The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules in special (...) reduced normal form, and, then, on checking validity of such rules in models of singleexponential size in the rules. Also we consider the admissibility problem for TL(NBox+-wC) and show how to reduce the problem for admissibility to the decidability of TL(NBox+-wC) itself using definable universal modalities. (shrink)

We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object (...) of our investigation. We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit. (shrink)

Gabbay's separation theorem about linear temporal logic with past has proved to be one of the most useful theoretical results in temporal logic. In this paper, we establish an analogous statement a...

ABSTRACT In this paper we present a new semantic approach for propositional linear temporal logic with discrete time, strongly based in the well-order of IN (the set of natural numbers). We consider temporal connectives which express precedence, posteriority and simultaneity, and they provide a family of expressively complete temporal logics. The selection of the new semantics and connectives used in this work was principally to obtain a suitable executable temporal logic, which can be used for the (...) specification and control of process behaviour in discrete time in a similar way to thai presented by D. Gabbay in [GAB 89], Our new approach has two advantages: firstly, the connectives are defined intuitively so that they have interpretations which relate to properties of interest in real systems; secondly, it provides a new semantics that facilitates simpler proofs of many valid formulas and metatheorems. To confirm this second advantage, we use our semantics to give a formal proof of the Separation Theorem for one of these logics (specifically LN3). The great interest of this Separation Theorem for the executable temporal logic is emphasised by D. Gabbay in [GAB 89], [GAB 88]. (shrink)

Analogous to prism adaptation, sensorimotor compensation for existing neural delays has been clearly demonstrated. This system can also adapt to new delays, both internal and external. This seems to occur at least partially in the sensor systems, and works for discrete, stationary events. This provides additional evidence for visual prediction, but not in a manner that is consistent with spatial extrapolation.

Pris en charge par des organismes spécifiques, les chômeurs sont dans l’obligation de mener des échanges réguliers avec leurs conseillers. Ces interactions articulent trois temporalités distinctes : un rythme des rendez-vous, un horaire de début et une durée. À partir de l’observation d’entretiens entre des chômeurs et leurs conseillers dans plusieurs types d’organismes d’accompagnement, nous interrogeons le pouvoir discrétionnaire que possèdent les agents administratifs en matière de temporalités, ainsi que les marges de négociation détenues par les publics. Cette perspective présente (...) le rapport des chômeurs et des conseillers comme un processus d’ajustements ou de conflits temporels. Elle montre que les temporalités administratives du chômage sont inégalement contrôlées et disputées au niveau des guichets, avec des résultats différents d’une institution à l’autre. Le pouvoir discrétionnaire des conseillers est particulièrement élevé en matière de rythmes de convocation. En revanche, les chômeurs disposent de ressources singulières pour discuter les horaires en Arbeitsagentur ou pour contester les durées à Pôle emploi. Les chômeurs en régime d’assistance, au sein des Jobcenter, apparaissent singulièrement démunis dans ces luttes temporelles. (shrink)

Temporal propositions are mapped to sets of strings that witness (in a precise sense) the propositions over discrete linear Kripke frames. The strings are collected into regular languages to ensure the decidability of entailments given by inclusions between languages. (Various notions of bounded entailment are shown to be expressible as language inclusions.) The languages unwind computations implicit in the logical (and temporal) connectives via a system of finite-state constraints adapted from finite-state morphology. Applications to Hybrid Logic and non-monotonic (...) inertial reasoning are briefly considered. (shrink)

This paper is concerned with tracing the implications of two ideas as they affect quantum theory. One, which descends from Leibniz and Mach, is that there is no space-time continuum, but that which are involved are spacial and temporal relations involving the distant matter of the universe. The other is that our universe is finite. The picture of the world to which we are led is that of an enormous space-time Feynman diagram whose vertices are events. A consequence of (...) finiteness is that between each pair of events, along a world line, there can be only finitely many intermediate events. A further change is that we are no longer required to believe that particles need be anywhere between events. The paper takes up nonrelativistic quantum theory in a way that is consistent with these ideas. By considering analogies between the Wiener and the Feynman integrals, and between the Wiener process and related discrete processes, there is obtained a straightforward theory for the Feynman integral. Propagators are worked out for many of the cases relevant to the nonrelativistic theory.The paper shows that, even when there are, along each world-line, no more than one event per Compton wavelength, agreement is good with the usual Schrödinger theory. (shrink)

This article provides an overview of recent developments in solving the timing problem (discreteness vs. continuity) in cognitive neuroscience. Both theoretical and empirical studies have been considered, with an emphasis on the framework of Operational Architectonics (OA) of brain functioning (Fingelkurts and Fingelkurts, 2001, 2005). This framework explores the temporal structure of information flow and interarea interactions within the network of functional neuronal populations by examining topographic sharp transition processes in the scalp EEG, on the millisecond scale. We conclude, (...) based on the OA framework, that brain functioning is best conceptualized in terms of continuity-discreteness unity which is also the characteristic property of cognition. At the end we emphasize where one might productively proceed for the future research. (shrink)

