A logic of intervals is proposed akin to the one published by Hamblin (Hamblin (1969) and (1971)). Like Hamblin's, the present system is also based on a single primitive. However, the work presented here differs from Hamblin's in a number of respects. Most importantly, the present system is explicitly based on mereological ideas in such a way that not only are the two notions of abutment and temporal order involved in Hamblin's primitive two-place relation "abuts at the earlier end" distinguished (...) ; the temporal ordering itself is built up from a symmetric mereological primitive. The present system is shown to be complete. (shrink)

We present the interval-valued intuitionistic fuzzy ordered weighted cosine similarity measure in this paper, which combines the interval-valued intuitionistic fuzzy cosine similarity measure with the generalized ordered weighted averaging operator. The main advantage of the IVIFOWCS measure provides a parameterized family of similarity measures, and the decision maker can use the IVIFOWCS measure to consider a lot of possibilities and select the aggregation operator in accordance with his interests. We have studied some of its main properties and particular (...) cases such as the interval-valued intuitionistic fuzzy ordered weighted arithmetic cosine similarity measure and the interval-valued intuitionistic fuzzy maximum cosine similarity measure. The IVIFOWCS measure not only is a generalization of some similarity measure, but also it can deal with the correlation of different decision matrices for interval-valued intuitionistic fuzzy values. Furthermore, we present an application of IVIFOWCS measure to the group decision-making problem. Finally the existing similarity measures are compared with the IVIFOWCS measure by an illustrative example. (shrink)

This work focuses on a multiagent system with time-varying interval uncertainty in the system matrix, where multiple agents interact through an undirected topology graph and only the bounding matrices on the uncertainty in the system matrix are known. A reduced-order interval observer, which is named the reduced-order neighborhood interval observer, is designed to estimate the relative state of each agent and those of its neighbors. It is shown that the reduced-order IO can guarantee the consensus of the (...) uncertain multiagent system. Finally, simulation examples are proposed to verify the theoretical findings. (shrink)

Starting from a connected, partially ordered set of events, it is shown that results of the measurement of time are elements of a partially ordered and filtering field, as used in a previous paper. Moreover, some relations between physical formulas and properties of the field are proved. Finally, some open problems and suggestions are pointed out. For the convenience of the reader not acquainted with elementary algebraic methods, proofs are given in detail.

We consider a new fragment of first-order logic with two variables. This logic is defined over interval structures. It constitutes unary predicates, a binary predicate and a function symbol. Considering such a fragment of first-order logic is motivated by defining a general framework for event-based interval temporal logics. In this paper, we present a sound, complete and terminating decision procedure for this logic. We show that the logic is decidable, and provide a NEXPTIME complexity bound for satisfiability. This (...) result shows that even a simple decidable fragment of first-order logic has NEXPTIME complexity. (shrink)

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.

Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems enable us to verify validity and entailment of these temporal logics. We show how to incorporate in the systems various relations between intervals (...) and/or various time orderings. (shrink)

According to the local risk-neutrality theorem an agent who has the opportunity to invest in an uncertain asset does not buy it or sell it short iff its expected value is equal to its price, independently of the agent's attitude towards risk. Contrary to that it is shown that, in the context of expected utility theory with differentiable vNM utility function, but without the assumption of stochastic constant returns to scale, nondegenerate intervals of no-trade prices may exist. With a quasiconcave (...) expected utility function they do if, and only if, the agent is risk averse of order one. (shrink)

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic (...) completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, Łukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates. (shrink)

The notion of emergence has accompanied philosophy of science since the late XIX century, claiming that in some systems there are properties in certain levels that cannot be deduced from properties of their components as seen in more fundamental levels. Throughout the XX century, emergence has been characterized by four pillars: unpredictability, novelty, restriction and downward causation. These four pillars have been related to the assumption of a hierarchical order of reality in different levels of organization. In this paper, we (...) show that it is possible to explain the nature of the emergent properties through the nearly-decomposability criterion introduced by Herbert Simon. (shrink)

In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for (...) short). It combines features of the classical tableau method for first-order logic with those of explicit tableau methods for modal logics with constraint label management, and it can be easily tailored to most propositional interval temporal logics proposed in the literature. We prove its soundness and completeness, and we show how it has been implemented. (shrink)

