This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time (...) with a modality for possible paths. We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees. (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)

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)

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.

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

This work aims to make tense logic a more robust tool for ontologists, philosophers, knowledge engineers and programmers by outlining a fusion of tense logic and ontology of time. In order to make tense logic better understandable, the central formal primitives of standard tense logic are derived as theorems from an informal and intuitive ontology of time. In order to make formulation of temporal propositions easier, temporal operators that were introduced by Georg Henrik von Wright are (...) developed, and mapped to the ontology of time. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal (...) frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

We consider several natural fragments of the alternating-time temporal logics ATL* and ATL with restrictions on the nesting between temporal operators and strategic quantifiers. We develop optimal decision procedures for satisfiability in these fragments, showing that they have much lower complexities than the full languages. In particular, we prove that the satisfiability problem for state formulae in the full `strategically flat' fragment of ATL* is PSPACE-complete, whereas the satisfiability problems in the flat fragments of ATL and (...) ATL$^{+}$ are $\Sigma^P_3$-complete. We note that the nesting hierarchies for fragments of ATL* collapse in terms of expressiveness above nesting depth 1, hence our results cover all such fragments with lower complexities. (shrink)

The basic principles of Cipra's metaphysics (according to his book "Metamorphoses of Metaphysics") are analyzed with respect to Cipra's request for the revision of classical logical principles (of identity, excluded middle and contradiction). In Cipra's metaphysics, the principle of identity holds for being, necessity and past only, the principle of excluded middle does not hold for coming-to-be, possibility and present, and the principle of contradiction does not hold for the actuality, reality (freedom) and future. A propositional and first-order temporal (...) model and semantics are defined for such a concept of metaphysical time. The propositional ockhamistic branching time model is extended, in a first-order model, with a non-empty set of object shapes and an equivalence relation between object shapes in time, so that, for example, different, previously equivalent object shapes can in future contradict one another. (shrink)

We develop an approach to temporal logic that replaces the traditional objective, agent- and event-independent notion of time with a constructive, event-dependent notion of time. We show how to make this event-dependent time entropic and hence well-defined. We use sheaf-theoretic techniques to render event-dependent time functorial and to construct memories as sequences of observed and constructed events with well-defined limits that maximize the consistency of categorizations assigned to objects appearing in memories. We then develop a (...) condensed formalism that represents memories as pure constructs from single events. We formulate an empirical hypothesis that human episodic memory implements a particular constructive functor. (shrink)

The branching time analysis grounds the possibilities entailed by temporal indeterminism in a branching temporal structure. I construct a spatial analog of the branching time analysis – the branching space analysis – according to which the possibilities entailed by spatial indeterminism are grounded in branching spatial structure. The construction proceeds in such a way as to show the analogies between the branching space and branching time analyses. I argue (...) that the two views are a package. In particular: the theoretical virtues of the one are theoretical virtues of the other and so if one ought to be accepted, then the other should also be accepted. And: if one ought to be denied, then the other ought to be denied as well. Thus, the branching space analysis functions either as a counterexample to the reductive strategy embodied in the branching time analysis or as a reasonable extension of it – as a lesson learned from it. (shrink)

As the title suggests, this paper is something of a leftover – or perhaps a new branch – to my "Meaning in Time: on temporal externalism and Kripkenstein’s skeptical challenge". In that work I essayed to portray my understanding of the sceptical challenge uncovered by Saul Kripke’s reading of Wittgenstein’s later works in a nutshell as to its nature and resolution. Here, my task is to dig a little deeper into the key phrase of the earlier paper, namely (...) the claim that meanings, facts grounding meaning facts, and ascriptions of meaning have an important historical dimension to them. In particular, I explore the ideas that (i) the problem of finitude is fundamentally a logical and not a metaphysical problem and (ii) Devitt's development of Kripke's causal-historical theory of reference implies a natural explanation for how at least the meanings of some terms can have a historical dimension. (shrink)

An examination of McTaggart’s [1908] argument for the unreality of time.