Temporal stability and change in neutral contexts can transform continuous experiences into distinct and memorable events. However, less is known about how shifting emotional states influence these memory processes, despite ample evidence that emotion impacts non-temporal aspects of memory. Here, we examined if emotional stimuli influence temporal memory for recent event sequences. Participants encoded lists of neutral images while listening to auditory tones. At regular intervals within each list, participants heard emotional positive, negative, or neutral sounds, which (...) served as “emotional event boundaries” that divided each sequence into discrete events. Temporal order memory was tested for neutral item pairs that either spanned an emotional sound or were encountered within the same auditory event. Encountering a highly arousing event boundary led to faster response times for items encoded within the next event. Critically, we found that highly arousing sounds had different effects on binding ongoing versus ensuing sequential representations in memory. Specifically, highly arousing sounds were significantly more likely to enhance temporal order memory for ensuing information compared to information that spanned those boundaries, especially for boundaries with negative valence. These findings suggest that within aversive emotional contexts, fluctuations in arousal help shape the temporal organisation of events in memory. (shrink)

Within legal contexts, a claim to knowledge requires that the evidence appealed to fulfills conditions established by legal norms that belong to the so-called Evidence Law. In addition, the epistemic justification presupposed by this kind of knowledge is temporally affected by the changing character of the evidence and the judicial discretion usually exercised in the applications of the Evidence Law. As such, these two scenarios involve three modalities: temporal, epistemic, and deontic. The present paper philosophically discusses the links between (...) these modal dimensions in the above legal context. Based on the discussion, a formal tense-epistemic-deontic logic is developed. That is, the paper characterizes a formal language formally representing the three dimensions through specific logical operators, constructs a formal semantics for the language, and specifies a formal logical system. Finally, the soundness and completeness of the system with respect to the semantics is proved. (shrink)

We address how listeners perceive temporal regularity in music performances, which are rich in temporal irregularities. A computational model is described in which a small system of internal self‐sustained oscillations, operating at different periods with specific phase and period relations, entrains to the rhythms of music performances. Based on temporal expectancies embodied by the oscillations, the model predicts the categorization of temporally changing event intervals into discrete metrical categories, as well as the perceptual salience of deviations from (...) these categories. The model's predictions are tested in two experiments using piano performances of the same music with different phrase structure interpretations (Experiment 1) or different melodic interpretations (Experiment 2). The model successfully tracked temporal regularity amidst the temporal fluctuations found in the performances. The model's sensitivity to performed deviations from its temporal expectations compared favorably with the performers' structural (phrasal and melodic) intentions. Furthermore, the model tracked normal performances (with increased temporal variability) better than performances in which temporal fluctuations associated with individual voices were removed (with decreased variability). The small, systematic temporal irregularities characteristic of human performances (chord asynchronies) improved tracking, but randomly generated temporal irregularities did not. These findings suggest that perception of temporal regularity in complex musical sequences is based on temporal expectancies that adapt in response to temporally fluctuating input. (shrink)

This article explores Gadamer’s description of time(s) and situates it within his aesthetic account and hermeneutics. Bringing together all of Gadamer’s major discussions on time, I develop a consistent account which I then challenge. Whereas Heidegger famously describes transcendental temporality with an emphasis on futurity, Gadamer accentuates a historical temporal awareness and itsdiscontinuous nature. Gadamer’s notion of time is best understood, paradoxically, as a timeless temporality, when time is defined as the sequential movement along discrete points. I argue that (...) Gadamer’s unique description of temporality, which has been largely ignored by scholars, is essential to his understanding of experience and, therefore, to our understanding of his philosophical hermeneutics. (shrink)

Recent discussions in the philosophy of science have devoted considerable attention to the analysis of conceptual issues relating to the methodology of explanation and prediction in the sciences. Part of this literature has been devoted to clarifying the very ideas of explanation and prediction. But the discussion has also ranged over various related topics, including the status of laws to be used for explanatory and predictive purposes, the logical interrelationships between explanatory and predictive reasonings, the differences in the strategy of (...) explanatory argumentation in different branches of science, the nature and possibility of teleological explanation, etc. The aim of the present article is to examine the issues involved in such questions from the specialized perspective afforded by one particular kind of physical systems--namely, systems, here to be characterized as discrete state systems, whose behavior has been studied extensively in the scientific literature under the general heading of Markov chains. These systems have been chosen as our focus because their behavior over time can be analyzed at once with great ease and with extraordinary precision. (shrink)

The well known Master Argument of ancient Stoic logician Diodorus Cronus is an argument in favour of the philosophical doctrine of fatalism. Perhaps in antiquity this argument was a subject of the most celebrated controversy about temporal truth and modality. This argument is a subject of logical analysis, especially in connection with temporal logic, also today. 1 The most elegant tense-logical formulation of the Master Argument has been given by A. N. Prior. Discreteness and irreflexivity of time are (...) semantical assumptions of Prior’s formulation of the argument. The assumption of discreness is troublesome. 2 The problem of this assumption is a subject of M. J. White’s paper “The Necessity of the Past and ModalTense Logic Incompleteness”. 3. (shrink)

