal values influence users’ emotions, preferences, motivations, and ways of performing tasks—and hence, information needs. Studies of user acceptance indicate that personal traits like values and related soft issues are important for the user’s approval of software. If a user’s dominant personal value were known, software could automatically show an interface variant which offers information and functionality that best matches his or (...) her dominant value. A user’s dominant personal value is the one that most strongly influences his or her attitudes and behaviors. However, existing methods for measuring a user’s values are work intensive and/or interfere with the user’s privacy needs. If interface tailoring for very large groups of users is planned, value approximation has to be achieved on a large scale to assign individualized software to all users of the software. Our work focuses on approximating the dominant values of a user with less effort and less impact on privacy. Instead of probing for a user’s values directly, we explore the potential of approximating these values based on the user’s preferences for key tasks. Producing tailored versions of software is a separate topic not in the focus here. In this paper we rather describe a method to identify user values from task preferences and an empirical study of applying parts of this method. We are proposing the method in this paper for the first time except for a preliminary version orally presented at a workshop. The method consists of a research process and an application process. In the research process a researcher has to identify key tasks occurring in a context under investigation which have a relationship to personal values. These key tasks can be used in the application process to approximate the dominant values of new users in a similar context. In this empirical study we show that the research process of our method allows us to determine key tasks which approximate values in the shared context of nursing. The majority of the nurses were found to have one of the three following dominant values: benevolence, self-direction, or hedonism. Data confirmed common expectations: that nurses with the value of benevolence, when compared to all other nurses, had a higher preference for tasks which helped people immediately or improved their circumstances of the treatment. In relation to all other nurses, participants with self-direction disliked tasks which affected their personal freedom, and users with hedonism had a lower preference for tasks which involved physical work and preferred tasks which promised gratification. Our findings advance measurement of personal values in large user groups by asking questions with less privacy concern. However, the method requires substantial efforts during the initial research process to prepare such measurements. Future work includes replicating our method in other contexts and identifying value-dependent tasks for users with other values than the three values our empirical study mainly focused on. (shrink)

The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...) be computed from the calculus. (shrink)

FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system which consists of (...) linear operational rules and only two branching structural rules, the latter expressing a generalized rule of bivalence. This system naturally leads to defining an infinite hierarchy of tractable depth-bounded approximations to FDE. Namely, approximations in which the number of nested applications of the two branching rules is bounded. (shrink)

Non-classical logic via approximation of self-referential sentences by dynamical systems are consistently presented. The new 6-valued truth values (here A=Liar, V=TruthTeller) are presented as a function of the classical truth values xi ∈ {0,1}, which resulted in a philosophical standpoint known as Suszko’s Thesis. Three-valued truth tables were created corresponding to Priest’s tables of the same name. In the process of constructing 4-valued truth tables, two more new truth values (va, av) were revealed that do not coincide with the (...) four original ones. Therefore, the closed tables turned out to be 6-valued. Prof Dunn’s 4-valued truth tables are compared with our 4-valued truth tables. De Morgan’s laws are confirmed by six-valued truth tables. Constructed 3-, 4- and 6-valued lattices obeying De Morgan’s laws. (shrink)

The Approximate Number System (ANS) is a system that allows us to distinguish between collections based on the number of items, though only if the ratio between numbers is high enough. One of the questions that has been raised is what the representations involved in this system represent. I point to two important constraints for any account: (a) it doesn’t involve numbers, and (b) it can account for the approximate nature of the ANS. Furthermore, I argue that representations of pure (...) magnitude with vehicles that have an imprecision in the value of the unit of measurement (further clarified through a formal model from measurement theory) fit both these requirements. (shrink)

