ObjectivesPhysical activity has been shown to protect executive functions against the deleterious effects of poorer sleep among older adults ; however, it is unknown whether memory is protected too, and if this relationship differs by age. The present study investigated the relationship between cardiorespiratory fitness, sleep, and memory in both older and young adults.MethodsThis observational study recruited 26 OA and 35 YA. Participants completed the Rockport 1-mile walk test to evaluate cardiorespiratory fitness. Participants wore an actigraph (...) for 1 week to measure habitual sleep and returned for a second visit to perform the memory tests. The interaction between cardiorespiratory fitness and sleep to predict memory was assessed separately in OA and YA.ResultsIn OA, cardiorespiratory fitness significantly moderated the relationship between memory and sleep quality, specifically number of nighttime awakenings, sleep efficiency, and wake after sleep onset. Further analyses reveal that a high number of nighttime awakenings and low sleep efficiency significantly predicted worse memory performance in the low fit OA, but high fit OA. Notably, every nighttime awakening was associated with a nearly 4% decrease in memory in low fit OA, but not high fit OA. Wake after sleep onset did not significantly predict memory in either fitness group. No interaction was found when looking at sleep duration or self-report sleep quality in OA and no significant interactions were observed between fitness, sleep, and memory in YA.ConclusionOverall, the results suggest that cardiorespiratory fitness may act as a protective buffer for memory in OA with poor sleep quality. These same was not true for YA suggesting that the protective effects of cardiorespiratory fitness on sleep-related memory impairments may be age specific. (shrink)

The current study examined the effects of cardiorespiratory fitness, identified with a continuous graded cycle ergometry, and aerobic exercise on cognitive functioning and entropy of the electroencephalogram (EEG) in 30 adolescents between the ages of 13 and 14 years. Higher and lower fit participants performed an executive function task after a bout of acute exercise and after rest while watching a film. EEG entropy, using the sample entropy measure, was repeatedly measured during the 1500ms post-stimulus interval to evaluate (...) changes in entropy over time. Analysis of the behavioural data for lower and higher fit groups revealed an interaction between fitness levels and acute physical exercise. Notably, lower fit, but not higher fit, participants had higher error rates for NoGo relative to Go trials in the rest condition, whereas in the acute exercise condition there were no differences in error rates between groups; higher fit participants also had significantly faster reaction times in the exercise condition in comparison with the rest condition. Analysis of EEG data revealed that higher fit participants demonstrated lower entropy post-stimulus than lower fit participants in the left frontal hemisphere, possibly indicating increased efficiency of early stage stimulus processing and more efficient allocation of cognitive resources to the task demands. The results suggest that EEG entropy is sensitive to stimulus processing demands and varies as a function of physical fitness levels, but not acute exercise. Physical fitness, in turn, may enhance cognition in adolescence by facilitating higher functionality of the attentional system in the context of lower levels of frontal EEG entropy. (shrink)

The functional neural mechanisms underlying the cognitive benefits of aerobic exercise have been a subject of ongoing research in recent years. However, while most neuroimaging studies to date which examined functional neural correlates of aerobic exercise have used simple stimuli in highly controlled and artificial experimental conditions, our everyday life experiences require a much more complex and dynamic neurocognitive processing. Therefore, we have used a naturalistic complex information processing fMRI paradigm of story comprehension to investigate the role of an aerobically (...) active lifestyle in the processing of real-life cognitive-demanding situations. By employing the inter-subject correlation approach, we have identified differences in reliable stimulus-induced neural responses between groups of aerobically active and non-active cognitively intact older adults. Since cardiorespiratory fitness has previously been suggested to play a key role in the neuroprotective potential of aerobic exercise, we have investigated its dose-response relationship with regional inter-subject neural responses. We found that aerobically active lifestyle and cardiorespiratory fitness were associated with more synchronized inter-subject neural responses during story comprehension in higher order cognitive and linguistic brain regions in the prefrontal and temporo-parietal cortices. In addition, while higher regional inter-SC values were associated with higher performance on a post-listening memory task, this was not translated to a significant between-group difference in task performance. We, therefore, suggest that the modulatory potential of aerobic exercise and cardiorespiratory fitness on cognitive processing may extend beyond simple and highly controlled stimuli to situations in which the brain faces continuous real-life complex information. Additional studies incorporating other aspects of real-life situations such as naturalistic visual stimuli, everyday life decision making, and motor responses in these situations are desired to further validate the observed relationship between aerobic exercise, cardiorespiratory fitness, and complex naturalistic information processing. (shrink)