The kappa effect is a well-reported phenomenon in which spatial distance between discrete stimuli affects the perception of temporal distance demarcated by the corresponding stimuli. Here, we report a new phenomenon that we propose to designate as thelexical kappa effectin which word distance, a non-magnitude relationship of discrete stimuli that exists in the lexical space of the mental lexicon, affects the perception of temporal distance. A temporal bisection task was used to assess the subjective perception of the (...) time interval demarcated by two successively presented words. Word distance was manipulated by varying the semantic (Experiment 1) or phonological (Experiment 2) similarity between the two words. Results showed that the temporal distance between the two words was perceived to be shorter when the corresponding two words were lexically closer. We explain this effect within the internal clock framework by assuming faster detection of the word that terminated timing when it is preceded by a semantically or phonologically similar word. (shrink)

Logics of discrete time are, in Arthur Prior’s words, “applicable in limited fields of discourse in which we are concerned with what happens in a sequence of discrete states,” independent of “any serious metaphysical assumption that time is discrete.” This insight is applied to natural language semantics, a widespread assumption in which is that time is, as is the real line, dense. “Limited fields of discourse” are construed as finite sets of temporal propositions, inducing bounded notions of temporal (...) granularity that can be refined to expand the discourse. The construal is developed in line with Prior’s view of what is “metaphysically fundamental”. (shrink)

According to the Buddhist concept of ‘dependent origination’ (pratītyasamutpāda), discrete factors come into existence because of a combination of causes (hetu) and conditions (pratyaya). Such discrete factors, further, are combinations of five aggregates (pañ caskandha) that, themselves, are subject to constant change. Discrete factors, therefore, lack a self-nature (ātman). The passing through time of discrete factors is characterized by the ‘characteristic marks of the conditioned’: birth (utpāda), change in continuance (sthityanyathātva), and passing away (vyaya); or, alternatively: birth (jāti), duration (sthiti), (...) decay (jarā), and impermanence (anityatā). In the interpretation of the precise nature of these characteristic marks of the conditioned, and their relation to the discrete factor they characterize, different opinions were prevalent within the Sarvāstivāda School of Buddhist philosophy, with, judging from later scholastic literature, the views of the Dārṣṭāntika/sautrāntika and the Vaibhāṣika sub-schools as most prominent ones. The Indian and Chinese Madhyamaka philosophers pointed to the fallacies in the Sarvāstivāda interpretations of the nature of the characteristic marks of the conditioned and their relation to the discrete factors they characterize, and, hence, to the fallacies in the Sarvāstivāda interpretations of the concepts ‘time’ and ‘temporality’. (shrink)

Against a remarkable hardware oblivion in discussions of algorithmic intelligence, this article insists that algorithmic thought, or abstract computation, cannot be separated from its technological implementation. It requires a material medium for an abstract mechanism to become a procedural event. Temporality is both the condition and the limiting (and irritating) factor in the computational function. ‘Radical’ media archaeology is proposed as a method for such an analysis, and the neologism of techno lógos to describe some aspects of algorithmic reason which (...) only unfold in the moment of its techno-processual coming-into-being. Some core operations, such as the time-discrete rhythm of actual computing algorithms, are discussed, where the ‘tempoReal’ flashes up in computing. In a wider sense, the time-discreteness of digital computing is related to an aesthetics of existence which acknowledges the machine element within human reasoning itself, while at the same time re-actualizing previous cultural techniques of non-narrative chronology. Turing the ‘man’ himself, in the sense of the Turing machine, can be addressed ‘itself’, in its archival sense as a sequence of expressions by symbols. (shrink)

The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with (...) respect to (iii) the presence in T1 of so-called systematic frame constants, which are meant to hold at exactly one point in a temporal structure and to enable us to express the irreflexivity of such structures. Those frame constants will be seen to play a paramount role in our axiomatization of T1. (shrink)

Causal sets are a particular class of partially ordered sets, which are proposed as basic models of discrete space-time, specially in the field of quantum gravity. In this context, we show the existence of temporal foliations for any causal set, or more generally, for a causal space. Moreover, we show that automorphisms of a large class of infinite causal sets fall into two classes 1) Automorphisms of spacelike hypersurfaces in some given foliation, or 2) Translations in time. More generally, (...) we show that for any automorphism \ of a generic causal set \, there exists a partition of \ into finitely many subcausets, on each of which or above hold. These subcausets can be assumed connected if, in addition, there are enough distinct orbits under \. (shrink)

We present a modal logic for the class of subset spaces based on discretely descending chains of sets. Apart from the usual modalities for knowledge and effort the standard temporal connectives are included in the underlying language. Our main objective is to prove completeness of a corresponding axiomatization. Furthermore, we show that the system satisfies a certain finite model property and is decidable thus.