Logic has sometimes been seen as an alternative to metaphysics and to speculation. In this paper it is argued that a different story should be told when it comes to temporal logic and tense-logic in particular. A. N. Prior’s first formulation of tense logic was mainly established in order to qualify the discussion of certain metaphysical and conceptual problems. Although temporal logic has now been developed in various abstract and rather technical ways, it may still serve as a (...) great help for anyone who wants to clarify the discussion of important existential questions like the nature of time, determinism, future contingency or freedom of choice. (shrink)

Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I compare that way with (...) other two ways based on Łukasiewicz’s three-valued logic and branching temporal logic. (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)

This paper argues for the following disjunction: either we do not live in a world with a branching temporal structure, or backwards time travel is nomologically impossible, given the initial state of the universe, or backwards time travel to our space-time location is impossible given large-scale facts about space and time. A fortiori, if backwards time travel to our location is possible, we do not live in a branching universe.

Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics (...) with interactions between time and knowledge. We discuss some complications that occur, even in the single-agent case, when interactions between time and knowledge are assumed and show how the method of incremental tableaux can be adapted to work in EXPSPACE, respectively 2EXPTIME, for these logics, thereby also matching the upper bounds obtained for them by Halpern and Vardi. (shrink)

Expert knowledge regularly informs personal and civic-decision making. To decide which experts to trust, lay publics —including policymakers and experts from other domains—use different epistemic and non-epistemic cues. Epistemic cues such as honesty, like when experts are forthcoming about conflicts of interest, are a popular way of understanding how people evaluate and decide which experts to trust. However, many other epistemic cues, like the evidence supporting information from experts, are inaccessible to lay publics. Therefore, lay publics simultaneously use second-order social (...) cues in their environment to inform decisions to trust. These second-order social cues, or ‘social indicators of trust’, prevent lay publics from having to trust blindly. Social indicators of trust therefore inform lay publics’ epistemic vigilance, or constant low level-monitoring of testimony from experts. This special issue examines the nature, acquisition and application of social indicators of trust for scientific experts and institutions. It also raises questions about the types of trust asked of lay publics and challenges traditional normative assumptions about the relationship between science and lay publics through study of attitudes, values, and experiences. The issue descriptively re-examines the structure of institutions, their role and methods for ferrying information, as well as how social indicators operate in times of crisis. In this collection of works, we bridge history, science, philosophy of science, science and technology studies, science communication and social epistemology, to broaden the discourse on trust in experts and more accurately reflect the imperfect yet indispensable endeavour that trusting is. (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)

In his 1925/26 lecture Logic: The Question of Truth Heidegger turns to an interpretation of the Critique of Pure Reason in order to elucidate his own understanding of time. The largely overlooked lecture series, I argue, is at the root of Heidegger’s exposition of the concept of time and its relationship with human existence (Dasein). Although Heidegger claims that Kant’s concept of time is confined to that of ‘world-time,’ Heidegger develops the first exposition of his understanding (...) of time as ur-temporality via critical analysis of the Critique of Pure Reason. The investigation reveals the conceptual context behind the relationship between time and Dasein, which develops out of Heidegger’s first in-depth interpretation of the Critique of Pure Reason. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory (...) of rest and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit counterparts to modal logics. The behavior and interaction of agents in distributed system is often modeled using logics of knowledge and time. In this paper, we sketch some preliminary ideas on how the modal knowledge part of such logics of knowledge and time (...) could be replaced with an appropriate justification logic. (shrink)

The main question of metasemantics, or foundational semantics, is why an expression token has the meaning (semantic value) that it in fact has. In his reading of Ludwig Wittgenstein’s later work, Saul Kripke presented a skeptical challenge that threatened to make the foundational question unanswerable. My first contention in this paper is that the skeptical challenge indeed poses an insoluble paradox, but only for a certain kind of metasemantic theory, against which the challenge effectively works as a reductio ad absurdum (...) argument. My second contention is that as a result of rejecting the theory which entails a paradoxical outcome, we will see that the foundational question essentially involves a temporal dimension. After arguing that the skeptical challenge gives us a strong reason to adopt a historical view of meaning, I shall further argue against certain authors who claim that meanings not only have histories but futures as well, or that the meaning of a word may change retroactively in time as a consequence of counterfactual change in its future use. The major aim of the paper is thus to bring together the arguably interrelated debates about the skeptical challenge and temporal externalism in philosophy of language. (shrink)

The book deals with conceptualization of time in different languages and in different kinds of discourse (folklore, poetry, fiction). Special attention is paid to some culture-specific models of time as well as to linguistic means related to temporal semantics: nouns, adjectives, adverbs, prepositions, prefixes, particles, and other temporal modifiers. The concept of time is also considered in its logical, axiological and historical aspects.