Associations between cardiorespiratory fitness and brain health in healthy older adults have been reported using a variety of cardiorespiratory fitness estimates. Using commonly used methods to determine CRF, we assessed the relationship between CRFe and executive function performance. Healthy older adults, underwent three CRF tests: a Maximal Graded Exercise Test performed on a cycle ergometer, the Rockport Fitness Walking Test, and a Non-Exercise Prediction Equation. Executive function was assessed by a computerized cognitive assessment using an (...) N-Back task and a Stroop task. Multiple hierarchical regression analyses were conducted to assess the relationship between different CRFe and executive function performance. Regardless of age and education, cardiorespiratory fitness estimated from the Maximal Graded Exercise Test and the Rockport Fitness Walking Test was significantly associated with the global switch cost. All CRFe were associated with the interference cost. No association was observed between CRFe and local switching costs or the updating costs. In the present study, not all subcomponents of executive function were related to CRFe. Interestingly, the executive functions that were associated with CRFe are those that are known to be the most affected by aging. (shrink)

Physical literacy has received considerable attention in the field of physical education and physical activity worldwide. According to recent studies, the level of physical fitness among Chinese university students is gradually decreasing. This study aims to examine the impact of the PF level on PA and PL, as well as the relationships among PF, PA, and PL, in Chinese university students. Participants comprised 798 university students in Chongqing, China. Participants completed the tests of vital capacity, cardiorespiratory fitness, (...) muscular strength, and flexibility, according to the National Physical Fitness Measurement Standards Manual, as well as questionnaires on PA and PL. The independent t-tests were conducted to examine sex differences in the evaluated variables, and the Pearson’s correlation between each PF test and PL attributes and PA was calculated according to sex. In addition, the independent t-tests were conducted to determine whether the PF level had an effect on PL attributes and PA at various intensities. Significant sex differences were found in the PF domains of vital capacity, muscular strength, and aerobic fitness, with higher scores in men than in women, but not in the PF domain of flexibility and total PL score. Furthermore, the PF domains of muscular strength and aerobic fitness were significantly and positively correlated with the PL attributes of confidence and physical competence in both men and women, while the PF domains of vital capacity and aerobic fitness were significantly and positively correlated with the PL attribute of motivation in men. In addition, PL was significantly and positively associated with cardiorespiratory fitness, vital capacity, muscular strength, and flexibility among participants in the fit group. These findings support advocating for increased participation in PA in university students and using PL as a tool to improve PF components. (shrink)

AimThe aim of our study was to analyze physical activity levels, sitting time, physical fitness, and their relationship with depressive symptoms after home confinement in previously active older adults.MethodsThis cross-sectional study sample comprised 68 older adults from a community-based exercise program conducted in Porto, Portugal. After home confinement, participants were assessed in person for lower-body strength, cardiorespiratory fitness, agility/dynamic balance, handgrip strength, and anthropometry. Telephone interviews were performed to evaluate depressive symptoms with the Geriatric Depression Scale – (...) 15 items and physical activity levels through the International Physical Activity Questionnaire. Individuals were also asked to self-report changes in their physical activity levels and time spent sitting.ResultsNinety percent of older adults self-reported a decrease in overall physical activity levels, and nearly 65% increased daily sitting time during the home confinement. However, previously active older adults still presented high levels of physical fitness after 11 weeks of home confinement. Overall, 52.9% of participants scored 5 or more points on GDS-15, which is suggestive of depression. Higher levels of moderate-to-vigorous physical activity and cardiorespiratory fitness were found in the non-depressed group compared with the depressed group. Finally, results from multiple regression analysis revealed that MVPA was negatively associated with depression. This model explained 16.4% of the variability seen in depression score, controlled for age, gender, and education.ConclusionEven reporting a decline in physical activity, older adults who previously participated in a formal exercise program, still presented high levels of physical fitness after 11 weeks of home confinement. However, MVPA, but not physical fitness, seems to be an associated depression score in previously active older adults. These results reinforce the importance of older adults to remain physically active, since higher levels of MVPA may have a protective effect on depressive symptoms and, therefore, mitigate the negative impact of home confinement on mental health. Future longitudinal research studies are needed to ascertain these results. (shrink)