The technical results presented here on continuity and approximate implication are obviously incomplete. In particular, a syntactic characterization of approximate implication is highly desirable. Nevertheless, I believe the results above do show that the theory has considerable promise for application to the areas mentioned at the top of the paper.Formulation and defense of realist interpretations of science, for example, require approximate truth because we hardly ever have evidence that a particular scientific theory corresponds perfectly with a portion of the real (...) world. Realists need to assert, then, that evidence for a theory is evidence for its approximate truth, not its truth (see [3] and [18]). Approximate truth is, however, a vague notion, and specification of quantity terms and of a sense of approximation are needed to make precise applications of it. Suitability of both vocabulary and sense of approximation depend on the subject matter, and their selection is a partly empirical matter that raises complex issues. In light of the number of common inferences which are not continuous, realists also need to be concerned about indiscriminate use of deductive logic to derive consequences from approximately true theories. These issues will be considered further in a future paper.Approximate truth also has potential application in areas of artificial intelligence that require inference from inaccurate data. In the ‘qualitative’ physical theories of de Kleer and Brown [6], for example, ‘qualitative’ values are derived by partitioning the real numbers into regions. Inferences leading from inside to outside a region must be identified and avoided, and approximate implication and continuity may prove useful in doing this. More generally, growing use of predicate logic as a programming language invites application of the theory of approximate truth as a symbolic substitute for numerical evaluation of computation errors. This too will be the subject of a future paper. (shrink)

The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very false, etc. The truth-value set, , of FL is assumed to be generated by a context-free grammar, with a semantic rule providing a means of computing the meaning of each linguistic truth-value in (...) as a fuzzy subset of [0, 1].Since is not closed under the operations of negation, conjunction, disjunction and implication, the result of an operation on truth-values in requires, in general, a linguistic approximation by a truth-value in . As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very, quite, more or less, etc. (shrink)

In many areas of scientific inquiry, the phenomena under investigation are viewed as functions on the real numbers. Since observational precision is limited, it makes sense to view these phenomena as bounded functions on the rationals. One may translate the basic notions of recursion theory into this framework by first interpreting a partial recursive function as a function on Q. The standard notions of inductive inference carry over as well, with no change in the theory. When considering the class of (...) computable functions on Q, there are a number of natural ways in which to define the distance between two functions. We utilize standard metrics to explore notions of approximate inference — our inference machines will attempt to guess values which converge to the correct answer in these metrics. We show that the new inference notions, NV∞, EX∞, and BC∞, infer more classes of functions than their standard counterparts, NV, EX, and BC. Furthermore, we give precise inclusions between the new inference notions and those in the standard inference hierarchy. We also explore weaker notions of approximate inference, leading to inference hierarchies analogous to the EXn and BCn hierarchies. Oracle inductive inference is also considered, and we give sufficient conditions under which approximate inference from a generic oracle G is equivalent to approximate inference with only finitely many queries to G. (shrink)

Using the World Values Survey (WVS) as a background the paper discusses a tension between the general evaluative outlook of Swedish teacher students and the educational values established by The Swedish National Agency for Education (SNAE). According to the results from WVS, which maps evaluative differences between approximately 80 countries in the world, Sweden stands out as a country that rejects traditional values and embraces so called secular self-expression values. However, the values established by SNAE include both traditional values, such (...) as “sharing a common cultural heritage”, and secular self-expression values, such as “individual freedom and integrity”. Against this background we conducted a survey of 179 Swedish teacher students in order to investigate the relation between their evaluative outlook and the values they are supposed to convey to their pupils as established by SNAE. The result of the survey indicates that these students do not differ in any significant respect from the Swedish population in general as regards secular vs traditional evaluations. The fact that the traditional values emphasized by SNAE seem to be scarcely represented among the teacher students, makes questionable whether they will be present in their future teaching. On the assumptions that there are important educational values among the traditional as well as the secular self-expression ones, and that values are reproduced within an educational system, we argue that there is reason to take the imbalance in the evaluative outlook of the students seriously. (shrink)