"Time. Perception. Imagination. Phenomenological Studies on the Question of Time by Augustine, Kant and Husserl". (rus), SPb, 2013. Summary: The monograph is devoted to the key elements of the philosophy of time which determine the necessity of historicism in the analysis of subjectivity. The main idea which defined the composition and design of this work is to trace how the Kantian definition of time as the “form of inner sense” is revealed in Husserl’s phenomenology. The original (...) intention was to understand all three components of this definition. Firstly, what is the inner form, in terms of phenomenology, what are the principles of its constitution and how one can talk about the property of formation? Secondly, what is the meaning of the term "inner" in philosophy, where the division into internal and external has always been a formality, not affecting the essence of things? And finally, what sort of “sensibility” is assumed in transcendental science, bound to become the basis of understanding the history and culture. Presumably, these three Kantian concepts constituted the original plan to analyze the nature of cognitive capabilities of the subject, claiming the gnoseological stage on which the philosophy of time is unfolded. In other words, this work deals with the historical and philosophical analysis of the phenomenological principles by which the concept of time as developed in the twentieth century emerged in the framework of phenomenology. The analyze of the structure of the subject assumes that time, perception and imagination combine in a special type of inner synthesis, which may not be relevant to certain aspects of the method but maintain the basis for a kind of anthropology of time, in continuation of the traditional “inner” contemplation. I consider the inner structure of time with the account of philosophy of St. Augustine, who in many respects not only anticipated the conclusions of phenomenology, but also in his reflections encompassed deeper layers of inner experience. The first chapter is devoted to the doctrine of St. Augustine, in which the theory of time is analyzed in conjunction with the doctrine of “inner word”, specifics of memory representations and notion of inner sense. Additionally, I consider St. Augustine’s reflections about numbers that constitute the basis of aesthetic perception of music (De Musica). Thus, the philosophy of St. Augustine already covers the whole spectrum of anthropology of time, including the question of relation between time and eternity, which remains practically unexplored in phenomenology and serves as the proof of that in interactions between philosophy and theology the tradition remains important. The second chapter of this study is devoted to analysis of the transcendental aesthetic of Kant, which includes all the methodological possibilities of considering the category of time as a formal condition for any experience, consequentially serving as a foundation for further logical development by Husserl, which includes the critical disengagement of the founder of phenomenology from Kant's transcendentalism. Particular attention is paid to the origin of the concept of inner sense, as well as possible interpretations of the function of imagination, which as a transcendental ability remains the most interesting type of synthesis. Handwritten fragments of Kant’s works are also of interest to the character of the imagery as considered in detail by Husserl. Chapter three discusses the phenomenology of inner time consciousness, represented in those important aspects, without which it is impossible to speak about the internal structure of temporal experience - the subjectivity of time, retention, "living present", and the character of synthesis. Particular attention is paid to Husserl's polemics with those representatives of psychological branch in the studies of consciousness, whose ideas greatly influenced the very motivation for creating the method. Apart from the well-known criticism of Brentano, the third chapter highlights the rarely analyzed psychological ideas that motivated the choice of Husserl’s terminology - the "Präsenzzeit” by W. Stern, the "psychological analysis" by A. Meinong, and the “fusion” (Verschmelzung) by K. Stumpf. Chapter four deals with the need to analyze the specifics of image as an element of consciousness and imagery as such, which includes a system of objectified acts. Thus is revealed the very nature of synthetic connections in the acts of consciousness, as well as the presumably imaginative character of the constitution of temporal form. (shrink)