One of time's most puzzling aspects concerns its ontological status: on the one hand, it is a subjective and relative notion, based on our conscious experience of successive events; yet, on the other hand, our civilization and technology are based on the understanding that something like objective, absolute Time exists. Some philosophers have taken this paradox so far as to conclude that time is unreal; others, accepting the existence of absolute time, have engaged in heated debates regarding its structure, be (...) it linear or circular, bounded or unbounded, dense or discrete. (shrink)

Recent studies have revealed that the temporal lobe, a cortical region thought to be in charge of episodic and semantic memory, is involved in creative insight. This work examines the contributions of discrete temporal regions to insight. Activity in the medial temporal regions is indicative of novelty recognition and detection, which is necessary for the formation of novel associations and the “Aha!” experience. The fusiform gyrus mainly affects the formation of gestalt-like representation and perspective taking. The anterior (...) and posterior middle temporal gyri are individually associated with extensive semantic processing and inhibiting salient or routine word associations, which are necessary to form non-salient, novel and remote associations. The anterior and posterior superior temporal gyri are individually responsible for integrating/binding and accessing various types of available conceptual representations. Based on the current knowledge, an integrated model of the temporal lobe's role in insight and some future directions are proposed. (shrink)

The broad objective of this paper is to expound the model of temporal awareness as per Buddhaghosa and compare it with Bergson’s account of duration. As per Buddhaghosa, the notions of time, consciousness, and causation are inter-related. Accordingly, to understand the nature of temporal consciousness, it is required that a moment of consciousness is unpacked, its constituents analysed, and its structuring process penetrated, that is, how momentary mental events are related to each other in a way that leads (...) to an experience of succession and duration. The paper is divided into three sections. The aim of the first section is to show that mental events, for Buddhaghosa, are not discrete, independent entities but are dependently originated. The aspect of dependent origination is further illustrated through _paṭiccasamuppāda_ and _paṭṭhāna_. In the second section, the constitution of temporality as per Bergson is discussed. Henri Bergson too commit to the position that mental events, to start with, are not discrete, disconnected but rather are fused together in inter-penetrating causal relationships. So, the model of temporality of Bergson as the movement of fused consciousness states, as a heterogenous multiplicity as opposed to discrete multiplicity provides a helpful framework through which Buddhaghosa’s model of temporality can be interpreted. In the final section, Buddhaghosa’s model of time-consciousness is discussed by elucidating the structure of the momentary _citta_ (consciousness). Further, the tension that prevails between the momentary and the durational level aspect of consciousness and between simultaneity and succession is discussed vis-à-vis temporal awareness. For Buddhaghosa, a case is made for the experience of duration as fundamental to consciousness, but which is grounded in, rather than opposed to, moments of consciousness. It is posited that, in Buddhaghosa, there is a construction of temporal experience but one that is not opposed with the real duration; unlike in Bergson, where a distinction seems to be made between the ultimate reality of duration when contrasted with the construction or projection of continuity based upon moments of consciousness. (shrink)

We experience the world around us as a smooth and continuous flow. However, there is growing evidence that the stream of sensory inputs is not elaborated in an analog way but is instead organized in discrete or quasi-discrete temporal processing windows. These discrete windows are suggested to depend on rhythmic neural activity in the alpha (and theta) frequency bands, which in turn reflect changes in neural activity within, and coupling between, cortical areas. In the present study, we investigated a (...) possible causal link between oscillatory brain activity in the alpha range (8–12 Hz) and the temporal resolution of visual perception, which determines whether sequential stimuli are perceived as distinct entities or combined into a single representation. To this aim, we employed a two-flash fusion task while participants received focal transcranial alternating current stimulation (tACS) in extra-striate visual regions including V5/MT of the right hemisphere. Our findings show that 10-Hz tACS, as opposed to a placebo (sham tACS), reduces the temporal resolution of perception, inducing participants to integrate the two stimuli into a unique percept more often. This pattern was observed only in the contralateral visual hemifield, providing further support for a specific effect of alpha tACS. The present findings corroborate the idea of a causal link between temporal windows of integration/segregation and oscillatory alpha activity in V5/MT and extra-striate visual regions. They also stimulate future research on possible ways to shape the temporal resolution of human vision in an individualized manner. (shrink)

In view of the primacy assigned to the 'present' in traditional metaphysics, in terms of the ways in which questions about existence are expressed, the following discussion takes the question of the temporalizing of the present as its theme. This involves unravelling the historical traces of the thought of the present as a finite, closed, objective point of a successive continuum of discrete moments (a real oscillation between the now and the not-now) by returning to the phenomenological sense of the (...) present as the stretching out of an opening – the 'living Present' (lebendige Gegenwart) – which bears its continuity of presence and non-presence within itself (without restriction to linearity). The transition itself suggests something like a quantum-leap and, in another sense, it also extends beyond the bounds of this simile (and the discontinuity that is implied) by evoking the image of a 'twist' or a 'turn.’ In order to grasp the significance of this turn we shall first examine – re turn to – its main obstacle: the concept of time as a linear and corpuscular continuum. The traditional model of time as a succession of 'now-points' (a notion that 1 still infects discourse on temporality) has always undermined our understanding of 'presence' as that which maintains itself (abides) through succession. In effect, presence must be 'maintained' [maintenant] within the 'now.' Yet, if the 'now' is constantly shifting into non-being through its replacement by a new 'now' then presence must be infused with its own negation and a certain discontinuity. How is it possible, then, to speak of the 'persistence' of 'identity' as something unitary (simultaneous with itself) existing through plurality and successive fragmentation into non-being? Furthermore, in reference to motion, what is entailed in the possibility of experiencing the transition of a selfsame (particular) object from one spatial location to another: how is it that the object 'endures' through its spatial and temporal transition? Since antiquity the question of simultaneity has been taken for granted – generally being consigned to mere spatial models.. (shrink)