Given a locale L and any set-indexed family of continuous mappings , fi:L→Li with compact and completely regular co-domain, a compactification η:L→Lγ of L is constructed enjoying the following extension property: for every a unique continuous mapping exists such that . Considered in ordinary set theory, this compactification also enjoys certain convenient weight limitations.Stone–Čech compactification is obtained as a particular case of this construction in those settings in which the class of [0,1]-valued continuous mappings is a set for all L. (...) This will follow by the proof that–also in the point-free context–a compactification that allows for the extension of [0,1]-valued mappings suffices for deriving the full reflection.A constructive proof that the class is a set whenever L is locally compact and L′ is set-presented and regular is also obtained; together with the described compactification, this makes it possible to characterize the class of locales for which Stone–Čech compactification can be defined constructively. (shrink)

The Ganser syndrome, or talking past the point, (originally identifying symptoms of inmates on remand when questioned by prison doctors), is explored as a form of insubordination against the stigmatizing effects of overdetermined diagnostic categories. The strategies of approximation that characterize the syndrome are likened to comedy routines/vaudeville styles and to their employment of punning, clownery, and ambiguity to challenge the more privileged cultural values of clarity, literalness, and precision. The seeming craftiness of Ganserians is related to the aesthetic (...) tactics of the trickster figure and to the physical buffoonery of hysterics. Stylistically, this paper synthesizes the languages of critical theory, Gracie Allen routines, personal narrative, jokes, and poetic reflections on the notion of being approximate. (shrink)

We study and compare two combinatorial lowness notions: strong jump-traceability and well-approximability of the jump, by strengthening the notion of jump-traceability and super-lowness for sets of natural numbers. A computable non-decreasing unbounded function h is called an order function. Informally, a set A is strongly jump-traceable if for each order function h, for each input e one may effectively enumerate a set Te of possible values for the jump JA, and the number of values enumerated is at most h. A′ (...) is well-approximable if can be effectively approximated with less than h changes at input x, for each order function h. We prove that there is a strongly jump-traceable set which is not computable, and that if A′ is well-approximable then A is strongly jump-traceable. For r.e. sets, the converse holds as well. We characterize jump-traceability and strong jump-traceability in terms of Kolmogorov complexity. We also investigate other properties of these lowness properties. (shrink)

The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary “*” operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation of (...) Thomas–Fermi theory, and a new quantization rule which—unlike semiclassical quantization—is non-invariant under action transformations of the Hamiltonian, in the same qualitative manner as the true eigenvalues. The quasiclassical eigenvalues are shown to be significantly more accurate than the corresponding semiclassical values, for a variety of 1D and 2D systems. In addition, certain standard refinements of semiclassical theory are shown to be easily incorporated into the quasiclassical formalism. (shrink)

In this paper incomplete data sets, or data sets with missing attribute values, have three interpretations, lost values, attribute-concept values and ‘do not care’ conditions. Additionally, the process of data mining is based on two types of probabilistic approximations, global and saturated. We present results of experiments on mining incomplete data sets using six approaches, combining three interpretations of missing attribute values with two types of probabilistic approximations. We compare our six approaches, using the error rate computed as a result (...) of ten-fold cross validation as a criterion of quality. We show that for some data sets the error rate is significantly smaller (5% level of significance) for lost values, for some data sets the smaller error rate is associated with attribute-concept values, and sometimes with ‘do not care’ conditions. Again, for some approaches the error rate is significantly smaller for saturated probabilistic approximations than for global probabilistic approximations, while for some approaches it is the other way around. Thus, for an incomplete data set, the best approach to data mining should be chosen by trying all six approaches. (shrink)