In this paper we analyze how the semantics of the Alternating-time Temporal Logic ATL$^*$ deals with agents' commitments to strategies in the process of formula evaluation. In (\acro{atl}$^*$), one can express statements about the strategic ability of an agent (or a coalition of agents) to achieve a goal $\phi$ such as: ``agent $i$ can choose a strategy such that, if $i$ follows this strategy then, no matter what other agents do, $\phi$ will always be true''. However, strategies in (...) \acro{atl} are \emph{revocable} in the sense that in the evaluation of the goal $\phi$ the agent $i$ is no longer restricted by the strategy she has chosen in order to reach the state where the goal is evaluated. -/- Here we discuss some alternatives leading to amendments of that semantics. In particular, we consider variants of \acro{atl}$^*$ where strategies, on the contrary, are \emph{irrevocable}. Unlike in the standard semantics of \acro{atl}, memory plays an essential role in the semantics based on irrevocable strategies. -/- Further, we propose and discuss various syntactic and semantics mechanisms for handling commitments to strategies and release from such commitments in the semantics of ATL$^*$, leading to more expressive and semantically refined versions of that logic. (shrink)

This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space-time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only (...) be coherently formulated on a model with at least two temporal dimensions, and that this results in severing the link between branch attrition and the flow of time. I argue that ‘no backward branching’ prohibits Belnap’s theory from capturing the modal content of indeterministic physical theories, and results in it ascribing to the world a time-asymmetric modal structure that lacks physical justification. (shrink)

In this article, I seek to explore Hip Hop as an expression of marronage. I identify marronage as an existential mode of being which restitutes human temporality. Slavery and flight from slavery constituted two inextricable historical processes, therefore logics of marronage must also constitute contemporary human experience. I argue that Hip Hop offers a distinct way of affirming and expressing one’s existence through what has been called a “maroon consciousness.” In the same way that maroons created new worlds free (...) from the tyranny of slavery, Hip Hop offers the Hip Hoppa a space free from colonial logics. (shrink)

The master argument posits a metaphysical thesis: Diodorus does away with Aristotle’s dunamis understood as a power simultaneously oriented toward being and non-being and proclaims that possibilities that fail to actualize are simply nothing. My contention is that this claim is not a mere application of Diodorus’ contribution to modal logic. Rather, Diodorus creates an ontologico-temporal concept of possibility and impossibility. Diodorus envisions the future as the past that the future will become. Since what will have been can never (...) be the accomplishment of a possibility that did not obtain, and since the future is destined to become past, any futural possibility that doesn’t actualize is neither futural nor even possible. (shrink)

This book advertises itself as an exploration of the world-time parallel, that is, the parallel between the modal dimension, on the one hand, and the temporal dimension, on the other. It is that, and much more. As the authors point out, there is reasonable agreement that we can model times, through temporal logic, in ways that are analogous to those by which we model modality through the logic of possible worlds. But this formal parallel has almost universally (...) been taken to be a merely formal parallel: thus it is held that no metaphysical conclusions ought to be drawn from it. Thus, it is generally thought that one is free to accept an argument for actualism, say, but to reject a parallel argument for presentism. Rini and Cresswell compellingly argue that this is a mistake: the temporal and the modal are more than merely formally analogous. (shrink)

Aristotle argues that time depends on soul to count it, but adds that motion, which makes time what it is, may be independent of soul. The claim that time depends on soul or mind implies that there is at least one measurable property of natural beings that exists because of the mind’s activity. This paper argues that for Aristotle time depends partly on soul, but more importantly on motion, which defines a continuum. This argument offers a (...) robust metaphysics of time. In contrast to modern philosophy of physics, for Aristotle the continuum of motion is prior in being to time, while time is a hybrid of the real continuum of motion and the activity of mind. (shrink)

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on (...) structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality. (shrink)

The article reviews some analyses of temporal language in logical approaches to natural language semantics. It considers some asymmetries between past and future, manifested in language, which motivate the “standard view” of the non-reversibility of time and the persistence of the past. It concludes with a puzzle about the changing past which challenges the standard view.

