odel-L¨ ob computability logic. In order to make things relatively self-contained, I sketch the essential ideas of GL, and discuss the significance of its fixpoint theorem. Then I give the algorithm embodied in the program in a little more detail. It should be emphasized that nothing new is presented here — all the theory and methodology are due to others. The main interest is, in a sense, psychological. The approach taken here has been declared in the literature, more than once, (...) to be of theoretical interest only, being too unwieldly in practice. Experimentation shows this is not so provided formulas are not too complicated. A copy of the program can be obtained by ftp from venus.gc.cuny.edu. It is in the subdirectory “/pub/fitting,” under the name “glfixpt.pro.” Log on as “anonymous” and use your full e-mail address as password. If there are difficulties with ftp, send e-mail to the author at mlfl[email protected]. The Prolog code is standard, and should run under any implementation, though minor modifications may be necessary for some systems. These modifications are described in the last section, and also in the program itself. (shrink)

We present a logic programming language, which we call Proflog, with an operational semantics based on tableaus, and a denotational semantics based on supervaluations. We show the two agree. Negation is well-behaved, and semantic non-computability issues do not arise. This is accomplished essentially by dropping a domain closure requirement. The cost is that intuitions developed through the use of classical logic may need modification, though the system is still classical at a level once removed. Implementation problems are discussed very briefly (...) — the thrust of the paper is primarily theoretical. (shrink)

The paper presents and discusses the so-called Wrong Kind of Reasons Problem (WKR problem) that arises for the fitting-attitudes analysis of value. This format of analysis is exemplified for example by Scanlon's buck-passing account, on which an object's value consists in the existence of reasons to favour the object- to respond to it in a positive way. The WKR problem can be put as follows: It appears that in some situations we might well have reasons to have pro-attitudes toward objects (...) that are not valuable. Or vice versa: we might have reasons not to have pro-attitudes toward some valuable objects. The paper goes through several attempts to solve (or dissolve) the WKR problem and argues that none of them is fully satisfactory. (shrink)

This study examines the relationship among the employees–organization pro-environmental values fit, supervisors’ PEVs and employees’ pro-environmental behaviors. Informed by the PEB, organizational values and employee–organization fit literature, we propose and test hypotheses that under egoistic, altruistic and biosphere-value orientations, E–O PEVs fit versus non-fit have significant effects on employees’ private-sphere PEB and public-sphere PEB, identifying supervisors’ PEVs as a moderator. An empirical investigation indicates that the effect of E–O PEVs fit on employees’ private-sphere PEB and public-sphere PEB varies as the (...) value orientation differs. More specifically, under the context of altruistic and biosphere-value orientations, if the organizational PEVs do not match the employees’ PEVs, especially when the former exceeds the latter, employees’ PEB will rise as the organizational PEVs increase. As for egoistic value orientation, when organizational PEVs exceed employees’ PEVs, not only will public-sphere PEB stop decreasing and tend to stabilize, but also private-sphere PEB will rise to a slight degree. Furthermore, compared with altruistic and biospheric values dimensions, supervisors who promote egoistic PEVs will have a more significant effect on the relationship between global E–O PEVs fit and employees’ PEB. Finally, we suggest that the goals of an organization and its supervisors need to be combined within the actual situation of Chinese corporations to truly implement corporate green practices by balancing the profit goal and the environmental goal. (shrink)

In this paper, I argue for Fit, a prudential version of the claim that attitudes must fit their objects, the claim that there is an extra benefit when one's reactions fit their objects. I argue that Fit has surprising and powerful consequences for theories of well-being. Classic versions of the objective list theory, hedonism, desire views, and loving-the-good theories do not accommodate Fit. Suitable modifications change some of the views substantially. Modified views give reactions a robust role as sources of (...) well-being, and they accept that objects call for some attitudes but not others. I argue that objective list theories and loving-the-good theories require the most minimal changes to accommodate Fit, so we have a pro tanto reason to favor these views over alternatives. (shrink)

According to an influential tradition in value analysis, to be valuable is to be a fitting object of a pro-attitude – a fitting object of favoring. If it is fitting to favor an object for its own sake, then, in this view, the object has final value. If it is fitting to favor an object for the sake of its effects, then its value is instrumental. Disvalue is connected in the analogous way to disfavoring, i.e., to con-attitudes. For a history (...) of this fitting-attitudes analysis, or FA-analysis for short, see the following text. The label itself was coined rather recently, though, in Rabinowicz and Rønnow-Rasmussen. (shrink)