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)

BackgroundPhysical activity and Physical fitness have received tremendous attention in the field of physical and mental health. However, limited attention has been given to the associations of self-reported physical fitness with some health-related outcomes. Given the COVID-19 pandemic is still active in many Chinese regions, assessing health-related physical fitness in adolescents using field-based assessment is unrealistic, therefore, this study was conducted via a self-reported questionnaire.PurposeThe present cross-sectional study was aimed at delving into the relationship between self-reported physical (...) fitness with self-rated health, depression, anxiety, and body satisfaction in adolescents. Three thousand eight hundred and seven study participants from 12 public schools in South-eastern China were recruited and 2,407 of them provided valid data on variables that this study needed for analysis.Materials and methodsStudy participants were asked to self-report their sociodemographic factors, independence, and outcomes. Generalized linear models were used to explore the associations of self-reported physical fitness with depression, anxiety, and body satisfaction. A total of 2,407 children and adolescents with a mean age of 13.82 years were included in the final study analysis.ResultsHigher self-reported levels of general physical fitness and cardiorespiratory fitness were associated with better self-rated health, and body satisfaction but with lower risks of depression and anxiety.ConclusionThe current study offered evidence on the roles of self-reported physical fitness and health-related outcomes. To facilitate health in children and adolescents, advocating fitness education, and promotion could be a feasible approach. (shrink)

Physical activity, body composition and sedentary behavior may affect the health of children. Therefore, this study examined the effect of an educational hybrid physical education program on physical fitness, body composition and sedentary and PA times in adolescents. A 9-month group-randomized controlled trial was conducted in 150 participants allocated into the control group and experimental group. Cardiorespiratory fitness, speed, strength, agility, flexibility and body mass index were assessed through previously validated field tests. Sedentary time, PA at school (...) and afterschool were evaluated with the Youth Activity Profile-Spain questionnaire. Significant differences were observed concerning to the CG in APA-weekend, speed-agility and agility. Regarding the intervention, cardiorespiratory fitness, speed-agility, strength, flexibility, agility, PA in school, APA-weekday, APA-weekend, APA-week, and sedentary time increased significantly in the EG. The use of a hybrid program based on teaching personal and social responsibility and gamification strategies produced enhancements in cardiorespiratory fitness, agility, speed, APA-weekdays and APA-weekends, reducing the sedentary time. (shrink)

Assessing physical fitness has emerged as a proxy of the health status of children and adolescents and therefore as relevant from a public health point of view. DAFIS is a project included in Plan Galicia Saudable of the regional government of Galicia. DAFIS consists of an on-line software devoted to record the results of a standard physical fitness protocol carried out as a part of the physical education curriculum. The aims of this study were: to obtain normative values (...) of physical fitness of the Galician school population evaluated in the DAFIS project, and to identify a reduced number of components and tests able to capture a significant amount of the variability in the physical fitness of children and adolescents. From an initial sample of 27784 records, 15287 cases were considered after filtering. Generalized Additive Models for Location, Scale and Shape were used for obtaining percentile curves and tables for each sex. Furthermore, a principal components analysis was performed, selecting the number of components by applying the Kaiser’s rule and selecting a subset of variables considering the correlation between each variable and the components. Percentile curves and normative values are reported for each test and sex. Physical fitness was better in boys than in girls throughout age groups, except for flexibility that was consistently higher in girls. Two main components were detected throughout age groups: the first one representing body composition and partially cardiorespiratory fitness and the second one muscular fitness. For boys and girls, waist to height ratio had the highest correlations with the first component in four out of six age groups. The highest correlation with the second component, was most frequently observed for the handgrip test both in boys and girls. This study provides evidence about the utility of school community actions like DAFIS aimed to track the health-related fitness of children and adolescents. The results suggest that fat mass distribution and muscular performance concentrate a high proportion physical fitness variance. (shrink)