The dorsal anterior cingulate cortex is a key node in the human salience network. It has been ascribed motor, pain-processing and affective functions. However, the dynamics of information flow in this complex region and how it responds to inputs remain unclear and are difficult to study using non-invasive electrophysiology. The area is targeted by neurosurgery to treat neuropathic pain. During deep brain stimulation surgery, we recorded local field potentials from this region in humans during a decision-making task requiring motor output. (...) We investigated the spatial and temporal distribution of information flow within the dACC. We demonstrate the existence of a distributed network within the anterior cingulate cortex where discrete nodes demonstrate directed communication following inputs. We show that this network anticipates and responds to the valence of feedback to actions. We further show that these network dynamics adapt following learning. Our results provide evidence for the integration of learning and the response to feedback in a key cognitive region. (shrink)

This chapter examines some issues concerning the structure of time. It considers arguments for and against Temporal Finitism. Temporal Discretism is a kind of Finitism: any finitely extended interval is made up of only finitely many indivisible units of time. In the chapter, the authors assume for the sake of argument that Intervalism is true, that is, that some temporally extended intervals and processes are among the world's fundamental entities. The main argument for Intervalism is that it (...) follows from the metaphysical impossibility of certain infinitary scenarios involving super‐tasks. Strong Intervalism denies that instants are fundamental, while Moderate Intervalism, or Interval‐Boundary Dualism, embraces the fundamentality of both instants and intervals. Infinitary Intervalism is relative to the three competing theories of Aristotelian Temporal Finitism, Temporal Discretism, and Instantism. In the chapter, the authors also assume that all Intervalists are either Discretists or Aristotelian Finitists, and that all Instantists are Temporal Infinitists. (shrink)

In our previous work we have introduced loop-type sequent calculi for propositional linear discrete tense logic and proved that these calculi are sound and complete. Decision procedures using the calculi have been constructed for the considered logic. In the present paper we restrict ourselves to the logic with the unary temporal operators “next” and “henceforth always”. Proof-theory of the sequent calculus of this logic is considered, focusing on loop specification in backward proof-search. We describe cyclic sequents and prove that (...) any loop consists of only cyclic sequents. A class of sequents for which backward proof-search do not require loop-check is presented. It is shown how sequents can be coded by binary strings that are used in backward proof-search for the sake of more efficient loop-check. (shrink)

ABSTRACT In this paper we define two logics, KLn and BLn, and present tableau-based decision procedures for both. KLn is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BLn is somewhat similar; it is a temporal logic that contains connectives for representing the beliefs of agents. In addition to a complete formal (...) definition of the two logics and their decision procedures, the paper includes a brief review of their applications in AI and mainstream computer science, correctness proofs for the decision procedures, a number of worked examples illustrating the decision procedures, and some pointers to further work. (shrink)

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' (...) temporal logic of linear discrete time with gaps follows. (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

We develop a timeout extension of propositional linear temporal logic to specify timing properties of timeout-based models of real-time systems. A timeout is used to model the execution of an action marking the end of a delay. With a view to expressing such timeout constraints, ToLTL uses a dynamic variable to abstract the timeout behaviour in addition to a variable which captures the global clock and some static timing variables which record time instances when discrete events occur. We propose (...) a corresponding timeout tableau for satisfiability checking of the ToLTL formulas. Further we prove that the validity checking for such an extended logic remains PSPACE-complete. Under discrete time semantics, with bounded timeout increments, the model-checking problem which verifies if a ToLTL-formula holds in a timeout Kripke structure is also shown to be PSPACE complete. We further prove that ToLTL, when interpreted over discrete time, can be embedded in the monadic second-order logic with.. (shrink)

