In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions have been considered and axiomatic systems which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, we (...) use indexes as names for temporal flows and give new proofs of completeness. Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works. The only system considered which remains incomplete is the one which defines surjectivity, even ifwe consider a sequence ofnatural extensions ofthe previous one. (shrink)

The language of linear temporal logic can be interpreted on the class of dynamic topological systems, giving rise to the intuitionistic temporal logic ${\sf ITL}^{\sf c}_{\Diamond \forall }$, recently shown to be decidable by Fernández-Duque. In this article we axiomatize this logic, some fragments, and prove completeness for several familiar spaces.

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.

ABSTRACT Many temporal and modal logic languages can be regarded as subsets of first order logic, i.e. the semantics of a temporal logic formula is given as a first order condition on points of the underlying models (Kripke structures). Often the set of possible models is restricted to models which are trees. A temporal logic language is (first order) expressively complete, if for every first order condition for a node of a tree there exists an equivalent (...) class='Hi'>temporal formula which expresses the same condition. In this paper expressive completeness of the temporal logic language with the set of operators U (until), S (since), and X k (k-next) is proved, and the result is extended to various other tree-like structures. (shrink)

The paper offers a formalization of reasoning about distributed multi-agent systems. The presented propositional probabilistic temporal epistemic logic |$\textbf {PTEL}$| is developed in full detail: syntax, semantics, soundness and strong completeness theorems. As an example, we prove consistency of the blockchain protocol with respect to the given set of axioms expressed in the formal language of the logic. We explain how to extend |$\textbf {PTEL}$| to axiomatize the corresponding first-order logic.

We present a completeness proof for Propositional Interval Temporal Logic with finite time which avoids certain difficulties of conventional methods. It is more gradated than previous efforts since we progressively reduce reasoning within the original logic to simpler reasoning in sublogics. Furthermore, our approach benefits from being less constructive since it is able to invoke certain theorems about regular languages over finite words without the need to explicitly describe the associated intricate proofs. A modified version of regular expressions called (...) Fusion Expressions is used as part of an intermediate logic called Fusion Logic. Both have the same expressiveness as PITL but are lower-level notations which play an important role in the hierarchical structure of the overall completeness proof. In particular, showing completeness for PITL is reduced to showing completeness for Fusion Logic. This in turn is shown to hold relative to completeness for conventional linear-time temporal logic with finite time. Logics based on regular languages over finite words and!-words offer a promising but elusive framework for formal specification and verification. A number of such logics and decision procedures have been proposed. In addition, various researchers have obtained complete axiom systems by embedding and expressing the decision procedures directly within the logics. The work described here contributes to this topic by showing how to exploit some interesting links between regular languages and interval-based temporal logics. (shrink)

Causes always seem to come prior to their effects. What might explain this asymmetry? Causation's temporal asymmetry isn't straightforwardly due to a temporal asymmetry in the laws of nature—the laws are, by and large, temporally symmetric. Nor does the asymmetry appear due to an asymmetry in time itself. This Element examines recent empirical attempts to explain the temporal asymmetry of causation: statistical mechanical accounts, agency accounts and fork asymmetry accounts. None of these accounts are complete yet and (...) a full explanation of the temporal asymmetry of causation will likely require contributions from all three programs. (shrink)

In this paper we present BTC, which is a complete logic for branchingtime whose modal operator quantifies over histories and whose temporal operators involve a restricted quantification over histories in a given possible choice. This is a technical novelty, since the operators of the usual logics for branching-time such as CTL express an unrestricted quantification over histories and moments. The value of the apparatus we introduce is connected to those logics of agency that are interpreted on branching-time, as for (...) instance Stit Logics. (shrink)

A complete axiomatic system CTL$_{rp}$ is introduced for a temporal logic for finitely branching $\omega^+$-trees in a temporal language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL$^{*}$ into CTL$_{rp}$. In particular, that yields a complete axiomatization for the translations of all valid CTL$^{*}$-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive (...) medium for reasoning about branching time. (shrink)