Consistent findings about the inverse association of social network level with coronary heart disease mortality and morbidity suggest the importance of investigating biological pathways of association. Differences in plasma fibrinogen level were investigated among middle-aged men with weak and strong structural and functional social network ties. Men with low scores in the adequacy of social participation variable (structural) had higher mean values of plasma fibrinogen than those with high scores. The difference remained after adjustment for age, smoking and cardiovascular health (...) status and after possible modifying factors were taken into account, but did not remain significant after allowing for physical fitness. Men with high scores in overall support (functional) had higher plasma fibrinogen levels compared to the men with low scores. This difference persisted after age and cardiovascular health status were taken into account but was explained by smoking. The data suggest that smoking and cardiorespiratory fitness are important mediating or modifying factors between structural and functional aspects of social network ties and plasma fibrinogen. (shrink)

ObjectiveTo assess the impact of the closure of group-based cardiac rehabilitation training during the first COVID-19 lockdown in spring 2020 on patients’ physical activity, cardiorespiratory fitness, and cardiovascular risk, and to describe the patient experience of lockdown and home-based exercise training during lockdown.DesignMixed methods study. Prospectively collected post-lockdown measurements were compared to pre-lockdown medical record data. Quantitative measurements were supplemented with qualitative interviews about the patient experience during lockdown.SettingOutpatient CR centre in Salzburg, Austria.ParticipantsTwenty-seven patients [six female, mean age (...) 69 years] who attended weekly CR training sessions until the first COVID-19 lockdown in March 2020.Outcome MeasureQuantitative: exercise capacity, cardiovascular risk. Qualitative: individual semi-structured interviews.ResultsExercise capacity had significantly reduced from pre- to post-lockdown: mean power in maximal ergometry 165 vs. 151, p < 0.001; submaximal ergometer training 99 vs. 97, p = 0.038. There was no significant difference in Framingham risk score and other cardiovascular risk factors. Qualitative data showed that almost all patients had kept physically active during lockdown, but 17 said they had been unable to maintain their exercise levels, and 15 felt their cardiorespiratory fitness had deteriorated. Many patients missed the weekly CR training and the motivation and sense of community from training together with others. Several patients stated that without professional supervision they had felt less confident to carry out home-based exercise training at high intensity.ConclusionThis study highlights the importance of group-based supervised exercise training for patients who engage well in such a setting, and the detrimental impact of disruption to this type of CR service on physical activity levels and exercise capacity. Additionally, learning from the COVID-19 pandemic may inform the development and implementation of remote CR modalities going forward. (shrink)

Previous research has explored the intensity of dance class, rehearsal and performance, and attempted to document the body’s physiological adaptation to these activities. Dance activity is frequently described as: complex, diverse, non-steady state, intermittent, of moderate to high intensity, and with notable differences between training and performance intensities and durations. Many limitations are noted in the methodologies of previous studies creating barriers to consensual conclusion. The present study therefore aims to examine the previous body of literature and in doing so, (...) seeks to highlight important methodological considerations for future research in this area to strengthen our knowledge base. Four recommendations are made for future research. Firstly, research should continue to be dance genre specific, with detailed accounts of technical and stylistic elements of the movement vocabulary examined given wherever possible. Secondly, a greater breadth of performance repertoire, within and between genres, needs to be closely examined. Thirdly, a greater focus on threshold measurements is recommended due to the documented complex interplay between aerobic and anaerobic energy systems. Lastly, it is important for research to begin to combine temporal data relating to work and rest periods with real-time measurement of metabolic data in work and rest, in order to be able to quantify demand more accurately. (shrink)