According to an influential tradition in value analysis, to be valuable is to be a fitting object of a pro-attitude – a fitting object of favoring. If it is fitting to favor an object for its own sake, then, in this view, the object has final value. If it is fitting to favor an object for the sake of its effects, then its value is instrumental. Disvalue is connected in the analogous way to disfavoring, i.e., to con-attitudes. For a history (...) of this fitting-attitudes analysis, or FA-analysis for short, see the following text. The label itself was coined rather recently, though, in Rabinowicz and Rønnow-Rasmussen. (shrink)

A fitting-attitude analysis which understands value in terms of reasons and pro- and con-attitudes allows limited wriggle room if it is to respect a radical division between good and good-for. Essentially, its proponents can either introduce two different normative notions, one relating to good and the other to good-for, or distinguish two kinds of attitude, one corresponding to the analysis of good and the other to good-for. It is argued that whereas the first option faces a counterintuitive scope issue, an (...) attitudinal approach couched in terms of ‘for someone's sake’ attitudes has the unwelcome consequence that whatever is good for someone is also necessarily good. It is argued that this consequence can be avoided if we modify the standard way of formulating the fitting-attitude analysis of final impersonal value. (shrink)

Susan Wolf has developed a promising answer to the problem of the meaning of – or better in – life’. Wolf’s hybrid-view of meaning in life can be briefly summarized by the catchphrase: ‘meaning arises when subjective attraction meets objective attractiveness’. Accordingly, on her account, both an objective and a subjective element are needed for a life to be meaningful. For the objective element at least four characteristics can be identified in Wolf’s writings: the element must be subject-independent (independency claim), (...) it must ground the subject’s fulfilment (grounding claim), the subject must be able to recognize it as source of fulfilment (possibility of recognition claim) and the subject can be fallible regarding this recognition (possibility of fallibility claim). Apart from this, Wolf is silent about objectivity. This is a gap in her account. Additionally, objectivity seems to be a highly metaphysically burdened category. Therefore, searching for an alternative account might be worthwhile. I argue that objectivity should be replaced by rationality. Judgments about meaning in life are evaluative judgments. It is argued that evaluations are expressions of pro- or con-attitudes and that these expressions can be rational. If one has a pro-attitude towards a certain project of one’s life, and if it is rational to have it, then there is to that extent meaning in life. So, meaning arises when subjective attraction meets rational attractiveness. (shrink)

Orsi and Garcia argue that fitting-attitude analysis of value is vulnerable to an explanatory objection. On FA-analysis, for an object to be valuable is for it to be a fitting target of an attitude—a pro-attitude if its value is positive and a con-attitude if it is negative. For different kinds of value different kinds of attitudes are fitting: desire for desirability, admiration for admirability, etc. To explain the fittingness relation we therefor need to appeal to the features of the relevant (...) attitude, but these seldom, if ever, are needed for explaining the object’s value. This explanatory disparity between the analysans and the analysandum implies that FA-analysis must be incorrect. In our reply to Orsi and Garcia, we provide a refutation of their objection. We argue that the features of a fitting attitude do have a right place in the explanation of an object’s value, even though they are not among the properties that make the object valuable. They help to explain this value-making relation itself. (shrink)

According to the “fitting-attitudes” (FA) account of value, for a thing to be valuable is for it to be the fitting object of a pro-attitude. Value here is analyzed in terms of reasons for and against favoring, admiring, desiring, preferring, loving, etc. a thing. Whichever particular FA analysis you prefer, the basic idea is just that a thing’s value depends on extant reasons to be favorably (or disfavorably) disposed toward it. Of course, proponents of FA analyses deny that just any (...) such reasons suffice to ground a thing’s value. The reasons must be of the right sort. If I threaten to stab you in the face unless you become favorably disposed toward Rob Schneider movies, you now have a reason to do just that. But it seems clear that while my threat does make Rob Schneider movies to you worth liking, it does not make them valuable or good. The difficulty then is to distinguish the right kind of reasons from the wrong kind. Several writers have recently tried to offer principled ways of resolving the so-called “wrong kind of reasons” (WKR) problem, though I will not closely examine them here. Instead I wish to focus on one particular FAaccount of value whom some have suggested is immune to WKR-style problems, specifically the one Michael Zimmerman offers in The Nature of Intrinsic Value. I argue that even Zimmerman’s account incurs WKR difficulties, and that it can actually help illustrate a certain deep problem with FA accounts in general. (shrink)