I analyze Deleuze’s concept of temporality in terms of its ontology and axiological (political and aesthetic) aspects. For Deleuze, the concept of temporality is non-monolithic, in the senses that it is modified throughout his works — the monographs, lectures, and those works that were co-authored with Félix Guattari — and that it is developed through reference to a dizzying array of concepts, thinkers, artistic works, and social phenomena. -/- I observe that Deleuze’s concept of temporality involves a complex ontology of (...) difference, which I elaborate through reference to Deleuze’s analyses of Ancient Greek and Stoic conceptualizations of time. From Plato through to Chrysippus, temporality gradually comes to be identified as a form that comprehends the variation of particulars. Deleuze modifies the ancients’ concept of time to suggest that time obtains as a form of ceaseless ontological variation. Through reference to Deleuze’s reading of Gilbert Simondon, I further suggest that Deleuze tends to conceive of temporality as an ontogenetic force which participates in the complex process of individuation. -/- A standout feature of this dissertation involves an analysis of how Deleuze’s concept of temporality is modified in his works on cinema. In Cinema 1: The Movement-Image and Cinema 2: The Time-Image, temporality comes to be characterized as something other than the measure of the movement of existents. In his detailed analyses of Bergson — in Cinema 1: The Movement-Image, Cinema 2: The Time-Image, and Bergsonism — Deleuze suggests that time involves an actualization of aspects of a virtual past as contemporaneous with the lived present. While not an outright denial of the relation of temporal succession, Deleuze’s claim implies a diminishment of this relation’s significance in an adequate elaboration of the nature of temporality. -/- Further, I observe —through reference to Deleuze’s readings of Marx, Kierkegaard, and Spinoza — that (the explicitly temporal) change of societal forms of economic organization is non-reducible to that suggested by linear evolution. The claim is that putatively discrete modes of economic organization do not enjoy temporal displacement with respect to one another. This suggests that linear evolutionary models of societal development are inadequate. This further implies that temporality is non-reducible to the relation of temporal succession. In concrete terms, societal change is characterized as immanent temporal variation. -/- Taken together, these analyses yield the conclusion that Deleuze tends to conceive of the nature of temporality as involving the ongoing realization of multiple — non-identical, sometimes contrary — aspects of a stochastic process of creation that is expressed in ontogenetic circumstances, social evolution, literary works, and filmic works. (shrink)

Various kinds of observations show that the ability of human beings to both consciously relive past events – episodic memory – and conceive future events, entails an active process of construction. This construction process also underpins many other important aspects of conscious human life, such as perceptions, language and conscious thinking. This article provides an explanation of what makes the constructive process possible and how it works. The process mainly relies on attentional activity, which has a discrete and periodic nature, (...) and working memory, which allows for the combination of discrete attentional operations. An explanation is also provided of how past and future events are constructed. (shrink)

Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogeneous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time steps, following (...) state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). Secondly, CA are abstract, as they can be specified in purely mathematical terms and implemented in physical structures. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine-like devices, CA with suitable rules can emulate a universal Turing machine, and therefore compute, given Turing's Thesis, anything computable.... (shrink)

Vagueness in event times pertains to the observation that one usually finds it difficult to slice the continuous flux of space-time into a series of events with clear-cut temporal boundaries. I argue that such vagueness originates from our ignorance of discrete changing points wherein states of affairs begin or cease to obtain. Applying the epistemic view on vagueness (Williamson 1994) to vagueness in event times, I contend that the lagging nature of knowledge prevents one from knowing the abrupt changes (...) taking place between contiguous minimal time intervals. In turn, vagueness in the conception of event times is construed in terms of epistemic modality (Jaszczolt 2009), viz. a gradation of a thinker’s epistemic certainty towards the occurrence of a physical change. (shrink)

The Transcendental Psychology Approach to the study of perception has been developed by A.I. Mirakyan at the Psychological Institute (Moscow, Russia) about 30 years ago. This article considers the results of theoretical and experimental investigations and provides a historical overview of the approach’s development. Started with the investigations of constancy in perception, it went beyond the traditional Product Basis Paradigm (relying on perceptual features for finding perceptual mechanisms) into Philosophical Metaphysics of “nothing” and “something” concepts for revealing the form-generating principles (...) as fundamental axiomatics of the Transcendental Psychology Approach. Several principles were developed and justified: structure-process anisotropy, spatial-temporal discreteness, the formation of anisotropic (particularly, symmetric) relations, the coexistence of alternatives, and some others. Principles are explanatory for the regulations of sensory-perceptual processes and are the direct object of further specification and experimental verification using hypothetical transcendental models of perceptual structures. The theory suggests that the internal mechanisms of these models would not naturally manifest themselves in experiments within the functional range of perception, and to see the phenomena, it is necessary to bring the perceptual system out of its natural functional range. The form-generating processes are named adiaphorous in the sense that they specifically generate new structures and forms, regardless of the characteristics of products used and produced in the processes. In general, it is possible to speak about the class of so-called structurally-generative processes that are specific to the process of transition between the system-generating structures studied by different hierarchically interrelated sciences. The proposed two-staged qualitative model of the perceptual process consists of two substantially different parts: the direct sensory perception and a process of form designation or sensory name assignment. Further investigations of structurally-generative processes seem likely to shed light on the mechanisms of brain function and to contribute strategically to new directions in philosophical psychology and neuroscience. (shrink)