A first-order temporal non-commutative logic TN[l], which has no structural rules and has some l-bounded linear-time temporal operators, is introduced as a Gentzen-type sequent calculus. The logic TN[l] allows us to provide not only time-dependent, resource-sensitive, ordered, but also hierarchical reasoning. Decidability, cut-elimination and completeness (w.r.t. phase semantics) theorems are shown for TN[l]. An advantage of TN[l] is its decidability, because the standard first-order linear-time temporal logic is undecidable. A correspondence theorem between TN[l] and a resource indexed (...) non-commutative logic RN[l] is also shown. This theorem is intended to state that “time” is regarded as a “resource”. (shrink)

This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take (...) place in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness. (shrink)

In this paper, we study temporal logic for finite linear structures and surjective bounded morphisms between them. We give a characterisation of such structures by modal formulas and show that every pair of linear structures with a bounded morphism between them can be uniquely characterised by a temporal formula up to an isomorphism. As the main result, we prove Kripke completeness of the logic with respect to the class of finite linear structures with bounded morphisms between them.

ABSTRACT A complete axiomatic system CTLrp is introduced for a temporal logic for finitely branching ω+ -trees in a language extended with so called reference pointers. Syntactic and semantic interpretations are constructed for the branching time computation tree logic CTL* into CTLrp. In particular, that yields a complete axiomatization for the translations of all valid CTL*-formulae. Thus, the temporal logic with reference pointers is brought forward as a simpler (with no path quantifiers), but in a way more expressive (...) medium for reasoning about branching time. (shrink)

Temporal justification logic is a new family of temporal logics of knowledge in which the knowledge of agents is modelled using a justification logic. In this paper, we present various temporal justification logics involving both past and future time modalities. We combine Artemov’s logic of proofs with linear temporal logic with past, and we also investigate several principles describing the interaction of justification and time. We present two kinds of semantics for our temporal justification logics, (...) one based on interpreted systems and Fitting models and the other based on Mkrtychev models, and further, we establish soundness and completeness. We show that the internalization property holds in some of the temporal justification logics. We further investigate the two well-known epistemic-temporal notions of no forgetting and no learning in the framework of justification logics. Finally, we present temporal justification logics that avoid the logical omniscience problem. (shrink)

The purpose of this paper is to describe a set of quantified temporal alethic-deontic systems, i.e., systems that combine temporal alethicdeontic logic with predicate logic. We consider three basic kinds of systems: constant, variable and constant and variable domain systems. These systems can be augmented by either necessary or contingent identity, and every system that includes identity can be combined with descriptors. All logics are described both semantically and proof theoretically. We use a kind of possible world semantics, (...) inspired by the so-called T × W semantics, to characterize them semantically and semantic tableaux to characterize them proof theoretically. We also show that all systems are sound and complete with respect to their semantics. (shrink)

The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t, contains a normal belief operator B t and a non-normal information operator I t which is analogous to the ‘only knowing’ operator discussed in the computer science literature. Soundness and completeness of the logic are proved and the relationship between the proposed logic, the AGM theory of belief revision and the notion of plausibility (...) is discussed. (shrink)

This work concerns the use of operators for past and future contingency in Priorean temporal logic. We will develop a system named C_t, whose language includes a propositional constant and prove that (I) C_t is complete with respect to a certain class of general frames and (II) the usual operators for past and future necessity are definable in such system. Furthermore, we will introduce the extension C_t(lin) that can be interpreted on linear and transitive general frames. The theoretical result (...) of the current work is that contingency can be treated as a primitive notion in reasoning about temporal modalities. (shrink)

Current debate in the metaphysics of time ordinarily assumes that we should be realists about time. Recently, however, a number of physicists and philosophers of physics have proposed that time will play no role in a completed theory of quantum gravity. This paper defends fictionalism about temporal thought, on the supposition that our world is timeless. We argue that, in the face of timeless physical theories, realism about temporal thought is unsustainable: some kind of anti-realism must be adopted. (...) We go on to provide an argument against eliminativism about temporal thought. While it doesn't follow from this argument that fictionalism about temporal thought is true, we suggest that this nonetheless shows that fictionalism should be regarded as the preferred view. (shrink)

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 introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's (...) and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions. (shrink)