The detrimental effect of human behavior on the environment is undeniable. Attitudes are recognized as a predictor of the pro-environmental behavior; therefore, having good quality tools in Colombia to measure them is strategic to assess interventions. This study aims to establish psychometric indicators for the pro-environmental attitudes questionnaire Colombian version to a sample of 415 volunteers aged 18–70 years. We used the 28-item PEAQ already linguistically adapted for Colombia. We applied the following questionnaires: Environmental awareness, environmental values, and the pro-environmental (...) at work questionnaire. We used a one-parameter Rasch model and Winsteps program to assess the PEAQ's one-dimensionality and item statistics by gender, and estimated Spearman's rho coefficient between the PEAQ scores and the scales for concurrent validity. The PEAQ in this study has 24 items because 4 items did not fit into the Rasch model criteria. Its one-dimensionality was supported by an explained variance and the first residual variance. The coefficients, α = 0.95 and Ω = 0.95; Rasch for persons = 0.90; and Rasch for items = 0.95. The correlation between the PEAQ and the EC, EV, and PEWQ scales were Spearman's rho coefficient = 0.859, 0.795, and 0.885, respectively. Thus, the PEAQ Colombian version's psychometric indicators support it as a valid and reliable instrument to measure pro-environmental attitudes in this country. (shrink)

It is tempting to think that all of normativity, such as our reasons for action, what we ought to do, and the attitudes that it is fitting for us to have, derives from what is valuable. But value-first approaches to normativity have fallen out of favour as the virtues of reasons- and fittingness-first approaches to normativity have become clear. On these views, value is not explanatorily prior to reasons and fit; rather the value of things is understood in terms of (...) the pro-attitudes it is fitting to have, or that we have reasons to have, towards these things. The value-first accounts of reasons and fit that have been proposed have been direct accounts of reasons and fit. On these views, the fittingness of an attitude is explained in terms of the value of having it or the value of the object of that attitude. This chapter details and surveys these problems, explaining which are yet to be overcome, and explaining which problems direct value-first accounts can overcome. This chapter then explores the prospects of an indirect value-first account of reasons and fit. It argues that it avoids the problems that direct value-first accounts face and may be as explanatorily powerful as fittingness- and reasons-first accounts of value and normativity more generally. (shrink)

The objective of the study was to develop a structural model that explores the relationship between Mathematics Performance and students’ self-regulated learning skills, grit, and expectancy-value towards science, technology, engineering and mathematics (STEM). The research collected survey data from 664 senior high school students from 17 STEM high schools, and conducted a covariance-based structural equation modeling (SEM) analysis. The results of the SEM analysis indicate that the Re-specified Self-Regulated Learning Skill – Expectancy-Value towards STEM – Grit – Mathematics Performance (Re-specified (...) SRL-EV-GR-MP) model is the most parsimonious fit, offering the best empirical support for the theoretical model of the study. The research findings suggest that the mathematics performance of senior high school students in STEM curriculum is attributed to their high expectancies for success and perceived values of the STEM tasks, high grit, and high self-regulated learning skills. Moreover, the research also observed evidence of mediating and moderating grit effects in the concurrent effects of expectancy-values towards STEM and self-regulated learning skills towards students’ mathematics performance. (shrink)

The paper argues that Toni Rønnow-Rasmussen’s fitting-attitude analysis of ‘good’ and ‘good for’ allows us to interpret and justify Kant’s Formula of Humanity (FH) in a constructive way. His classification of ‘good’ as a non-relational intrinsic final value and ‘good for’ as a relational extrinsic final value sheds light on two main features of FH, namely that it requires us to display a specific attitude to human beings, while also obligating us to recognize this value in the relational dimension. Based (...) on a reflection of what attitudes toward persons are fitting, we might well come to endorse that persons are “ends in themselves” and merit respect and recognition. I then argue (by way of an ethical reading of Kant’s demand to leave the state of nature and move to a rightful civil condition) that we have, in addition to a fitting attitude, deontic normative reasons (not mere pro tanto reasons) for making this very attitude toward persons the principal standard for our relations to others and to ourselves. (shrink)