Let κ be a regular cardinal, and let B be a subalgebra of an interval algebra of size κ. The existence of a chain or an antichain of size κ in B is due to M. Rubin (see [7]). We show that if the density of B is countable, then the same conclusion holds without this assumption on κ. Next we also show that this is the best possible result by showing that it is consistent with 2 ℵ 0 (...) = ℵ ω 1 that there is a boolean algebra B of size ℵ ω 1 such that length(B) = ℵ ω 1 is not attained and the incomparability of B is less than ℵ ω 1 . Notice that B is a subalgebra of an interval algebra. For more on chains and antichains in boolean algebras see, e.g. [1] and [2]. (shrink)

Most of the descriptions of interval time structures in the first order predicate calculus are based on linear time. However, in the case of intervals, abandoning the condition oflinearity (e.g.LIN in van Benthem's systems) is not sufficient. In this paper, some properties of non-linear time structures are discussed. The most important one is the characterization of location of intervals in a fork of branches. This is connected with the fact that an interval can contain non-collinear subintervals. As a (...) result of non-linearity, some basic properties of interval structures must be formulated in a weaker form. Moreover, time must be filled by intervals to indicate that time cannot pass without events occurring in it. Finally, it is shown that when intervals cannot contain non-collinear subintervals, most of the conditions described in the paper are satisfied. (shrink)

The empirical-transcendental debate in philosophy of technology, as debates go, took a turn toward the counterposing of the two perspectives, ‘empirical’-pragmatic-pragmatist versus ‘transcendental’-critical. Postphenomenology aligns itself with the former standpoint, and it is in this spirit that commentators have criticized it for its too-instrumentalist stance and lack of overarching, i.e., transcendental orientation. But the positions may have become too starkly delineated in order for the debate to reach any breakthrough: a seemingly unbridgeable gap yawns between the stances of ‘technology with (...) a small “t”’ and ‘Technology with a capital “T.”' Is there any way to reorient the debate? In this paper I propose to do so by considering whether there would be some way of arriving from one end of the spectrum to the other—crossing the gap. Exploring the purported wasteland in between “technology” and “Technology” by way of object-oriented ontology (OOO)—Harman, Morton—we can find it actually filled with countless gaps, adhering to every thing. Following the radical insights of OOO, we’d have to attest to a ‘thing-transcendentality.’ The ‘gap,’ then, that seemed so threatening and all-encompassing, becomes smeared out, levelled down to a multiplicity of perspectives. And this casts the debate, with its purported strict tension between ‘empirical’ and ‘transcendental’ positions, in fresh terms, opening up new ways for studying how the two interrelate. (shrink)

Neither question (1) nor question (2) posed on page 446 have been adequately answered in this paper. Regarding (1) we have merely given functor maps onto the object languages of physical theories and regarding (2) we have merely described the algebraic structure of observables. A more satisfactory treatment will most likely involve (1) a generalization to algebraic categories, universal algebra and model theory in such a way as to capture the full inference structure of (perhaps van Fraassen's modal) quantum logic, (...) and (2) the introduction of the category of differentiable manifolds in order to capture the full symplectic structure of (perhaps Chernoff-Marsden's) Hamiltonian dynamics. (See van Fraassen [4] and Chernoff-Marsden [5] in Other References.)Finally, the intriguing suggestion of Finkelstein that “category theory is to metaphysics what group theory is to physics” deserves serious consideration. Indeed, although the theme has not been touched on explicitly in this paper it was central in motivating the project initially. However, it is more properly to be developed in a context external to a symposium on quantum logic. (shrink)

The purpose of this paper is to develop an approach to multiattribute group decision making under interval-valued hesitant fuzzy environment. To do this, this paper defines some new operations on interval-valued hesitant fuzzy elements, which eliminate the disadvantages of the existing operations. Considering the fact that elements in a set may be interdependent, two generalized interval-valued hesitant fuzzy operators based on the generalized Shapley function and the Choquet integral are defined. Then, some models for calculating the optimal (...) fuzzy measures on the expert set and the ordered position set are established. Because fuzzy measures are defined on the power set, it makes the problem exponentially complex. To simplify the complexity of solving a fuzzy measure, models for the optimal 2-additive measures are constructed. Finally, an investment problem is offered to show the practicality and efficiency of the new method. (shrink)