In most cases, we think that what settles what act it is right to perform is sensitive to what we take the facts about the world to be. But those facts include many controversial metaphysical claims about the world. I argue that depending on what metaphysical model we take to be correct, we will have very different views about what the right actions are. In particular, I argue that if a particular metaphysical model — the branching universe model — (...) is correct, then many of our ethical intuitions are false. We need to think carefully about the relation between ethical and metaphysical intuitions, and ethical and metaphysical theories. (shrink)

John Perry has argued that language, thought and experience often contain unarticulated constituents. I argue that this idea holds the key to explaining away the intuitive appeal of the A-theory of time and the endurance theory of persistence. The A-theory has seemed intuitively appealing because the nature of temporal experience makes it natural for us to use one-place predicates like past to deal with what are really two-place relations, one of whose constituents is unarticulated. The endurance view can (...) be treated in a similar way; the temporal boundaries of temporal parts of objects are unarticulated in experience and this makes it seem that the very same entity exists at different times. (shrink)

This book surveys the ways in which languages of different types refer to past, present, and future events and how these referents are related to the knowledge and attitudes of discourse participants. The book is the culmination of fifteen years of research by the author. Four major language types are examined in-depth: tense-based English, tense-aspect-based Polish, aspect-based Chinese, and mood-based Kalaallisut. Each contributes to a series of logical representation languages, which together define a common logical language that is argued to (...) underlie all language types. The four types differ in whether they choose to grammaticalize discourse reference to times (tense), events (aspect), and/or attitudes (mood), and how non-grammaticalized elements are inferred. The common logical language is a dynamic update logic, building on DRT and Centering Theory, but with a novel architecture—e.g. the distinction between focal vs. peripheral attention plays a key role, parallel to focal vs. peripheral vision. (shrink)

The topic is time travel of the sort depicted in H. G. Wells’ classic novel, The Time Machine—Wellsian time travel. The range of proper applicability of the concept of Wellsian time travel is investigated. The results of this investigation are applied to provide a new argument against the metaphysical possibility of time travel in absolute time. Alternatively, the argument is against the possibility of Wellsian time travel relative to a single temporal frame (...) of reference. The argument leaves open the prospect that an object nontrivially moves relative to one temporal reference frame from one time to another relative to another temporal reference frame. The argument does not turn on closed timelike curves or “causal loops” of any kind. It does however invoke the prospect of backward causation—a consequence of backward time travel in conjunction with common sense—but it invokes this possibility only in the weak sense of mere logical consistency. (shrink)

The seventeenth century Muslim philosopher Muhammad Sadr al-Din Shirazi, known as Mulla Sadra, introduced the idea of substantial motion in Islamic philosophy. This view is characterized by a continuity criterion for diachronic identity, a four-dimensional view of individual substances, the notion that possibilities change, and the continual creation of all creatures. Modern philosophical logic provides means to model a variety of claims about individuals, substances, modality and time. In this paper, the semantics of formal systems discussed by Carnap, Bressan (...) and Gupta are reviewed with regard to the issue of substance and identity. Next a model introduced by Storrs McCall is described that is able to build upon and yet resolve some of the issues about substance and identity as characterized by Bressan and others. McCall’s model is also shown to be able to provide an illustration of Mulla Sadra’s doctrine of substantial motion. (shrink)

Open theists argue that God's relationship to time, as conceived in classical theism, is erroneous. They explain that it is contradictory for an atemporal being to act in a temporal universe, including experiencing its temporal successions. Contrary to the atemporalists, redemptive history has shown that God interacts with humans in time. This relational nature of God nullifies the classical notion of God as timelessly eternal. Therefore, it lacks a philosophical and theological basis. Because God is in (...) time, He does not know all future contingencies and, therefore, changes. This study examines open theism's appropriation of the A and B theories of time to the divine-human relationship. The study argues that divine temporality does not solve the tension of divine-human relationships, especially in relation to the future. Further, historical divine temporality does not negate the fact of divine atemporality. It mainly stems from God's choice to create temporal creatures and His relationship with them. Furthermore, if it is not logically and metaphysically contradictory for an omnipresent being to act in space, then it follows that an atemporal being can act in time. Whether time is understood from the metric or psychological point of view, it does not transcend God, and therefore, the limitation it places on human creatures with respect to the future does not apply to God. Lastly, although a few philosophers reject the notion of eternity as timelessly eternal, the doctrine has a philosophical and theological basis in the Scripture. (shrink)