Background: The new human coronavirus that leads to COVID-19 has spread rapidly around the world and has a high degree of lethality. In more severe cases, patients remain hospitalized for several days under treatment of the health team. Thus, it is important to develop and use technologies with the aim to strengthen conventional therapy by encouraging movement, physical activity, and improving cardiorespiratory fitness for patients. In this sense, therapies for exposure to virtual reality are promising and have been (...) shown to be an adequate and equivalent alternative to conventional exercise programs.Aim: This is a study protocol with the aim of comparing the conventional physical therapy intervention with the use of a non-immersive VR software during COVID-19 hospitalization.Methods: Fifty patients hospitalized with confirmed diagnosis of COVID-19 will be divided in two groups under physiotherapy treatment using conventional or VR intervention: Group A: participants with COVID-19 will start the first day of the protocol with VR tasks in the morning and then in the second period, in the afternoon, will perform the conventional exercises and Group B: participants with COVID-19 will start the first day with conventional exercises in the morning and in the second period, in the afternoon, will perform activity with VR. All participants will be evaluated with different motor and physiologic scales before and after the treatment to measure improvements.Conclusion: Considering the importance of benefits from physical activity during hospitalization, VR software shows promise as a potential mechanism for improving physical activity. The results of this study may provide new insights into hospital rehabilitation.Trial Registration:ClinicalTrials.gov, identifier: NCT04537858. Registered on 01 September 2020. (shrink)

A well-known problem with Hintikka-style logics of knowledge is that of logical omniscience. One knows too much. This breaks down into two subproblems: one knows all tautologies, and one’s knowledge is closed under consequence. A way of addressing the second of these is to move from knowledge simpliciter, to knowledge for a reason. Then, as consequences become ‘further away’ from one’s basic knowledge, reasons for them become more complex, thus providing a kind of resource measurement. One kind of reason is (...) a formal proof. Sergei Artemov has introduced a logic of explicit proofs, LP. I present a semantics for this, based on the idea that it is a logic of knowledge with explicit reasons. A number of fundamental facts about LP can be established using this semantics. But it is equally important to realize that it provides a natural logic of more general applicability than its original provenance, arithmetic provability. (shrink)

The family of all stable models for a logic program has a surprisingly simple overall structure, once two naturally occurring orderings are made explicit. In a so-called knowledge ordering based on degree of definedness, every logic program P has a smallest stable model, sk P — it is the well-founded model. There is also a dual largest stable model, S k P, which has not been considered before. There is another ordering based on degree of truth. Taking the meet and (...) the join, in the truth ordering, of the two extreme stable models sk P and S.. (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.

In the tech report Artemov and Yavorskaya [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting [5]. We also give an Mkrtychev semantics. Motivation and intuition (...) for FOLP can be found in Artemov and Yavorskaya [4], and are not fully discussed here.This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with. (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.

LP can be seen as a logic of knowledge with justifications. See [S. Artemov, The logic of justification, The Review of Symbolic Logic 1 477–513] for a recent comprehensive survey of justification logics generally. Artemov’s Realization Theorem says justifications can be extracted from validities in the more conventional Hintikka-style logic of knowledge S4, in which they are not explicitly present. Justifications, however, are far from unique. There are many ways of realizing each theorem of S4 in the logic LP. If (...) the machinery of justifications is to be applied to artificial intelligence, or better yet, to everyday reasoning, we will need to work with whatever justifications we may have at hand—one version may not be interchangeable with another, even though they realize the same S4 formula. In this paper we begin the process of providing tools for reasoning about justifications directly. The tools are somewhat complex, but in retrospect this should not be surprising. Among other things, we provide machinery for combining two realizations of the same formula, and for replacing subformulas by equivalent subformulas. The results are algorithmic in nature—semantics for LP plays no role. We apply our results to provide a new algorithmic proof of Artemov’s Realization Theorem itself. This paper is a much extended version of [M.C. Fitting, Realizations and LP, in: S. Artemov, A. Nerode , Logical Foundations of Computer Science—New York ’07, in: Lecture Notes in Computer Science, vol. 4514, Springer-Verlag, 2007, pp. 212–223]. (shrink)