This paper explores the value of skepticism towards the Approximate Number System (ANS). I sketch some of the main arguments levied against ANS-based interpretations of numerical cognition data and argue that there are empirical and conceptual reasons to reject wholesale replacement of the ANS with an Analog Magnitude System (AMS). To simplify the discussion, I focus for the most part on a recent critical review representative of this new wave of revisionist skepticism (Leibovich, T., Katzin, N., Harel, M., & (...) Henik, A., 2017). I start with a brief review of some of the reasons offered to deny that experiments studying our numerical abilities reveal the presence of a system dedicated to representing quantities of discrete objects, before turning briefly to empirical responses to these worries. I then offer a few reflections on why even if the empirical rebuttal were to fail, there are conceptual reasons to doubt that we are only equipped with an AMS. While some of these reasons involve methodological implications of AMS-based theories, other conceptual reasons to doubt AMS skepticism revolve around how ANS-skepticism seems to go against the history of the relation between the continuous and the discrete, and how one cannot be derived from the other. I then end with a potential reply to my worries involving an appeal to the Object-File System (OFS) as a source of discrete content in our numerical abilities and find it wanting. (shrink)

This paper addresses a common challenge with computational cognitive models: identifying parameter values that are both theoretically plausible and generate predictions that match well with empirical data. While computational models can offer deep explanations of cognition, they are computationally complex and often out of reach of traditional parameter fitting methods. Weak methodology may lead to premature rejection of valid models or to acceptance of models that might otherwise be falsified. Mathematically robust fitting methods are, therefore, essential to the progress of (...) computational modeling in cognitive science. In this article, we investigate the capability and role of modern fitting methods—including Bayesian optimization and approximate Bayesian computation—and contrast them to some more commonly used methods: grid search and Nelder–Mead optimization. Our investigation consists of a reanalysis of the fitting of two previous computational models: an Adaptive Control of Thought—Rational model of skill acquisition and a computational rationality model of visual search. The results contrast the efficiency and informativeness of the methods. A key advantage of the Bayesian methods is the ability to estimate the uncertainty of fitted parameter values. We conclude that approximate Bayesian computation is (a) efficient, (b) informative, and (c) offers a path to reproducible results. (shrink)

This paper develops an explicit, pragmatic solution to the problem of deciding when an explanans which only approximately "covers" a desired event-explanandum E is acceptable as an adequate explanation. It shows in detail how comparisons made by the explanation's audience with the numerical value in E are what determine how closely E must be approximated for success. With the aid of several physics examples, it spells out the principles that govern these explanandum-comparisons, the conditions under which those principles hold, (...) and the audience traits that influence which comparisons they take seriously. (shrink)

First, I show that the semantic thesis of scientific realism may be relaxed significantly—to allow that some scientific discourse is not truth-valued—without making any concessions concerning the epistemic or methodological theses that lie at realism’s core. Second, I illustrate how relaxing the semantic thesis allows realists to avoid positing abstract entities and to fend off objections to the “no miracles” argument from positions such as cognitive instrumentalism. Third, I argue that the semantic thesis of scientific realism should be relaxed because (...) it is possible for scientific statements to be partially true, and hence approximately true, without being false. (shrink)

Fulford has argued that (1) the medical concepts illness, disease and dysfunction are inescapably evaluative terms, (2) illness is conceptually prior to disease, and (3) a model conforming to (2) has greater explanatory power and practical utility than the conventional value-free medical model. This ‘reverse’ model employs Hare's distinction between description and evaluation, and the sliding relationship between descriptive and evaluative meaning. Fulford's derivative ‘Values Based Medicine’ (VBM) readjusts the imbalance between the predominance of facts over values in medicine. (...) VBM allegedly responds to the increased choices made available by, inter alia, the progress of medical science itself. VBM attributes appropriate status to evaluative meaning, where strong consensus about descriptive meaning is lacking. According to Fulford, quasi-legal bioethics, while it can be retained as a kind of deliberative framework, is outcome-based and pursues ‘the right answer’, while VBM approximates a democratic, process-oriented method for dealing with diverse values, in partnership with necessary contributions from evidence-based medicine (EBM). I support the non-cognitivist underpinnings of VBM, and its emphasis on the importance of values in medicine. But VBM overstates the complexity and diversity of values, misrepresents EBM and VBM as responses to scientific and evaluative complexity, and mistakenly depicts ‘quasi-legal bioethics’ as a space of settled descriptive meaning. Bioethical reasoning can expose strategies that attempt to reduce authentic values to scientific facts, illustrating that VBM provides no advantage over bioethics in delineating the connections between facts and values in medicine. (shrink)