In light of the recent emergence of predictive techniques in law enforcement to forecast crimes before they occur, this paper examines the temporal operation of power exercised by predictive policing algorithms. I argue that predictive policing exercises power through a paranoid style that constitutes a form of temporal governmentality. Temporality is especially pertinent to understanding what is ethically at stake in predictive policing as it is continuous with a historical racialized practice of organizing, managing, controlling, and stealing (...) class='Hi'>time. After first clarifying the concept of temporal governmentality, I apply this lens to Chicago Police Department’s Strategic Subject List. This predictive algorithm operates, I argue, through a paranoid logic that aims to preempt future possibilities of crime on the basis of a criminal past codified in historical crime data. (shrink)

In discussion on consciousness and the hard problem, there is an unquestioned background assumption, namely, our experience is stored in the brain. Yet Bergson argued that this very question, “Is experience stored in the brain?” is the critical issue in the problem of consciousness. His examination of then-current memory research led him, save for motor or procedural memory, to a “no” answer. Others, for example Sheldrake, have continued this negative assessment of the research findings. So, has this assumption actually been (...) proven since Bergson? Do we know how experience is stored? Or that it is stored? Here, a recent review and model of memory is examined to see where this assumption actually stands. Again, the assessment will be that nothing has changed. The core of the problem, it will be argued, lies in two things: Firstly, the search for how/where experience is stored is motivated—rephrasing Bergson—in the classic metaphysic, a framework on space and time whose logic cannot be coherently, logically adhered to in attempting to explain how experience is stored. Secondly, the search generally assumes an inadequate theory of perception that is implicitly based in this classic metaphysic. If framed within Bergson’s model of perception and his temporal metaphysic, conjoined with J. J. Gibson’s model, the storage-search appears misguided from the start. (shrink)

This paper suggests that time could have a much richer mathematical structure than that of the real numbers. Clark & Read (1984) argue that a hypertask (uncountably many tasks done in a finite length of time) cannot be performed. Assuming that time takes values in the real numbers, we give a trivial proof of this. If we instead take the surreal numbers as a model of time, then not only are hypertasks possible but so is an (...) ultratask (a sequence which includes one task done for each ordinal number—thus a proper class of them). We argue that the surreal numbers are in some respects a better model of the temporal continuum than the real numbers as defined in mainstream mathematics, and that surreal time and hypertasks are mathematically possible. (shrink)

A “conceptual spaces” approach is used to formalize Aristotle’s main intuitions about time and change, and other ideas about temporal points of view. That approach has been used in earlier studies about points of view. Properties of entities are represented by locations in multidimensional conceptual spaces; and concepts of entities are identified with subsets or regions of conceptual spaces. The dimensions of the spaces, called “determinables”, are qualities in a very general sense. A temporal element is introduced (...) by adding a time variable to state functions that map entities into conceptual spaces. That way, states may have some permanency or stability around time instances. Following Aristotle’s intuitions, changes and events will not be necessarily instant phenomena, instead they could be processual and interval dependent. Change is defined relatively to the interval during which the change is taking place. Time intervals themselves are taken to represent points of view. To have a point of view is to look at the world as it is in the selected interval. Many important concepts are relativized to intervals, for instance change, events, identity, ontology, potentiality, etc. The definition of points of view as intervals allows to compare points of view in relation to all these concepts. The conceptual space approach has an immediate semantic and structural character, but it is tempting to develop also logics to describe them. A formal language is introduced to show how this could be done. (shrink)

The project format has become a standard and self-evident way to organize research work in today's accelerated university context, leading to the projectification of science. This paper argues that the project format is not a mere technical organizational tool, but that it challenges and reshapes research practices and ideals. The project format is embedded in a specific temporality which is called project time. The key characteristics of project time are scrutinized by distinguishing it from process time, which (...) refers to the internal organizational logic of research. In addition, project time is examined through Barbara Adam's theorizing on the commodification, control, compression and colonization of clock time. In the last part of the paper, temporal conflicts in project-based research are examined empirically by drawing upon interview material with Finnish academics working in the social sciences. (shrink)