Many powerful logics exist today for reasoning about multi-agent systems, but in most of these it is hard to reason about an infinite or indeterminate number of agents. Also the naming schemes used in the logics often lack expressiveness to name agents in an intuitive way.To obtain a more expressive language for multi-agent reasoning and a better naming scheme for agents, we introduce a family of logics called term-modal logics. A main feature of our logics is the use of modal (...) operators indexed by the terms of the logics. Thus, one can quantify over variables occurring in modal operators. In term-modal logics agents can be represented by terms, and knowledge of agents is expressed with formulas within the scope of modal operators. (shrink)

Kripke’s work on modal logic has been immensely influential. It hardly needs remarking that this is not his only work. Here we address his pioneering applications of fixpoint constructions to the theory of truth, and related work by others. In his fundamental paper on this he explicitly described a modal version, applying a fixpoint construction world by world within a modal frame. This can certainly be carried out, and doubtless has been somewhere. Others have suggested a variety of other extensions (...) such as using the unit interval as the underlying space of truth values, or using a four valued logic instead of three, or various combinations of these. When many similar formal constructions have been proposed, one naturally asks what is the common core. Is there some setting in which things can be proved once and for all, with the various specific proposals seen as applications of this common core. In fact this is the case, with bilattices providing the desired structure. Much of such a development has already appeared in some form or other. It is the purpose of this article to bring everything together, and also add a few things. We present general results that, more or less, have everything currently in the fixpoint literature as special cases. Fortunately this does not make things more complicated, since the underlying proofs are essentially the same as they have always been. It is just that they are being carried out in generality rather than in specificity. (shrink)

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.

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)

Strict/tolerant logic, ST, evaluates the premises and the consequences of its consequence relation differently, with the premises held to stricter standards while consequences are treated more tolerantly. More specifically, ST is a three-valued logic with left sides of sequents understood as if in Kleene’s Strong Three Valued Logic, and right sides as if in Priest’s Logic of Paradox. Surprisingly, this hybrid validates the same sequents that classical logic does. A version of this result has been extended to meta, metameta, … (...) consequence levels in Barrio et al.. In my earlier paper Fitting I showed that the original ideas behind ST are, in fact, much more general than first appeared, and an infinite family of many valued logics have Strict/Tolerant counterparts. This family includes both Kleene’s and Priest’s logic individually, as well as first degree entailment. For instance, for both the Kleene and the Priest logic, the corresponding strict/tolerant logic is six-valued, but with differing sets of strictly and tolerantly designated truth values. The present paper extends that generalization in two directions. We examine a reverse notion, of Tolerant/Strict logics, which exist for the same structures that were investigated in Fitting. And we show that the generalization extends through the meta, metameta, … consequence levels for the same infinite family of many valued logics. Finally we close with remarks on the status of cut and related rules, which can actually be rather nuanced. Throughout, the aim is not the philosophical applications of the Strict/Tolerant idea, but the determination of how general a phenomenon it is. (shrink)

We introduce a subclass of Kripke's fixed points in which falsehood is the preferred truth value. In all of these the truthteller evaluates to false, while the liar evaluates to undefined (or overdefined). The mathematical structure of this family of fixed points is investigated and is shown to have many nice features. It is noted that a similar class of fixed points, preferring truth, can also be studied. The notion of intrinsic is shown to relativize to these two subclasses. The (...) mathematical ideas presented here originated in investigations of so-called stable models in the semantics of logic programming. (shrink)

Classical first-order logic can be extended in two different ways to serve as a foundation for mathematics: introduce higher orders, type theory, or introduce sets. As it happens, both approaches have natural analogs for quantified modal logics, both approaches date from the 1960’s, one is not very well-known, and the other is well-known as something else. I will present the basic semantic ideas of both higher order intensional logic, and intensional set theory. Before doing so, I’ll quickly sketch some necessary (...) background material from quantified modal logic. Except for standard material concerning propositional modal logics, the paper is essentially self-contained. (shrink)