The paper considers the symmetries of a bit of information corresponding to one, two or three qubits of quantum information and identifiable as the three basic symmetries of the Standard model, U(1), SU(2), and SU(3) accordingly. They refer to “empty qubits” (or the free variable of quantum information), i.e. those in which no point is chosen (recorded). The choice of a certain point violates those symmetries. It can be represented furthermore as the choice of a privileged reference frame (e.g. that (...) of the Big Bang), which can be described exhaustively by means of 16 numbers (4 for position, 4 for velocity, and 8 for acceleration) independently of time, but in space-time continuum, and still one, 17th number is necessary for the mass of rest of the observer in it. The same 17 numbers describing exhaustively a privileged reference frame thus granted to be “zero”, respectively a certain violation of all the three symmetries of the Standard model or the “record” in a qubit in general, can be represented as 17 elementary wave functions (or classes of wave functions) after the bijection of natural and transfinite natural (ordinal) numbers in Hilbert arithmetic and further identified as those corresponding to the 17 elementary of particles of the Standard model. Two generalizations of the relevant concepts of general relativity are introduced: (1) “discrete reference frame” to the class of all arbitrarily accelerated reference frame constituting a smooth manifold; (2) a still more general principle of relativity to the general principle of relativity, and meaning the conservation of quantum information as to all discrete reference frames as to the smooth manifold of all reference frames of general relativity. Then, the bijective transition from an accelerated reference frame to the 17 elementary wave functions of the Standard model can be interpreted by the still more general principle of relativity as the equivalent redescription of a privileged reference frame: smooth into a discrete one. The conservation of quantum information related to the generalization of the concept of reference frame can be interpreted as restoring the concept of the ether, an absolutely immovable medium and reference frame in Newtonian mechanics, to which the relative motion can be interpreted as an absolute one, or logically: the relations, as properties. The new ether is to consist of qubits (or quantum information). One can track the conceptual pathway of the “ether” from Newtonian mechanics via special relativity, via general relativity, via quantum mechanics to the theory of quantum information (or “quantum mechanics and information”). The identification of entanglement and gravity can be considered also as a ‘byproduct” implied by the transition from the smooth “ether of special and general relativity’ to the “flat” ether of quantum mechanics and information. The qubit ether is out of the “temporal screen” in general and is depicted on it as both matter and energy, both dark and visible. (shrink)

The article is devoted to social problems of modern science (as it were interpreted Max Weber) considered in the context of the system-communicative approach by N. Luhmann. In contrast to the modern work of art, the modern science, as M. Weber believes, is associated with the fundamental unattainability of “true being”, and, as a result, with the transitory character of any scientific achievement. The specialty of modern science, as Weber noted, is determinated, on the one hand by its self-understanding, due (...) to the “peculiarity of the current moment”, and, on the other, by its transformation into a kind of blind spot of scientific observation. As a result, Weber formulated the main problem of the meaning of modern science: he wondered why any scientist needs a science under (1) external alienation and (2) inaccessibility of a scientific object? Moreover, the category of truth not just acquires its special value, but also sets a special meaning to the purpose of scientific communication, that becomes an object but not a property of scientific search. The main content of the article is the study of the Weberian concepts of the external (science as a profession) and internal (science as vocation) social factors of modern science as they were interpreted by E. von Kahler, G. Rickert, M. Scheller, K. Loewit. The authors discuss their attempts to modernize the fundamental Weberian distinction of truth/value as a principle of inclusion in the scientific community, that was formulated as a response to the “Weber’s challenge”. The authors argue that von Kahler criticized the Weberian concept for the incompatibility of the spatial and temporal discreteness of science within the “organic understanding” of the unity of the world. At the same time Scheler and Rickert payed special attention to the problem of subject specification of science. K. Levit discussed the possibility of Weber’s substitution of objectivity as a key distinction of modern knowledge with some opposite attribute. In the final part, the authors summarize the inconsistency of predictions about the further internal differentiation of scientific disciplines and the rejection of research motive for “genuine being”. (shrink)

A Master-like argument, in the usage of the present paper, is an argument that employs a reductio ad impossibile principle to transmit the necessity of what are or become past truths to the remainder of time by means of necessary conditionals of some sort. The conclusion of such an argument is some no-unactualized-possibilities principle. This paper argues that the formulation of a Master-like argument by A. N. Prior in a mixed modal temporal propositional logic introduces certain artifacts into the (...) logical analysis of the argument. One of these, a principle of temporal discreteness, is not essential to a Master-like argument. Another, a principle of forwards temporal linearity, is technically essential; but it is usually tacitly presupposed by the necessary temporal conditionals employed to 'tie together' past and future time in less formal accounts of Master-like arguments. (shrink)

Linear temporal logic with Since and Until modalities is expressively equivalent, over the class of complete linear orders, to a fragment of first-order logic known as FOMLO. It turns out that LTL, under some basic assumptions, is expressively complete if and only if it has the property, called separation, that every formula is equivalent to a Boolean combination of formulas that each refer only to the past, present or future. Herein we present simple algorithms and their implementations to perform (...) separation of the LTL with Since and Until, over discrete and complete linear orders, and translation from FOMLO formulas into equivalent temporal logic formulas. We additionally show that the separation of a certain fragment of LTL results in at most a double exponential size growth. (shrink)