Although the dream narrative, of (bio)logical necessity, originates with the dreamer, s/he typically does not know this. For the dreamer, the dream world is the real world. In this article I argue that this nightly misattribution is best explained in terms of the concept of mental ownership (e.g., Albahari, 2006; Klein, 2015a; Lane, 2012). Specifically, the exogenous nature of the dream narrative is the result of an individual assuming perspectival, but not personal, ownership of content s/he authored (i.e., “The content (...) in my head is not mine. Therefore it must be peripherally perceived”). Situating explanation within a theoretical space designed to address questions pertaining to the experienced origins of conscious content has a number of salutatory consequences. For example, it promotes predictive fecundity by bringing to light empirical generalizations whose presence otherwise might have gone unnoticed (e.g., the severely limited role of mental time travel within the dream narrative). -/- . (shrink)

In discussion on consciousness and the hard problem, there is an unquestioned background assumption, namely, our experience is stored in the brain. Yet Bergson (1896) argued that this very question, “Is experience stored in the brain?” is the critical issue in the problem of consciousness. His examination of then-current memory research led him, save for motor or procedural memory, to a “no” answer. Others, for example Sheldrake (2012), have continued this negative assessment of the research findings. So, has this assumption (...) actually been proven since Bergson? Do we know how experience is stored? Or that it is stored? Here, a recent review and model of memory is examined to see where this assumption actually stands. Again, the assessment will be that nothing has changed. The core of the problem, it will be argued, lies in two things: Firstly, the search for how/where experience is stored is motivated – rephrasing Bergson – in the classic metaphysic, a framework on space and time whose logic cannot be coherently, logically adhered to in attempting to explain how experience is stored. Secondly, the search generally assumes an inadequate theory of perception that is implicitly based in this classic metaphysic. If framed within Bergson’s model of perception and his temporal metaphysic, conjoined with J. J. Gibson’s model, the storage-search appears misguided from the start. (shrink)

ABSTRACT: An introduction to Stoic logic. Stoic logic can in many respects be regarded as a fore-runner of modern propositional logic. I discuss: 1. the Stoic notion of sayables or meanings (lekta); the Stoic assertibles (axiomata) and their similarities and differences to modern propositions; the time-dependency of their truth; 2.-3. assertibles with demonstratives and quantified assertibles and their truth-conditions; truth-functionality of negations and conjunctions; non-truth-functionality of disjunctions and conditionals; language regimentation and ‘bracketing’ devices; Stoic basic principles of propositional logic; (...) 4. Stoic modal logic; 5. Stoic theory of arguments: two premisses requirement; validity and soundness; 6. Stoic syllogistic or theory of formally valid arguments: a reconstruction of the Stoic deductive system, which consisted of accounts of five types of indemonstrable syllogisms, which function as nullary argumental rules that identify indemonstrables or axioms of the system, and four deductive rules (themata) by which certain complex arguments can be reduced to indemonstrables and thus shown to be formally valid themselves; 7. arguments that were considered as non-syllogistically valid (subsyllogistic and unmethodically concluding arguments). Their validity was explained by recourse to formally valid arguments. (shrink)

This paper presents an axiomatic formalization of a theory of top-level relations between three categories of entities: individuals, universals, and collections. We deal with a variety of relations between entities in these categories, including the sub-universal relation among universals and the parthood relation among individuals, as well as cross-categorial relations such as instantiation and membership. We show that an adequate understanding of the formal properties of such relations – in particular their behavior with respect to time – is critical (...) for geographic information processing. The axiomatic theory is developed using Isabelle, a computational system for implementing logical formalisms. All proofs are computer verified and the computational representation of the theory is available online. (shrink)