Many philosophers appeal to the “fallacy of approximation”, or “problem of second best”. However, despite the pervasiveness of such appeals, there has been only a single attempt to provide a systematic account of what the fallacy is. We identify the shortcomings of this account and propose a better one in its place. Our account not only captures all the contexts in which approximation-based reasoning occurs but also systematically explains the several different ways in which it can be in (...) error. (shrink)

FDE, LP and K3 are closely related to each other and admit of an intuitive informational interpretation. However, all these logics are co-NP complete, and so idealized models of how an agent can think. We address this issue by shifting to signed formulae, where the signs express imprecise values associated with two bipartitions of the corresponding set of standard values. We present proof systems whose operational rules are all linear and have only two structural branching rules that express a generalized (...) Principle of Bivalence. Each of these systems leads to defining an infinite hierarchy of tractable approximations to the respective logic, in terms of the maximum number of allowed nested applications of the two branching rules. Further, each resulting hierarchy admits of an intuitive 5-valued non-deterministic semantics. (shrink)

We define rational Hermite interpolants to vector-valued functions and show that, in the context of Clifford algebras, the numerator and denominator polynomials belong to a complex extension of the Lipschitz group. We also discuss the problem of constructing an algebraic representation for the generalized inverse of a vector, which is at the heart of the usual development of vector rational approximation.

The identification of regularities in time-dependent functional structures leads to turn patterns, observed according to a given time resolution, into functional attractors on which it is first possible to found any complex system. Rationality is introduced under the form of probabilities for functions to make up a given attractor beyond the first rough descriptive pattern. These physically characterized attractors are the medium enabling the definition of value as an extension of the Prospect Theory overall utility, considering that the actions (...) produced by their functions are outcomes which are modulated by PT psychological value functions and an operational value appears naturally as an optimization taking account of diminishing sensitivity to action efficiency. Nevertheless, this diminishing sensitivity, when applied to negative actions, introduces also a bias of negative externalities underestimation. An attractor-based complex system evolution in an industrial context is described according to Manufacturing Readiness Level and to the main milestones of an industrial project, corresponding to singular points of maturity expressed in terms of probability—or decision—weighting, up to the system release to the market. So, a maturity assessment heuristics is proposed both for the system development and for its marketing. The supply and demand law is established, highlighting that the ideal case of a purely mature economy can be a good approximation reducing the complexity of the exchanges analysis. Equilibria are discussed as depending on an initial point from which the usual Gaussian probability distribution and a speculative weight qualify equilibrium. (shrink)

The depth-bounded approach seeks to provide realistic models of reasoners. Recognizing that most useful logics are idealizations in that they are either undecidable or likely to be intractable, the approach accounts for how they can be approximated in practice by resource-bounded agents. The approach has been applied to Classical Propositional Logic (CPL), yielding a hierarchy of tractable depth-bounded approximations to that logic, which in turn has been based on a KE/KI system. -/- This Thesis shows that the approach can be (...) naturally extended to useful nonclassical logics such as First-Degree Entailment (FDE), the Logic of Paradox (LP), Strong Kleene Logic (K3 ) and Intuitionistic Propositional Logic (IPL). To do this, we introduce a KE/KI-style system for each of those logics such that: is formulated via signed formulae, consist of linear operational rules and branching structural rule(s), can be used as a direct-proof and a refutation method, and is interesting independently of the approach in that it has an exponential speed-up on its tableau system counterpart. The latter given that we introduce a new class of examples which we prove to be hard for all tableau systems sharing the V/& rules with the classical one, but easy for their analogous KE-style systems. Then we focus on showing that each of our KE/KI-style systems naturally yields a hierarchy of tractable depth-bounded approximations to the respective logic, in terms of the maximum number of allowed nested applications of the branching rule(s). The rule(s) express(es) a generalized rule of bivalence, is (are) essentially cut rule(s) and govern(s) the manipulation of virtual information, which is information that an agent does not hold but she temporarily assumes as if she held it. Intuitively, the more virtual information needs to be invoked via the branching rule(s), the harder the inference is for the agent. So, the nested application the branching rule(s) provides a sensible measure of inferential depth. We also show that each hierarchy approximating FDE, LP, and K3 , admits of a 5-valued non-deterministic semantics; whereas, paving the way for a semantical characterization of the hierarchy approximating IPL, we provide a 3-valued non-deterministic semantics for the full logic that fixes the meaning of the connectives without appealing to “structural” conditions. -/- Moreover, we show a super-polynomial lower bound for the strongest possible version of clausal tableaux on the well-known class of “truly fat” expressions (which are easy for KE), settling a problem left open in the literature. Further, we investigate a hierarchy of tractable depth-bounded approximations to CPL based only on KE. Finally, we propose a refinement of the p-simulation relation which is adequate to establish positive results about the superiority of a system over another with respect to proof-search. (shrink)