Life, whatsoever it is, is a temporal flux. Everything is doomed to change often apparently beyond our awareness. My body appears totally different now, so does my mind. I have gained new attitudes and new ambitions, and a substantial number of old ones have been discarded. But, I am still the same person in an ongoing manner. Besides, recent neuroscientific and psychological evidence has shown that our conscious perception happens as a series of discrete or bounded instants—it emerges in (...) temporally scattered, gappy, and discrete forms. But, if it is so, how does the brain persevere our self-continuity (or continuity of identity) in this gappy setting? How is it possible that despite moment-to-moment changes in my appearance and mind, I am still feeling that I am that person? How can we tackle with this second by second gap and resurrection in our existence which leads to a foundation of wholeness and continuity of ourself? How is continuity of self (collective set of our connected experiences in the vessel of time) that results in a feeling that one’s life has purpose and meaning preserved? To answer these questions, the problem has been comprehended from a philosophical, psychological, and neuroscientific perspective. I realize that first and foremost fact lies in the temporal nature of identity. Having equipped with these thoughts, in this article, it is hypothesized that according to two principles (the principle of reafference or corollary discharge and the principle of a time theory) self-continuity is maintained. It is supposed that there should be a precise temporal integration mechanism in the CNS with the outside world that provides us this smooth, ungappy flow of theSelf. However, we are often taken for granted the importance of self-continuity, but it can be challenged by life transitions such as entering adulthood, retirement, senility, emigration, and societal changes such as immigration, globalization, and in much unfortunate and extreme cases of mental illnesses such as schizophrenia. (shrink)

This paper takes as its queer object a serialized podcast. With its story about John B. McLemore, a clockmaker from Woodstock, Alabama, S-Town is a blockbuster success from the producers of Serial and This American Life. Against both affirmative and negative reception of S-Town – responses that tend to position the podcast either as transcending or as reproducing the idea of a backwards or lagging South – this paper argues that S-Town is an intermedial narrative incorporating various media that themselves (...) comprise competing temporalities. Indexing these alternative temporalities are the intricate designs of clocks and sundials that tell of mythological time and seasonal and diurnal rhythms. There are also tattoos and other inscriptions that mark both bodies and sundials. My argument attends to the animate and inanimate forms narratively contained within the podcast, touching on Rebecca Schneider’s idea of “interanimation” and Elizabeth Freeman’s challenges to “chrononormativity” in the process. From within this intermedial structure, John emerges as an intermediary whose engagement in processes of self-objectification and historical re-enactment complicates a normative timeframe and confounds conventional subject/object relations. Through a consideration of what I call the queerly intermedial form of the S-Town podcast, the essay looks beyond both discrete forms and regional/national concerns to gesture toward the significance of broader networks and spheres for thinking about time, space and being. (shrink)

We describe a novel computational theory of how individuals segment perceptual information into representations of events. The theory is inspired by recent findings in the cognitive science and cognitive neuroscience of event segmentation. In line with recent theories, it holds that online event segmentation is automatic, and that event segmentation yields mental simulations of events. But it posits two novel principles as well: first, discrete episodic markers track perceptual and conceptual changes, and can be retrieved to construct event models. Second, (...) the process of retrieving and reconstructing those episodic markers is constrained and prioritized. We describe a computational implementation of the theory, as well as a robotic extension of the theory that demonstrates the processes of online event segmentation and event model construction. The theory is the first unified computational account of event segmentation and temporal inference. We conclude by demonstrating now neuroimaging data can constrain and inspire the construction of process-level theories of human reasoning. (shrink)

Let a "smooth experience" be an experience with perfectly gradual changes in phenomenal character. Consider, as examples, your visual experience of a blue sky or your auditory experience of a rising pitch. Do the phenomenal characters of smooth experiences have continuous or discrete structures? If we appeal merely to introspection, then it may seem that we should think that smooth experiences are continuous. This paper (1) uses formal tools to clarify what it means to say that an experience is continuous (...) or discrete, and (2) develops a discrete model of the phenomenal characters of smooth experiences. As a result, I'll argue that introspection leaves open whether smooth experiences are continuous or discrete. Yet I’ll also argue—perhaps surprisingly—that the discrete theory may better fit our introspective evidence. Along the way, I explain why the sense of ‘continuity’ ascribed to smooth experiences is distinct from the sense of ‘continuity’ ascribed to the stream of consciousness. (shrink)

Life is a self-maintaining process based on metabolism. Something is said to be alive when it exhibits organization and is actively involved in its own continued existence through carrying out metabolic processes. A life is a spatio-temporally restricted event, which continues while the life processes are occurring in a particular chunk of matter (or, arguably, when they are temporally suspended, but can be restarted at any moment), even though there is continuous replacement of parts. Life is organized in discrete packages, (...) particular cells and multicellular organisms with differing degrees of individuality. Biological species, too, have been shown to be individuals, and not classes, as these collections of organisms are spatio-temporally localized, restricted, continuous, and somewhat cohesive entities, with a definite beginning and end. Assuming that all life on Earth has a common origin, all living organisms, cells, and tissues descending from this origin exhibit continuity of the life processes at the cellular level, as well as many of the features that define the individual character of species: spatio-temporal localization and restriction, continuity, historicity, and cohesiveness. Therefore, life on Earth is an ontological individual. Independent origins of life will have produced other such individuals. These provisionally called ‘life-individuals’ constitute a category of organization of life which has seldom been recognized. The discovery of at least one independent life-individual would go a long way toward the project of the universality of biology. (shrink)