The Logic of Causation: Definition, Induction and Deduction of Deterministic Causality is a treatise of formal logic and of aetiology. It is an original and wide-ranging investigation of the definition of causation (deterministic causality) in all its forms, and of the deduction and induction of such forms. The work was carried out in three phases over a dozen years (1998-2010), each phase introducing more sophisticated methods than the previous to solve outstanding problems. This study was intended as part of a (...) larger work on causal logic, which additionally treats volition and allied cause-effect relations (2004). The Logic of Causation deals with the main technicalities relating to reasoning about causation. Once all the deductive characteristics of causation in all its forms have been treated, and we have gained an understanding as to how it is induced, we are able to discuss more intelligently its epistemological and ontological status. In this context, past theories of causation are reviewed and evaluated (although some of the issues involved here can only be fully dealt with in a larger perspective, taking volition and other aspects of causality into consideration, as done in Volition and Allied Causal Concepts). Phase I: Macroanalysis. Starting with the paradigm of causation, its most obvious and strongest form, we can by abstraction of its defining components distinguish four genera of causation, or generic determinations, namely: complete, partial, necessary and contingent causation. When these genera and their negations are combined together in every which way, and tested for consistency, it is found that only four species of causation, or specific determinations, remain conceivable. The concept of causation thus gives rise to a number of positive and negative propositional forms, which can be studied in detail with relative ease because they are compounds of conjunctive and conditional propositions whose properties are already well known to logicians. The logical relations (oppositions) between the various determinations (and their negations) are investigated, as well as their respective implications (eductions). Thereafter, their interactions (in syllogistic reasoning) are treated in the most rigorous manner. The main question we try to answer here is: is (or when is) the cause of a cause of something itself a cause of that thing, and if so to what degree? The figures and moods of positive causative syllogism are listed exhaustively; and the resulting arguments validated or invalidated, as the case may be. In this context, a general and sure method of evaluation called ‘matricial analysis’ (macroanalysis) is introduced. Because this (initial) method is cumbersome, it is used as little as possible – the remaining cases being evaluated by means of reduction. Phase II: Microanalysis. Seeing various difficulties encountered in the first phase, and the fact that some issues were left unresolved in it, a more precise method is developed in the second phase, capable of systematically answering most outstanding questions. This improved matricial analysis (microanalysis) is based on tabular prediction of all logically conceivable combinations and permutations of conjunctions between two or more items and their negations (grand matrices). Each such possible combination is called a ‘modus’ and is assigned a permanent number within the framework concerned (for 2, 3, or more items). This allows us to identify each distinct (causative or other, positive or negative) propositional form with a number of alternative moduses. This technique greatly facilitates all work with causative and related forms, allowing us to systematically consider their eductions, oppositions, and syllogistic combinations. In fact, it constitutes a most radical approach not only to causative propositions and their derivatives, but perhaps more importantly to their constituent conditional propositions. Moreover, it is not limited to logical conditioning and causation, but is equally applicable to other modes of modality, including extensional, natural, temporal and spatial conditioning and causation. From the results obtained, we are able to settle with formal certainty most of the historically controversial issues relating to causation. Phase III: Software Assisted Analysis. The approach in the second phase was very ‘manual’ and time consuming; the third phase is intended to ‘mechanize’ much of the work involved by means of spreadsheets (to begin with). This increases reliability of calculations (though no errors were found, in fact) – but also allows for a wider scope. Indeed, we are now able to produce a larger, 4-item grand matrix, and on its basis find the moduses of causative and other forms needed to investigate 4-item syllogism. As well, now each modus can be interpreted with greater precision and causation can be more precisely defined and treated. In this latest phase, the research is brought to a successful finish! Its main ambition, to obtain a complete and reliable listing of all 3-item and 4-item causative syllogisms, being truly fulfilled. This was made technically feasible, in spite of limitations in computer software and hardware, by cutting up problems into smaller pieces. For every mood of the syllogism, it was thus possible to scan for conclusions ‘mechanically’ (using spreadsheets), testing all forms of causative and preventive conclusions. Until now, this job could only be done ‘manually’, and therefore not exhaustively and with certainty. It took over 72’000 pages of spreadsheets to generate the sought for conclusions. This is a historic breakthrough for causal logic and logic in general. Of course, not all conceivable issues are resolved. There is still some work that needs doing, notably with regard to 5-item causative syllogism. But what has been achieved solves the core problem. The method for the resolution of all outstanding issues has definitely now been found and proven. The only obstacle to solving most of them is the amount of labor needed to produce the remaining (less important) tables. As for 5-item syllogism, bigger computer resources are also needed. (shrink)