While Kripke's original paper on the theory of truth used a three-valued logic, we believe a four-valued version is more natural. Its use allows for possible inconsistencies in information about the world, yet contains Kripke's development within it. Moreover, using a four-valued logic makes it possible to work with complete lattices rather than complete semi-lattices, and thus the mathematics is somewhat simplified. But more strikingly, the four-valued version has a wide, natural generalization to the family of interlaced bilattices. Thus, with (...) little more work, the theory is extended to a broad class of settings. Indeed, a result like Theorem 6.2 would not even be possible to state without the interlaced bilattice machinery. We hope the notion of interlaced bilattice will make apparent further such connections. (shrink)

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)

Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing (...) strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

A sequent calculus of a new sort is extracted from the Prolog program leanTAP. This calculus is sound and complete, even though it lacks almost all structural rules. Thinking of leanTAP as a sequent calculus provides a new perspective on it and, in some ways, makes it easier to understand. It is also easier to verify correctness and completeness of the Prolog implementation. In addition, it suggests extensions to other logics, some of which are considered here.

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)

This book describes computability theory and provides an extensive treatment of data structures and program correctness. It makes accessible some of the author's work on generalized recursion theory, particularly the material on the logic programming language PROLOG, which is currently of great interest. Fitting considers the relation of PROLOG logic programming to the LISP type of language.

A generalization of conventional Horn clause logic programming is proposed in which the space of truth values is a pseudo-Boolean or Heyting algebra, whose members may be thought of as evidences for propositions. A minimal model and an operational semantics is presented, and their equivalence is proved, thus generalizing the classic work of Van Emden and Kowalski.

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)

Participants maneuvered a rat image through a circular region on the computer screen to find a hidden target platform, blending aspects of two well-known spatial tasks. Like the Morris water maze task, participants first experienced a series of learning trials before having to navigate to the hidden target platform from different locations and orientations. Like the dot-location task, they determined the location of a position within a two-dimensional circular region. This procedure provided a way to examine how the number of (...) surrounding cues (1, 2, or 3) affects the memory for spatial location in navigation. Memory performance was better when there were more cues and when targets were close to cues, consistent with the idea that cues bolster fine-grain memory, especially in proximal regions. Early and late measures of bias in memory reflected biases in a direction toward the nearest cue, implicating a cue-based category structure of the navigational space. Collectively, results suggest cue-based spatial memory representations that have been inferred from the dot-location task generalize to a navigation task within a simple, computer-based environment, as demonstrated by the good fits of the spatial model developed for the dot-location task (Fitting, Wedell, & Allen, 2005, 2007). (shrink)

£ The existence of a model for a logic program is generally established by lattice-theoretic arguments. We present three examples to show that metric methods can often be used instead, generally in a direct, straightforward way. One example is a game program, which is not stratified or locally stratified, but which has a unique supported model whose existence is easily established using metric methods. The second example is a program without a unique supported model, but having a part that is (...) ‘well-behaved.’ The third example is a program in which one part depends on another, illustrating how modularity might be treated metrically. Finally we use ideas from this third example to prove a general result from [3]. The intention in presenting these examples and the theorem is to stimulate interest in.. (shrink)

This is an expository paper in which the basic ideas of a family of Justification Logics are presented. Justification Logics evolved from a logic called LP, introduced by Sergei Artemov [1, 3], which formed the central part of a project to provide an arithmetic semantics for propositional intuitionistic logic. The project was successful, but there was a considerable bonus: LP came to be understood as a logic of knowledge with explicit justifications and, as such, was capable of addressing in a (...) natural way long-standing problems of logical omniscience. Since then, LP has become one member of a family of related logics, all logics of knowledge with explicit knowledge terms. In this paper the original problem of intuitionistic foundations is discussed only briefly. We concentrate entirely on issues of reasoning about knowledge. (shrink)