The objective of this study is to propose a new operation method based on the universal grey number to overcome the shortcomings of typical interval operation in solving system fault trees. First, the failure probability ranges of the bottom events are described according to the conversion rules between the interval number and universal grey number. A more accurate system reliability calculation is then obtained based on the logical relationship between the AND gates and OR gates of a fault (...) tree and universal grey number arithmetic. Then, considering an aircraft landing gear retraction system as an example, the failure probability range of the top event is obtained through universal grey operation. Next, the reliability of the aircraft landing gear retraction system is evaluated despite insufficient statistical information describing failures. The example demonstrates that the proposed method provides many advantages in resolving the system reliability problem despite poor information, yielding benefits for the function of the interval operation, and overcoming the drawback of solution interval enlargement under different orders of interval operation. (shrink)

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

Interval time-varying delay is common in control process, e.g., automatic robot control system, and its stability analysis is of great significance to ensure the reliable control of industrial processes. In order to improve the conservation of the existing robust stability analysis method, this paper considers a class of linear systems with norm-bounded uncertainty and interval time-varying delay as the research object. Less conservative robust stability criterion is put forward based on augmented Lyapunov-Krasovskii functional method and reciprocally convex combination. (...) Firstly, the delay interval is partitioned into multiple equidistant subintervals, and a new Lyapunov-Krasovskii functional comprising quadruple-integral term is introduced for each subinterval. Secondly, a novel delay-dependent stability criterion in terms of linear matrix inequalities is given by less conservative Wirtinger-based integral inequality approach. Three numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion. For the first example about closed-loop control systems with interval time-varying delays, the proposed robust stability criterion could get MADB about 0.3 more than the best results in the previous literature; and, for two other uncertain systems with interval time-varying delays, the MADB results obtained by the proposed method are better than those in the previous literature by about 0.045 and 0.054, respectively. All the example results obtained in this paper clearly show that our approach is better than other existing methods. (shrink)

In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and cardinality of the collection of initial intervals. The first theorem states that a partial order has no infinite antichains if and only if its initial intervals are finite unions of ideals. The second one asserts that a countable partial order is scattered and does not contain infinite antichains if and only if it has countably many initial intervals. (...) We show that the left to right directions of these theorems are equivalent to ACA0 and ATR0, respectively. On the other hand, the opposite directions are both provable in WKL0, but not in RCA0. We also prove the equivalence with ACA0 of the following result of Erdös and Tarski: a partial order with no infinite strong antichains has no arbitrarily large finite strong antichains. (shrink)

This paper presents a method to compute a posteriori probability intervals when the initial conditional information is also given with probability intervals. The right way to make an exact computation is with the associated convex set of probabilities. Probability trees are used to represent these initial conditional convex sets because they greatly save the space required. This paper proposes a simulated annealing algorithm, which uses probability trees to represent the convex sets in order to compute the a posteriori intervals.