ABSTRACT: We argue that the so-called ‘Primary’ and ‘Secondary’ Value Problems for knowledge are more easily solved than is widely appreciated. Pritchard, for instance, has suggested that only virtue-theoretic accounts have any hopes of adequately addressing these problems. By contrast, we argue that accounts of knowledge that are sensitive to the Gettier problem are able to overcome these challenges. To first approximation, the Primary Value Problem is a problem of understanding how the property of being knowledge confers (...) more epistemic value on a belief than the property of being true. The Secondary Value is a problem of understanding how, for instance, property of being knowledge confers more epistemic value on a belief than the property of being jointly true and justified. We argue that attending to the fact that beliefs are ongoing states reveals that there is no difficulty in appreciating how knowledge might ordinarily have more epistemic value than mere true belief or mere justified true belief. We also explore in what ways ordinary cases of knowledge might be of distinctive epistemic value. In the end, our proposal resembles the original Platonic suggestion in the Meno that knowledge is valuable because knowledge is somehow tied to the good of truth. (shrink)

The main goal of publicly funded biomedical research is to generate social value through the creation and application of knowledge that can improve the well-being of current and future people. Prioritising research with the greatest potential social value is crucial for good stewardship of limited public resources and ensuring ethical involvement of research participants. At the National Institutes of Health (NIH), peer reviewers hold the expertise and responsibility for social value assessment and resulting prioritisation at the project (...) level. However, previous research has shown that peer reviewers place more emphasis on a study’s methods (‘Approach’) than on its potential social value (best approximated by the criterion of ‘Significance’). Lower weighting of Significance may be due to reviewers’ views on the relative importance of social value, their belief that social value is evaluated at other stages of the research priority-setting process or the lack of guidance on how to approach the challenging task of assessing expected social value. The NIH is currently revising its review criteria and how these criteria contribute to overall scores. To elevate the role of social value in priority setting, the agency should support empirical research on how peer reviewers approach the assessment of social value, provide more specific guidance for reviewing social value and experiment with alternative reviewer assignment strategies. These recommendations would help ensure that funding priorities align with the NIH’s mission and the obligation of taxpayer-funded research to contribute to the public good. (shrink)

In this analysis, we develop a new approach to investigate the semianalytical solution of the delay differential equations. Mohand transform coupled with the homotopy perturbation method is called Mohand homotopy perturbation transform method and performs the solution results in the form of series. The beauty of this approach is that it does not need to compute the values of the Lagrange multiplier as in the variational iteration method, and also, there is no need to implement the convolution theorem as in (...) the Laplace transform. The main purpose of this scheme is to reduce the less computational work and the error analysis of the problems than others studied in the literature. Some illustrated examples are interpreted to confirm the accuracy of the newly developed scheme. (shrink)

Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A (...) is false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