The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal (alethic) part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of$$T \times W$$T×Wmodels, (...) and the proof-theoretical apparatus of semantic tableaux. The ‘quantified part’ of the systems includes relational predicates and the identity symbol. The quantifiers are, in effect, a kind of possibilist quantifiers that vary over every object in the domain. The tableaux rules are classical. The alethic part contains two types of modal operators for absolute and historical necessity and possibility. According to ‘boulesic logic’ (the logic of the will), ‘willing’ (‘consenting’, ‘rejecting’, ‘indifference’ and ‘non-indifference’) is a kind of modal operator. Doxastic logic is the logic of beliefs; it treats ‘believing’ (and ‘conceiving’) as a kind of modal operator. I will explore some possible relationships between these different parts, and investigate some principles that include more than one type of logical expression. I will show that every tableau system in the paper is sound and complete with respect to its semantics. Finally, I consider an example of a valid argument and an example of an invalid sentence. I show how one can use semantic tableaux to establish validity and invalidity and read off countermodels. These examples illustrate the philosophical usefulness of the systems that are introduced in this paper. (shrink)

The purpose of this paper is to describe a set of temporal alethic–deontic systems, i.e. systems that include temporal, alethic and deontic operators. All in all we will consider 2,147,483,648 systems. All systems are described both semantically and proof theoretically. We use a kind of possible world semantics, inspired by the so-called T x W semantics, to characterize our systems semantically and semantic tableaux to characterize them proof theoretically. We also show that all systems are sound and complete (...) with respect to their semantics. (shrink)

This paper investigates modular combinations of temporal logic systems. Four combination methods are described and studied with respect to the transfer of logical properties from the component one-dimensional temporal logics to the resulting combined two-dimensional temporal logic. Three basic logical properties are analyzed, namely soundness, completeness, and decidability. Each combination method comprises three submethods that combine the languages, the inference systems, and the semantics of two one-dimensional temporal logic systems, generating families of two-dimensional temporal languages (...) with varying expressivity and varying degrees of transfer of logical properties. The temporalization method and the independent combination method are shown to transfer all three basic logical properties. The method of full join of logic systems generates a considerably more expressive language but fails to transfer completeness and decidability in several cases. So a weaker method of restricted join is proposed and shown to transfer all three basic logical properties. (shrink)

A contrary-to-duty obligation (sometimes called a reparational duty) is a conditional obligation where the condition is forbidden, e.g. “if you have hurt your friend, you should apologise”, “if he is guilty, he should confess”, and “if she will not keep her promise to you, she ought to call you”. It has proven very difficult to find plausible formalisations of such obligations in most deontic systems. In this paper, we will introduce and explore a set of temporal alethic dyadic deontic (...) systems, i.e., systems that include temporal, alethic and dyadic deontic operators. We will then show how it is possible to use our formal apparatus to symbolise contrary-to-duty obligations and to solve the so-called contrary-to-duty (obligation) paradox, a problem well known in deontic logic. We will argue that this response to the puzzle has many attractive features. Semantic tableaux are used to characterise our systems proof theoretically and a kind of possible world semantics, inspired by the so-called T× W semantics, to characterise them semantically. Our models contain several different accessibility relations and a preference relation between possible worlds, which are used in the definitions of the truth conditions for the various operators. Soundness results are obtained for every tableau system and completeness results for a subclass of them. (shrink)

Temporal logic of causal knowledge over general partially ordered structures of local states is defined. The definition of knowledge captures the change of state due to action executions. The structures are a variant of flow event structures including prime event structures and branching processes of Petri Nets. Modalities corresponding to the causality, concurrency, and indistinguishability relations are used. Formulas are interpreted over local state occurrences. The logic is proved to be decidable and a complete axiomatization is provided.