Trapezoidal interval type-2 fuzzy sets are a special kind of type-2 fuzzy sets. TIT2FSs are useful in dealing with fuzziness inherent in decision data and the decision-making process. For multi-attribute group decision-making problems in which the attribute values and attribute weights are TIT2FSs, a new decision-making approach is proposed. On the basis of the concept of barycenters, a new approach to ranking TIT2FSs is given. Four kinds of geometric aggregation operators for TIT2FSs are developed, including the TIT2FS weighted geometric (...) average operator, TIT2FS ordered weighted geometric average operator, TIT2FS hybrid weighted geometric average operator, and extended TIT2FS hybrid weighted geometric average operator. The individual comprehensive values of alternatives are derived through the extended TIT2FS weighted geometric average operators. Using the TIT2FS hybrid weighted geometric average operator and the expert weights, the individual comprehensive values of alternatives are integrated into the collective ones, which are used to rank the alternatives. The practicability and effectiveness of the developed method are illustrated with a teaching quality assessment example. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Diacritics 31.3 (2001) 30-56 [Access article in PDF] The Priceless IntervalTheory in the Global Interstice Reingard Nethersole In a poignant scene in Goethe's Faust [1.2038-39] an eager student seeking what we would call curriculum advice today asks what subjects he should study. Counseled by Mephisto in the guise of the master, Faust, the student is admonished to read for anything but theory because: "Grey, my friend, is all theory, (...) / Green alone is life's golden tree." Uttered from within the epitome of an ivory tower image, a vaulted "gothic study," the advice gains rhetorical strength from alliterative, juxtaposed color metaphors which celebrate an organicist, holistic vision of life. Given current attitudes toward literary theory, many enthusiastic freshmen will receive similar guidance. Theoretical deliberation and mediation in the academy were not always popular, to be sure, but the resistance to theory was never as acute as it is now, when the very institutional space inhabited by thought is being curtailed largely because of financial considerations. Thus drawn into cost-benefit calculations that figure the student (in South Africa) as "client," the professor as "cost factor," and education as branded product, the University sees itself compelled, under the hegemony of the economic, to side with praxis in place of theory. "Doing" rather than thinking, action rather than reflection might have seemingly won the day, yet the controversy surrounding the relation between theory and literature on the one hand and theory and praxis on the other persists both inside and outside the academy.At the heart of a modern organization of knowledge, the dichotomy of theory and praxis is inscribed in Kant's Conflict of the Faculties. It will be remembered that Kant divided the domains of philosophy, theology, law, and medicine that constituted the University of his day into the "lower faculty," philosophy (lower from the point of view of government), and the "higher" faculties of theology, law, and medicine (higher because they are closer to government power). However, by granting philosophy (reason) implicit guardianship over the "higher faculties," lest these would revert to magical practices, Kant's Enlightenment philosophy placed a wedge between theory and praxis, a wedge that not only recast an ancient (Western) fissure between contemplation and action, a conscious I think and an active I do, but also opened a space for a troubled relationship between philosophy and the other faculties and between the faculties and state power—or as is the case today—economic power.Kant's university, of course, did not know the "humanities" of which history and literature were to become an integral part along with philosophy in the early nineteenth century, but by ranking reason below the utilitarian subjects or "faculties" while, at the same time, recognizing philosophy's preeminence as their imperative, Kant's positioning of thought/theory in relation to praxis 1 set up a tension between thinking and doing [End Page 30] that reverberates, for instance, in literary studies' perennial conflictual pairing between a "green" intuitive, untrammeled appreciation of literary texts and a "grey" theory. Moreover, supported by a particular modern, Western socioreligious structure (Protestantism) that values (bourgeois) industriousness or labor more than (aristocratic) leisure, the legacy of the "conflict of the faculties" implicates the connection between the university as institution of knowledge production in relation to the various domains of knowledge application and/or consumption.Concerned about the multiple changes that involve our being and acting in the world before an ever-expanding planetary horizon, which in turn profoundly alters the educational objective of institutions of higher learning in general and menaces such sites of thought as literary theory in particular, I shall, in the following, sketch the interval, a topos borrowed from musicological discourse, as a place for theory under global conditions. In addition I shall attempt to conjoin the disparate sides/sites of criticism and theory by cross-stitching Bill Readings's thoughts on the transformation of the university, descriptions of university "reform" currently under way in South Africa, and Goethe's text in order to illustrate the kind of subject/self produced by education or Bildung in contrast... (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

This paper provides variants of Arrow’s impossibility theorem, which states that there exists no non-dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi-order properties of semi-transitivity and the interval-order property. We prove that there exists a vetoer when the number of alternatives is greater than (...) or equal to six. (shrink)

Recently, Wilcox (JGPS 51: 65–87, 2020) argued against the so-called wide interval view and in favor of the principle of indifference as the correct response to unspecific evidence. Embedded in a formal model of the beliefs of an agent, the former presupposes imprecise probabilities and the latter numerically precise degrees of belief. His argument is illustrated by a thought experiment that comes with a fundamental intuition. According to Wilcox, the wide interval view is incompatible with this intuition and, (...) thus, undermined. In contrast, I show that the intuition behind the thought experiment is, in fact, compatible with the wide interval view if it is embedded into a specific conception of imprecise probabilities as model of belief. This conception is an extension of a framework which I call modified supervaluationism (MSV) and which I recently presented elsewhere (Karge 2021, 175–191). To accommodate the thought experiment’s fundamental intuition, it introduces a notion of second-order beliefs. (shrink)

Continuous environmental concerns regarding construction industry have been driving general constructors of mega infrastructure projects to incorporate green contractors. Although conventional multiple attributes decision-making methodologies have provided feasible ways to select contractor, high complexity in scenarios of megaprojects still challenges existing MADM methods in concurrently accommodating three key issues of decision hesitancy, attributes interdependency, and group attitudinal character. To elicit decision-makers’ hesitant fuzzy assessments more objectively and comprehensively, we define an expression tool called interval-valued dual hesitant fuzzy uncertain unbalanced (...) linguistic set and develop aggregation operators through its operations. To exploit attributes interdependency, we establish a synthesized attributes’ weighting model to fuse an attributes interdependency-based weighting vector and an argument-dependent weighting vector, which are, respectively, derived through Decision-Making and Trial Evaluation Laboratory technique and maximizing deviation method. To effectively utilize decision-makers’ group attitudinal characters, we also develop a TOPSIS-based method to rationally transform group ideal attitudes into order-inducing vectors. On the strength of the above methods, an integrated MADM approach is then constructed. Finally, illustrative case study and experiments are conducted to validate our approach. (shrink)