Background: People in both Taiwan and China originally descended from the Han Chinese, but the societies have been separated for approximately 38 years. Due to different political systems, variations exist in healthcare and nursing education systems in Taiwan and China. Objective: The purpose of this study was to examine the professional values of nursing students in Taiwan and China. Design: A cross-sectional design was applied in this study. The Nursing Professional Value Scale–Revised was used to measure the professional values (...) of the students. The questionnaire was distributed to eligible undergraduate students in a classroom setting. Ethical considerations: This study was approved by the Institutional Review Board at the first investigator’s university. Participants were informed that completion and return of the questionnaire was voluntary, and confidentiality was ensured by keeping the responses anonymous. Participants: A convenience sample included 292 Taiwanese students and 654 Chinese students. Findings: A total of 11 individual Nursing Professional Value Scale–Revised items showed significant differences between the two groups. These results reflect the differences in the perceived importance of these items between the groups. There was no significant difference between the two groups in the mean overall scores for the Nursing Professional Value Scale–Revised (p =.766) and three subscales (all p >.05). Conclusion: There are some differences in professional values between nursing students in Taiwan and China. Given the increasingly frequent and close interactions between Taiwan and China and the globalization of nursing, understanding these differences may help nursing educators identify students’ perceptions of their professional values and support the development of strategies to improve weaknesses in professional values. (shrink)

It is shown that in a range of models, the probability that a forager dies from starvation is, to a good approximation, an exponential function of energy reserves. Using a time and energy budget for a 19g passerine, we explore the consequences, in terms of starvation and predation, of various levels of energy reserves. It is shown that there exists an optimal level L of reserves at which total mortality (starvation plus predation) is minimized. L increases when the environment (...) deteriorates as a result of a decrease in either temperature or mean gross gain or an increase in the mean search time. The effect of combined deteriorations is greater than the sum of their individual effects. At L, the probability of predation is much higher than the probability of starvation. A simple analytic model suggests that this result will be fairly general, but also indicates conditions under which the result might not hold. (shrink)

We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order (...) to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely. (shrink)

Since the late 1990s, the number of apologies being offered by CEOs of large companies has exploded. Communication and management scholars have analyzed whether and why some of these apologies are more effective or more ethical than others. Most of these analyses, however, have remained at the anecdotal level. Moreover, the practical, economic consequences of apologies have not been examined. Almost no rigorous or systematic empirical work exists that examines whether stakeholders reward firms whose CEOs give apologies that are more, (...) rather than less, ethical; and punish firms whose corporate apologies are not ethically sound. This lacuna is surprising given that the whole purpose of an apology is to restore trust between the apologizer and the recipients of the apology. It is also surprising, given that stock market participants do appear, in at least some cases, to evaluate and respond to apologies by CEOs. When Johnson and Johnson was hit by the Tylenol poisonings, its stock price plummeted. One day after CEO James Burke’s apology—an apology widely praised for being ethically sound—approximately a half billion dollars of its previously lost stock value was restored. It appears, then, that a good CEO apology may lead to an increased stock value ceteris paribus. But is the Johnson and Johnson case representative of how the market responds in general to CEO apologies? (shrink)

As an initial approximation, pluralism may be understood as the combination of four theses. First, there are many incommensurable values whose realization is required for living a good life. Second, these values often conflict with each other, and, as a result, the realization of some excludes the realization of others. Third, there is no authoritative standard that could be appealed to to resolve such conflicts, because there is also a plurality of standards; consequently, no single standard would be always (...) acceptable to all fully informed and reasonable people. Fourth, there are, nevertheless, reasonable ways of resolving conflicts among incommensurable values. (shrink)