Despite an attempt to break with the hierarchical picture in traditional emergentist thought, non-standard accounts of emergence are often still committed to a premise that ontology is prior to epistemology. This paper aims to topple this last remnant of the traditional hierarchy by explicating a pragmatic view of emergence based on John Dewey’s work. Dewey argued that the traditional notion of ontology is premised on a view of existence as complete. Through a discussion of Dewey’s work it is argued that (...) this premise results in a process of reification that unduly excludes from ontology many precarious and indeterminate aspects involved both in everyday life and in philosophic and scientific inquiry. Building on a recent explication of transformational emergence the paper proposes a diachronic and non-hierarchical account of emergence, called pragmatic emergence. According to that account the relation between ontology and epistemology is a temporally reciprocal one. This means that ontological and epistemological features co-determine each other over time. Determinacy and continuity become historical features of a multitude of unfinished processes that we view from within. (shrink)

Are non-indexical action rationalizations necessarily incomplete because of a missing indexical component? Bermúdez argues that they are. Two things make the argument unpersuasive. First, it assumes that all action rationalizations involve attitudes that are about the agent. Second, it assumes that the attitudes expressible using ‘I’ are themselves indexical. Each is an assumption that believers in complete but non-indexical action rationalizations can and do reject. Surprisingly though, a more effective argument can be obtained by switching focus from indexical attitudes about (...) agents to indexical attitudes about times. The debate about the de se and the de nunc has much less in common than is standardly assumed. It is the de nunc not the de se which provides the knock-down case for essential indexicality. (shrink)

Compositional verification aims at managing the complexity of theverification process by exploiting compositionality of the systemarchitecture. In this paper we explore the use of a temporal epistemiclogic to formalize the process of verification of compositionalmulti-agent systems. The specification of a system, its properties andtheir proofs are of a compositional nature, and are formalized within acompositional temporal logic: Temporal Multi-Epistemic Logic. It isshown that compositional proofs are valid under certain conditions.Moreover, the possibility of incorporating default persistence ofinformation in (...) a system, is explored. A completion operation on aspecific type of temporal theories, temporal completion, is introducedto be able to use classical proof techniques in verification withrespect to non-classical semantics covering default persistence. (shrink)

In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL (...) formulas can be interpreted as modal formulas over a flow of time, where the logic of each instant is Łukasiewicz, with a finite or infinite number of truth values. As a main result, we obtain validity with respect to all flows of times that are non-branching to the future, and completeness with respect to all finite linear flows of time, or to an appropriate single infinite linear flow of time. It may be argued that this reduces the problem of establishing a meaningful interpretation of the truth values in BL logic to the analogous problem for Łukasiewicz logic. (shrink)

Time perspective theory provides a robust conceptual framework for analyzing human behavior in the context of time. So far, the concept has been studied and applied in multiple life domains, such as education, health, social relationships, environmental behavior, or financial behavior; however its explanatory potential has been completely neglected within the domain of sport. In the present paper we provide a deepened theoretical analysis of the potential role of temporal framing of human experience for sport-related attitudes, emotions, and athletic (...) performance. We propose a conceptual model in which time perspectives influence psychological functioning and performance of athletes via three major mechanisms: 1) magnitude and persistence of sport motivation and resulting athlete engagement, 2) regulation of affective states during sport performance, and 3) appraisal of one’s performance and coping with resulting emotions. We support the theoretical considerations based on the major assumptions of time perspective theory with research findings regarding the regulatory role of time perspectives in other life domains. We also highlight potential research paths that would allow us to empirically test the present model and determine the actual role of temporal perspectives in shaping crucial aspects of athletes’ psychological functioning, as well as levels of their sport performance. (shrink)

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of (...) the original temporal logic like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time. (shrink)

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted with respect (...) to a version of the bundle semantics. (shrink)

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted with respect (...) to a version of the bundle semantics. (shrink)