The purpose of this study was to determine the applicability of Buddhist practices in today’s workplaces. The findings were supported by interviews with Buddhist masters and Buddhist business practitioners, as well as literature review, through phenomenological analysis. As a means of presenting the main reasons why Buddhist practices should be considered in contemporary workplaces, a SWOT analysis is presented. In this analysis, a number of strengths for using Buddhist practices in workplaces are listed such as pro-scientific, greater personal responsibility, and (...) healthy detachment, while potential weaknesses such as non-harming, equanimity, and no competition are also reviewed. Both the strengths and the weaknesses could be listed in reverse if applied to a different extent. Among the opportunities were issues such as re-educating the world of business, enhancing personal ownership and a healthier society, while the threats comprised issues such as creating different imbalances, disinterest, and stationary development. (shrink)

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

ObjectiveTo determine to what extent physical fitness indicators and/or moderate to vigorous physical activity may account for final mathematics academic performance awarded at the end of primary school.MethodsSchool-aged youth were sampled in a repeated-measures, longitudinal design in Grade 6, and again in Grade 9. The youth completed a fitness test battery consisting of: flamingo balance test, standing long jump, backward obstacle course, plate tapping, sit ups, sit and reach, handgrip, and 20-m shuttle run. APmath scores were obtained for all children (...) at the end of Grade 5, end of Grade 8, and end of Grade 9. In a sub-sample of Grade 6 youth, MVPA was measured objectively via SenseWear Pro Armbands for seven consecutive days, with measurements repeated in Grade 9.ResultsMath scores decreased from Grade 6 to 9 for both boys and girls. MVPAOB was reduced by ∼45.7 min from Grade 6 to 9. Significant main and interaction effects are noted for each fitness indicator. A backward stepwise multiple regression analysis determined significant shared variance in final APmath grade to the change scores from Grade 6 to Grade 9 in: ΔAPmath, Δbackward obstacle course, Δsit and reach, and Δsit-ups [R2 = 0.494, F = 43.67, p < 0.0001]. A second regression was performed only for the youth who completed MVPAOB measurements. In this sub-sample, MVPAOB did not significantly contribute to the model.ConclusionLongitudinal changes in youth fitness and their delta change in APmath score accounted for 49.4% of the variance in the final math grade awarded at the end of Grade 9. Aerobic power, upper body strength, and muscular endurance share more common variance to final math grade in boys, whereas whole-body coordination was the more relevant index in girls; this finding suggests that future research exploring the relationship of AP and PF should not be limited to cardiorespiratory fitness, instead encompassing muscular and neuro-muscular components of PF. (shrink)

Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap’s four-valued logic, based on classical two-valued logic. Among other examples are those based on finite many-valued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical two-valued setting, but the result provides (...) a natural semantics for distributed logic programs, including those involving confidence factors. The classical two-valued and the Kripke/Kleene three-valued semantics become special cases, since the logics involved are natural sublogics of Belnap’s logic, the logic given by the simplest bilattice. (shrink)

A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences.

Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established.

Bilattices, introduced by M. Ginsberg, constitute an elegant family of multiple-valued logics. Those meeting certain natural conditions have provided the basis for the semantics of a family of logic programming languages. Now we consider further restrictions on bilattices, to narrow things down to logic programming languages that can, at least in principle, be implemented. Appropriate bilattice background information is presented, so the paper is relatively self-contained.

Suppose there are several experts, with some dominating others (expert A dominates expert B if B says something is true whenever A says it is). Suppose, further, that each of the experts has his or her own view of what is possible — in other words each of the experts has their own Kripke model in mind (subject, of course, to the dominance relation that may hold between experts). How will they assign truth values to sentences in a common modal (...) language, and on what sentences will they agree? This problem can be reformulated as one about many-valued Kripke models, allowing many-valued accessibility relations. This is a natural generalization of conventional Kripke models that has only recently been looked at. The equivalence between the many-valued version and the multiple expert one will be formally established. Finally we will axiomatize many-valued modal logics, and sketch a proof of completeness. (shrink)

Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.