Excerpt from A Study in the Theory of Value The thesis which I wish to defend in the present essay is a very common one, believed, I think, by most people, but usually only approximately and only half-heartedly, and expressed vaguely if expressed at all. Some such belief is in fact present whenever we reflect upon acts that stir our interest; but the belief baldly expressed in propositions sounds fanciful or weak or sentimental, and we avoid pronouncing it clearly (...) in much the same way as that in which we hurry over an expression in an unfamiliar language - partly from modesty, but. Mostly from fear of appearing ridiculous and from inner conviction Of ignorance. Our belief, in other words, not Only seems to us sentimental and weak when we approach the formulation of it in a creed, but it actually is sentimental and weak when thus formulated, and this for the reason that we have not taken the trouble to make the formulation accurate or definite. On the one hand we are afraid of seeming. Sentimental; on the other hand we do not know what our belief really is, nor what definite formula embodying it will stand the test of logical criticism. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

The Lee, Oehme and Yang (LOY) theory of time evolution in two state subspace of states of the complete system is discussed. Some inconsistencies in the assumptions and approximations used in the standard derivation of the LOY effective Hamiltonian, HLOY, governing this time evolution are found. Eliminating these inconsistencies and using the LOY method, approximate formulae for the effective Hamiltonian, H||, governing the time evolution in this subspace (improving those obtained by LOY) are derived. It is found, in contradistinction to (...) the standard LOY result, that in the case of neutral kaons (〈K 0 |H|||K 0 〉−〈¯K 0 |H|||¯K 0 〉), cannot take the zero value if the total system the preserves CPT-symmetry. Within the use of the method mentioned above formulae for H|| acting in the three state (three dimensional) subspace of states are also found. (shrink)

This essay considers Judy Wajcman’s book Pressed for Time: The Acceleration of Life in Digital Capitalism and an edited volume by her and Nigel Dodd entitled The Sociology of Speed: Digital, Organizational, and Social Temporalities. The essay claims that the two books challenge the one-dimensional and somewhat deterministic notion of a blanket, all-encompassing social acceleration dynamic, purportedly enveloping the whole of modernity, by offering new conceptual insights and empirical illustrations. Not only do the currently fashionable perspectives on acceleration in the (...) social sciences overlook the nuances in temporal experience and the inextricable link between “fast” and “slow,” they also neglect the emerging temporal divisions inherent in the expansive nature of new information and communication technologies. Both books, in addressing such nuances and divisions, represent key landmarks in the sociology of time/speed and contribute significantly to the emerging social study of temporal transformation. (shrink)

The method of approximate reasoning using a fuzzy logic introduced by Baldwin (1978 a,b,c), is used to model human reasoning in the resolution of two well known paradoxes. It is shown how classical propositional logic fails to resolve the paradoxes, how multiple valued logic partially succeeds and that a satisfactory resolution is obtained with fuzzy logic. The problem of precise representation of vague concepts is considered in the light of the results obtained.

Cost-benefit analysis —understood as a technique for evaluating governmental policies in light of individual well-being—rests upon a preference view of welfare. A policy’s effect on a given individual is measured, on a money scale, with reference to her preferences as between money and other goods, captured in her “utility” function. This chapter describes the methodology of CBA, and discusses the various conditions on individual preferences that are required for the existence of an individual utility function, for the use of money (...) as a scale for measuring policy effects, and for a nexus between an individual’s preference-satisfaction and her well-being. The chapter then turns to the topic of interpersonal welfare comparisons. Although CBA is often defended with reference to the criterion of Kaldor-Hicks efficiency, which eschews such comparisons, a more plausible defense embraces them and sees CBA as an approximation to a social welfare function. (shrink)

The example can be generalized. Suppose that ϕ and ψ are suffi- ciently different functions of an independent variable t. We may show that whenever X’s predictions for ϕ and ψ lie (weakly) between Z’s predictions and T’s predictions (the true values), then there are other quantities, interdefinable with ϕ and ψ, that reverse the ordering.

Most people interested in the problems of ethics aspire to two kinds of knowledge, one systematic, the other historical. They wish a systematic understanding of the field: knowledge of what are the various problems and their interrelations and knowledge of what has been done toward the solution of these problems. They also wish to learn what the great historical philosophers -- particularly those who have had the most important ideas about values and conduct -- have said about the subject. This (...) book is intended to enable the reader to approximate the achievement of these twin goals at once. (shrink)