BackgroundTemporal interference (TI) stimulation is a novel technique that enables the non-invasive modulation of deep brain regions. However, the implementation of this technology in humans has not been well-characterized or examined, including its safety and feasibility.ObjectiveWe aimed to examine the feasibility, safety, and blinding of using TI on human participants in this pilot study.Materials and methodsIn a randomized, single-blinded, and sham-controlled pilot study, healthy young participants were randomly divided into four groups [TI and transcranial alternating current stimulation (tACS) targeting the (...) right frontoparietal region, TI-sham, and tACS-sham]. Each participant was asked to complete N-back (N = 1 to 3) tasks before, during, and after one session of stimulation to assess their working memory (WM). The side effects and blinding efficacy were carefully assessed. The accuracy, reaction time (RT), and inverse efficiency score (IES, reaction time/accuracy) of the N-back tasks were measured.ResultsNo severe side effects were reported. Only mild-to-moderate side effects were observed in those who received TI, which was similar to those observed in participants receiving tACS. The blinding efficacy was excellent, and there was no correlation between the severity of the reported side effects and the predicted type of stimulation that the participants received. WM appeared to be only marginally improved by TI compared to tACS-sham, and this improvement was only observed under high-load cognitive tasks. WM seemed to have improved a little in the TI-sham group. However, it was not observed significant differences between TI and TI-sham or TI and tACS in all N-back tests.ConclusionOur pilot study suggests that TI is a promising technique that can be safely implemented in human participants. Studies are warranted to confirm the findings of this study and to further examine the effects of TI-sham stimulation as well as the effects of TI on deeper brain regions. (shrink)

I present a variant of with time, called, interpreted in standard Kripke semantics. On the syntactic level, is nothing but the extension of atemporal individual by: the future tense and past tense operators, and the operator of group agency for the grand coalition. A sound and complete axiomatisation for is given. Moreover, it is shown that supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment.

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about (...) the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in DEL. (shrink)

Amodal completion is the representation of those parts of the perceived object that we get no sensory stimulation from. While amodal completion is rife and plays an essential role in all sense modalities, philosophical discussions of this phenomenon have almost entirely been limited to vision. The aim of this paper is to examine in what sense we can talk about amodal completion in olfaction. We distinguish three different senses of amodal completion – spatial, temporal and (...) feature-based completion – and argue that all three are present and play a significant role in olfaction. (shrink)

We are purposive agents; but we—adult humans in a broadly modern world—are more than that. We are reflective about our motivation. We form prior plans and policies that organize our activity over time. And we see ourselves as agents who persist over time and who begin, develop, and then complete temporally extended activities and projects. Any reasonably complete theory of human action will need in some way to advert to this trio of features—to our reflectiveness, our planfulness, and our conception (...) of our agency as temporally extended. These are, further, features that have great significance for the kinds of lives we can live. For these two reasons I will say that these are among the core features of human agency. A theory of human action needs to say what these core features consist in and how they are related to each other. And such a theory needs also to clarify the relation between these core features of our agency and the possibility that we are fully embedded in an event causal order. (shrink)

Currently, anomalous lived temporality is not included in the main diagnostic criteria or standard symptom checklists. In this article, we present the Transdiagnostic Assessment of Temporal Experience, a structured interview that can be used by researchers and clinicians without a comprehensive phenomenological background to explore abnormal time experiences in persons with abnormal mental conditions regardless of their diagnosis. When extensive data gathered by this scale are available, it will be possible to delineate well-defined anomalous lived temporality profiles for each (...) psychopathological disorder. This instrument may also prove useful for clinicians by providing a more refined assessment of relevant psychopathological symptoms and an in-depth understanding of the patient’s abnormal behaviour as related to specific types of time experience. In the first part of the article, we provide a brief overview of the phenomenological concept of temporality, including pre-phenomenal and phenomenal time, synthesis, conation and synchronization, and of abnormal time experiences in persons affected by psychopathological conditions. In the following part, we describe the basic structure of the interview that comprises seven categories corresponding to the abnormal features of lived temporality: anomalies of synchrony, of time structure, of implicit time flow, of explicit time flow, and anomalous experiences of the past, the present and the future. The paper also includes a section on administration and scoring of the TATE scale, the complete interview and a Likert table for quantifying the frequency, intensity and interference with daily life of the phenomena explored. (shrink)