This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms . We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical (...) real and rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind , where φ has no additional truth-constants. (shrink)

Both perspective and leverage are needed in order to arrive at a place where it is possible to do the philosophical work required in order to adequately account for our present sociotechnical landscape. One of the key characteristics of this landscape is the collapse of scale, as things become more like fluid assemblages and the economic incentives of surveillance capitalism turn ordinary things into surveillance devices tuned for others’ profit. In this context we need a language not only of imagination (...) and humility in the face of countless gaps between things, but also one of entanglement, care, and response-ability. (shrink)

Both perspective and leverage are needed in order to arrive at a place where it is possible to do the philosophical work required in order to adequately account for our present sociotechnical landscape. One of the key characteristics of this landscape is the collapse of scale, as things become more like fluid assemblages and the economic incentives of surveillance capitalism turn ordinary things into surveillance devices tuned for others’ profit. In this context we need a language not only of imagination (...) and humility in the face of countless gaps between things, but also one of entanglement, care, and response-ability. (shrink)

This paper is an attempt to develop the many-valued first-order fuzzy logic. The set of its truth, values is supposed to be either a finite chain or the interval 0, 1 of reals. These are special cases of a residuated lattice L, , , , , 1, 0. It has been previously proved that the fuzzy propositional logic based on the same sets of truth values is semantically complete. In this paper the syntax and semantics of the first-order fuzzy (...) logic is developed. Except for the basic connectives and quantifiers, its language may contain also additional n-ary connectives and quantifiers. Many propositions analogous to those in the classical logic are proved. The notion of the fuzzy theory in the first-order fuzzy logic is introduced and its canonical model is constructed. Finally, the extensions of Gödel's completeness theorems are proved which confirm that the first-order fuzzy logic is also semantically complete. (shrink)

We prove that the positive fragment of first-order intuitionistic logic in the language with two individual variables and a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable. This holds true regardless of whether we consider semantics with expanding or constant domains. We then generalise this result to intervals \ and \, where QKC is the logic of the weak law of the excluded middle and QBL and QFL are first-order counterparts of Visser’s basic and formal logics, (...) respectively. We also show that, for most “natural” first-order modal logics, the two-variable fragment with a single monadic predicate letter, without functional symbols, constants, and equality, is undecidable, regardless of whether we consider semantics with expanding or constant domains. These include all sublogics of QKTB, QGL, and QGrz—among them, QK, QT, QKB, QD, QK4, and QS4. (shrink)

Decision analysts sometimes use the results of clinical trials in order to evaluate treatment alternatives. I discuss some problems associated with this, and in particular I point out that it is not valid to use the estimates from clinical trials as the probabilities of events which are needed for decision analysis. I also attempt to show that an approach based on objective statistical theory may have advantages over commonly used methods based on decision theory. These advantages include the recognition of (...) uncertain data, the introduction of a third alternative, namely suspension of judgement, and the possibility of modifying the choice of probabilities based on a clinical trial with reference to other available knowledge. I have not, however, shown in detail how this modification is done, but I think the concept is sufficiently promising to be applied to an actual clinical decision problem. (shrink)

IntroductionExercise at high intensity may cause lower affective responses toward exercise compared with moderate intensity exercise. We aimed to elucidate affective valence and enjoyment in high- and moderate-high interval exercise.MethodsTwenty recreationally active participants underwent three different treadmill running exercise sessions per week over a 3-week period, in randomized order; CE70: 45 min continuous exercise at 70% of heart rate maximum, INT80: 4 × 4 min intervals at 80% of HRmax, INT90: 4 × 4 min intervals at 90% of HRmax. (...) Pre-tests included graded submaximal steady state intensities and a test to exhaustion for determining peak oxygen uptake and HRmax. Affective valence was measured before, during and after the sessions using the Feeling Scale. Enjoyment was assessed before and after the sessions applying the Physical Activity Enjoyment Scale and during the sessions using the Exercise Enjoyment Scale.ResultsThe participants felt lower pleasure during INT90 sessions compared with INT80 and CE70 sessions, with no differences between INT80 and CE70 sessions. There were higher enjoyment after INT80 sessions versus CE70 sessions, and no differences between INT90 and CE70 or INT80. For enjoyment during exercise, CE70 were perceived more enjoyable, and INT80 and INT90 less enjoyable in week 2 and 3 than in week 1.ConclusionThe negative affective consequences associated with high intensity interval exercise can be alleviated by keeping the intensity at or around 80% of HRmax while preserving the beneficial enjoyment responses associated with interval exercise. (shrink)