One approach to the paradoxes of self-referential languages is to allow some sentences to lack a truth value (or to have more than one). Then assigning truth values where possible becomes a fixpoint construction and, following Kripke, this is usually carried out over a partially ordered family of three-valued truth-value assignments. Some years ago Matt Ginsberg introduced the notion of bilattice, with applications to artificial intelligence in mind. Bilattices generalize the structure Kripke used in a very natural way, while making (...) the mathematical machinery simpler and more perspicuous. In addition, work such as that of Yablo fits naturally into the bilattice setting. What I do here is present the general background of bilattices, discuss why they are natural, and show how fixpoint approaches to truth in languages that allow self-reference can be applied. This is not new work, but rather is a summary of research I have done over many years. (shrink)

In a forthcoming paper, Walter Carnielli and Abilio Rodrigues propose a Basic Logic of Evidence whose natural deduction rules are thought of as preserving evidence instead of truth. BLE turns out to be equivalent to Nelson’s paraconsistent logic N4, resulting from adding strong negation to Intuitionistic logic without Intuitionistic negation. The Carnielli/Rodrigues understanding of evidence is informal. Here we provide a formal alternative, using justification logic. First we introduce a modal logic, KX4, in which \ can be read as asserting (...) there is implicit evidence for X, where we understand evidence to permit contradictions. We show BLE embeds into KX4 in the same way that Intuitionistic logic embeds into S4. Then we formulate a new justification logic, JX4, in which the implicit evidence motivating KX4 is made explicit. KX4 embeds into JX4 via a realization theorem. Thus BLE has both implicit and explicit possibly contradictory evidence interpretations in a formal sense. (shrink)

Strict/tolerant logic is a formally defined logic that has the same consequence relation as classical logic, though it differs from classical logic at the metaconsequence level. Specifically, it does not satisfy a cut rule. It has been proposed for use in work on theories of truth because it avoids some objectionable features arising from the use of classical logic. Here we are not interested in applications, but in the formal details themselves. We show that a wide range of logics have (...) strict/tolerant counterparts, with the same consequence relations but differing at the metaconsequence level. Among these logics are Kleene’s K3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {K_3}$$\end{document}, Priest’s LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf {LP}}$$\end{document}, and first-degree entailment, FDE. The primary tool we use is the bilattice. But it is more than a tool, it seems to be the natural home for this kind of investigation. (shrink)

Nested sequent systems for modal logics are a relatively recent development, within the general area known as deep reasoning. The idea of deep reasoning is to create systems within which one operates at lower levels in formulas than just those involving the main connective or operator. Prefixed tableaus go back to 1972, and are modal tableau systems with extra machinery to represent accessibility in a purely syntactic way. We show that modal nested sequents and prefixed modal tableaus are notational variants (...) of each other, roughly in the same way that tableaus and Gentzen sequent calculi are notational variants. This immediately gives rise to new modal nested sequent systems which may be of independent interest. We discuss some of these, including those for some justification logics that include standard modal operators. (shrink)

This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This paper provides (...) much background, but is not self-contained. Some results from [9] are called on, and are not reproved here. [9] Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic. Online. Print publication forthcoming. (shrink)

The variety of semantical approaches that have been invented for logic programs is quite broad, drawing on classical and many-valued logic, lattice theory, game theory, and topology. One source of this richness is the inherent non-monotonicity of its negation, something that does not have close parallels with the machinery of other programming paradigms. Nonetheless, much of the work on logic programming semantics seems to exist side by side with similar work done for imperative and functional programming, with relatively minimal contact (...) between communities. In this paper we summarize one variety of approaches to the semantics of logic programs: that based on fixpoint theory. We do not attempt to cover much beyond this single area, which is already remarkably fruitful. We hope readers will see parallels with, and the divergences from the better known fixpoint treatments developed for other programming methodologies. (shrink)

First - order modal logic is very much under current development, with many different semantics proposed. The use of rigid objects goes back to Saul Kripke. More recently, several semantics based on counterparts have been examined, in a development that goes back to David Lewis. There is yet another line of research, using intensional objects, that traces back to Richard Montague. I have been involved with this line of development for some time. In the present paper, I briefly sketch several (...) of the approaches to first - order modal logic. Then I present one that I call FOIL in the Montague tradition that, I believe, is both expressive and natural. I briefly discuss in what sense it can be made to encompass the other approaches. Finally, I provide tableau rules to go with the FOIL semantics. (shrink)

There is an obvious difference between what a term designates and what it means. At least it is obvious that there is a difference. In some way, meaning determines designation, but is not synonymous with it. After all, “the morning star” and “the evening star” both designate the planet Venus, but don't have the same meaning. Intensional logic attempts to study both designation and meaning and investigate the relationships between them.