As this century has found new temporalities to replace linearity, discontinuities have become commonplace. Discontinuity, if carried to a pervasive extreme, destroys linearity…There were two enormous factors, beyond the general cultural climate, that promoted composers' active pursuit of discontinuities. These influences did not cause so much as feed the dissatisfaction with linearity that many artists felt. But the impact has been profound. One factor contributing to the increase of discontinuity was the gradual absorption of music from totally different cultures, which (...) had evolved over the centuries with virtually no contact with Western ideas…Cross-cultural exchange in music will, of course, never destroy aesthetic boundaries, but music of non-Western cultures continues to show Western composers new ways to use and experience time. The second tremendous influence on twentieth-century musical discontinuity was technological rather than sociological: the invention of recording techniques. Recording has not only brought distant and ancient musics into the here and now, it has also made the home and the car environment just as viable for music listening as the concert hall. The removal of music from the ritualized behavior that surrounds concertgoing struck a blow to the internal ordering of the listening experience. Furthermore, radios, records, and, more recently, tapes allow the listener to enter and exit a composition at will. An overriding progression from beginning to end may or may not be in the music, but the listener is not captive to that completeness. We all spin the dial, and we are more immune to having missed part of the music than composers might like to think. Jonathan D. Kramer is an associate professor of music theory and composition and director of electronic music at the College-Conservatory of Music of the University of Cincinnati. The present essay is part of his book, Time and Meaning in Music. (shrink)

A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n -Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus δ SLTL is defined.

The study of the meanings of temporal expressions in natural language can proceed in two ways. The first consists of borrowing an ontological theory concerning how time “really” is, and then showing how temporal expressions are interpreted in this model. Let us call this the physicalist approach. The other approach is to start off by studying the temporal presuppositions employed in the language, and defining a model as the structure which satisfies these conditions. This approach we shall (...) call the analytist approach. The two approaches share their goal, which is to provide a temporal model for natural language. However, they are driven by different motivations. The physicalist approach is ontology-driven. It views time as part of reality, and its structure as independent of linguistic considerations. It attempts to interpret the language in this model, possibly by adding assumptions about the language. The analytist approach, on the other hand, is language driven. It assumes that language “mirrors” reality to the extent in which it is describable in the language, and tries to define a temporal model based only on linguisticconsiderations. A theory is “complete”, in a sense, if it combines both approaches and its (analytist) language- driven model can be constructed in a (physicalist) ontology-driven structure. (shrink)

Time is more than a line drawn from the past to the future. It is a form of life, marked by the ancient hierarchy between those who have time and those who do not. This hierarchy still governs a present which clings to the fable of historical necessity and its experts. In opposition to this, Jacques Rancière shows how the break with the hierarchical conception of time implies a completely different idea of the modern. He sees the fulfilment of this (...) in two arts of movement, cinema and dance, which at the beginning of the twentieth century abolished the opposition between free and mechanical people, and exposed the rift between the revolution of artists and that of strategists. (shrink)

I present a new problem for the tense realist concerning the evaluation of cross-temporal claims, such as ‘John is now taller than Michael was in 1984’. Time can play two different roles in the evaluation of an utterance of a sentence: either as an element that completes the content expressed by the utterance (the completion role), or as part of the circumstances against which the content is evaluated (the evaluation role). It is this latter role that time plays (...) in the realist view of tenses. I argue that if the content of a cross-temporal sentence is taken at face value (as an ascription of a crosstemporally instantiated relation), time does not play the evaluation role. Therefore, the world of the tense realist seems to leave no room for cross-temporality. (shrink)

With the past and future tense propositional operators in its syntax, a formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. A completeness proof for the system is constructed and its absolute consistency proved. The completeness proof is given relative to a notion of logical validity provided by an intensional semantic system, which assumes an approach to sortals from a modern form of conceptualism.

We are purposive agents; but we—adult humans in a broadly modern world—are more than that. We are reflective about our motivation. We form prior plans and policies that organize our activity over time. And we see ourselves as agents who persist over time and who begin, develop, and then complete temporally extended activities and projects. Any reasonably complete theory of human action will need in some way to advert to this trio of features—to our reflectiveness, our planfulness, and our conception (...) of our agency as temporally extended. These are, further, features that have great significance for the kinds of lives we can live. For these two reasons I will say that these are among the core features of human agency. A theory of human action needs to say what these core features consist in and how they are related to each other. And such a theory needs also to clarify the relation between these core features of our agency and the possibility that we are fully embedded in an event causal order. (shrink)