We introduce the notion of τ-like partial order, where τ is one of the linear order types ω, ω*, ω + ω*, and ζ. For example, being ω-like means that every element has finitely many predecessors, while being ζ-like means that every interval is finite. We consider statements of the form “any τ-like partial order has a τ-like linear extension” and “any τ-like partial order is embeddable into τ” . Working in the framework of reverse mathematics, we show that (...) these statements are equivalent either to equation image or to equation image over the usual base system equation image. (shrink)

In this paper, I argue that a) Cartesian wonder is properly interpreted through Irigaray’s theory of phallic economy and that b) when Cartesian wonder is explicitly reinterpreted through Irigaray’s ethics of sexual difference, it must be considered in the mode of écriture. To support these two contentions, this paper unfolds in five parts. I begin by giving an account of Cartesian wonder and an account of Irigaray’s theory of phallic economy and the ethics of sexual difference. After showing how Cartesian (...) wonder is best read as part of the phallic economy, I turn to develop Cartesian wonder and Irigarayan wonder differently, in the mode of écriture [writing]. In order to do so, I first establish that Cartesian wonder, by virtue of its status as a precondition of rational discourse, is aroused through written things, and then I explore how Irigarayan wonder might best be considered between written entities, between two books as bodies. I thus read Descartes out from Irigaray, then back into and through Irigaray. (shrink)

A totally ordered group G is essentially periodic if for every definable non-trivial convex subgroup H of G every definable subset of G is equal to a finite union of cosets of subgroups of G on some interval containing an end segment of H; it is coset-minimal if all definable subsets are equal to a finite union of cosets, intersected with intervals. We study definable sets and functions in such groups, and relate them to the quasi-o-minimal groups introduced in (...) Belegradek et al. . Main results: An essentially periodic group G is abelian; if G is discrete, then definable functions in one variable are ultimately piecewise linear. A group such that every model elementarily equivalent to it is coset-minimal is quasi-o-minimal , and its definable functions in one variable are piecewise linear. (shrink)

We show that the theory of the partial ordering of the computably enumerable degrees in any given nontrivial interval is undecidable and has uncountably many 1-types.

Recent research has shown that human instrumental action is associated with systematic changes in time perception: The interval between a voluntary action and an outcome is perceived as shorter than the interval between a physically similar involuntary movement and an outcome. The study by, Ebert and Wegner suggests that this change in time perception is related to higher order agency experience. Notwithstanding certain issues arising from their study, which are discussed, we believe it offers validation of binding as (...) a measure of sense of agency. (shrink)

Russell and Walker proposed different ways of constructing instants from events. For an explanation of "time as a continuum," Thomason favored Walker's construction. The present article shows that Russell's construction fares as well. To this end, a mathematical characterization problem is solved which corresponds to the characterization problem that Thomason solved with regard to Walker's construction. It is shown how to characterize those event structures (formally, interval orders) which, through Russell's construction of instants, become linear orders isomorphic (...) to a given (or, deriving, to some—nontrivial ordered) real interval. As tools, separate characterizations for each of resulting (i) Dedekind completeness, (ii) separability, (iii) plurality of elements, (iv) existence of certain endpoints are provided. Denseness is characterized to replace Russell's erroneous attempt. Somewhat minimal nonconstructive principles needed are exhibited, and some alternative approaches are surveyed. (shrink)

This paper investigates the event-based consensus problem for the heterogeneous hybrid multiagent system. First, the heterogeneous hybrid MAS is proposed which contains continuous and discrete-time subsystems with second-order and first-order heterogeneous dynamics. Second, the event-triggered protocols are proposed, which mainly include the event-based control laws and event-triggered conditions for different kinds of agents. Then, the consensus conclusions of fixed topology and switching topologies are obtained based on graph theory and nonnegative matrix theory, which include the constraints on control parameters, coupling (...) gains, and sampling interval to guarantee consensus. Finally, a simulation example is given to verify the efficiency of the proposed protocols. (shrink)