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Past, Present and Future

Clarendon Press (1967)

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  1. Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization. [REVIEW]Lennart Åqvist - 1996 - Journal of Philosophical Logic 25 (1):45 - 100.
    The paper deals with the problem of axiomatizing a system T1 of discrete tense logic, where one thinks of time as the set Z of all the integers together with the operations +1 ("immediate successor") and-1 ("immediate predecessor"). T1 is like the Segerberg-Sundholm system WI in working with so-called infinitary inference ruldes; on the other hand, it differs from W I with respect to (i) proof-theoretical setting, (ii) presence of past tense operators and a "now" operator, and, most importantly, with (...)
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  • Chrysippus's Response to Diodorus's Master Argument.Harry Ide - 1992 - History and Philosophy of Logic 13 (2):133-148.
    Chrysippus claims that some propositions perish. including some true conditionals whose consequent is impossible and antecedent is possible, to which he appeals against Diodorus?s Master Argument. On the standard interpretation. perished propositions lack truth values. and these conditionals are true at the same time as their antecedents arc possible and consequents impossible. But perished propositions are false, and Chrysippus?s conditionals are true when their antecedent and consequent arc possible, and false when their antecedent is possible and consequent impossible. The claim (...)
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  • Axioms for Deliberative Stit.Ming Xu - 1998 - Journal of Philosophical Logic 27 (5):505-552.
    Based on a notion of "companions to stit formulas" applied in other papers dealing with astit logics, we introduce "choice formulas" and "nested choice formulas" to prove the completeness theorems for dstit logics in a language with the dstit operator as the only non-truth-functional operator. The main logic discussed in this paper is the basic logic of dstit with multiple agents, other logics discussed include the basic logic of dstit with a single agent and some logics of dstit with multiple (...)
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  • A Modal Perspective on the Computational Complexity of Attribute Value Grammar.Patrick Blackburn & Edith Spaan - 1993 - Journal of Logic, Language and Information 2 (2):129-169.
    Many of the formalisms used in Attribute Value grammar are notational variants of languages of propositional modal logic, and testing whether two Attribute Value Structures unify amounts to testing for modal satisfiability. In this paper we put this observation to work. We study the complexity of the satisfiability problem for nine modal languages which mirror different aspects of AVS description formalisms, including the ability to express re-entrancy, the ability to express generalisations, and the ability to express recursive constraints. Two main (...)
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  • Three-Valued Logic, Indeterminacy and Quantum Mechanics.Tomasz Bigaj - 2001 - Journal of Philosophical Logic 30 (2):97-119.
    The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must be already true (resp. false) (...)
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  • A Foundation for Presentism.Robert Pezet - 2017 - Synthese 194 (5):1809–1837.
    Presentism states that everything is present. Crucial to our understanding of this thesis is how we interpret the ‘is’. Recently, several philosophers have claimed that on any interpretation presentism comes out as either trivially true or manifestly false. Yet, presentism is meant to be a substantive and interesting thesis. I outline in detail the nature of the problem and the standard interpretative options. After unfavourably assessing several popular responses in the literature, I offer an alternative interpretation that provides the desired (...)
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  • Branch Dependence in the “Consistent Histories” Approach to Quantum Mechanics.Thomas Müller - 2007 - Foundations of Physics 37 (2):253-276.
    In the consistent histories formalism one specifies a family of histories as an exhaustive set of pairwise exclusive descriptions of the dynamics of a quantum system. We define branching families of histories, which strike a middle ground between the two available mathematically precise definitions of families of histories, viz., product families and Isham’s history projector operator formalism. The former are too narrow for applications, and the latter’s generality comes at a certain cost, barring an intuitive reading of the “histories”. Branching (...)
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  • Change We Can Believe In (and Assert).Meghan Sullivan - 2014 - Noûs 48 (3):474-495.
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  • Worlds, Times and Selves Revisited.Tero Tulenheimo - 2016 - Synthese 193 (11):3713-3725.
    In Prior’s tense-logical analysis, we can avoid mentioning instants in our language by construing them as propositions of a special kind. Instead of qualifying instants by predicates, we may qualify propositions by modalities. Prior shows that by changing the informal interpretation of our modal-like language, we can similarly attempt to avoid ontological commitments to worlds and even to selves and other bona fide individuals. As he notes, the paraphrasing strategy works too generally to be of direct metaphysical use. I wish (...)
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  • The Place of Subjects in the Metaphysics of Material Objects.Thomas Hofweber - 2015 - Dialectica 69 (4):473-490.
    An under-explored intermediate position between traditional materialism and traditional idealism is the view that although the spatiotemporal world is purely material, minds nonetheless have a metaphysically special place in it. One way this can be is via a special role that subjects have in the metaphysics of material objects. Some metaphysical aspect of material objects might require the existence of subjects. This would support that minds must exist if material objects exist and thus that a mindless material world is impossible. (...)
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  • Preface.Jerry Seligman - 1995 - Journal of Logic, Language and Information 4 (3):175-176.
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  • Actions and Outcomes: Two Aspects of Agency.Beth Huffer - 2007 - Synthese 157 (2):241-265.
    Agency can be construed as both the manner in which autonomous individuals embark on particular courses of action (or inaction), and the relationship between such agents and the outcomes of the courses of action on which they embark. A promising strategy for understanding both senses of agency consists in the combination of a modal logic of agency and branching time semantics. Such is the strategy behind stit theory, the theory of agentive action developed by Nuel Belnap and others. However, stit (...)
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  • Possible Worlds in “The Craft of Formal Logic”.Aneta Markoska-Cubrinovska - 2016 - Synthese 193 (11).
    “The Craft of Formal Logic” is Arthur Prior’s unpublished textbook, written in 1950–51, in which he developed a theory of modality as quantification over possible worlds-like objects. This theory predates most of the prominent pioneering texts in possible worlds semantics and anticipates the significance of its basic concept in modal logic. Prior explicitly defines modal operators as quantifiers of ‘entities’ with modal character. Although he talks about these ‘entities’ only informally, and hesitates how to name them, using alternately the phrases (...)
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  • Problems for Temporary Existence in Tense Logic.Meghan Sullivan - 2012 - Philosophy Compass 7 (1):43-57.
    A‐theorists of time postulate a deep distinction between the present, past and future. Settling on an appropriate logic for such a view is no easy matter. This Philosophy Compass article describes one of the most vexing formal problems facing A‐theorists. It is commonly thought that A‐theories can only be formally expressed in a tense logic: a logic with operators like P and F . And it seems natural to think that we live in a world where objects come to exist (...)
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  • Stuff.Paul Needham - 1993 - Australasian Journal of Philosophy 71 (3):270-290.
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  • Agency and Fictional Truth: A Formal Study on Fiction-Making.Giuseppe Spolaore - 2015 - Synthese 192 (5):1235-1265.
    Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon (...)
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  • Branching Time, Indeterminism and Tense Logic.Thomas Ploug & Peter Øhrstrøm - 2012 - Synthese 188 (3):367-379.
    This paper deals with the historical and philosophical background of the introduction of the notion of branching time in philosophical logic as it is revealed in the hitherto unpublished mail-correspondence between Saul Kripke and A.N. Prior in the late 1950s. The paper reveals that the idea was first suggested by Saul Kripke in a letter to A.N. Prior, dated September 3, 1958, and it is shown how the elaboration of the idea in the course of the correspondence was intimately intervowen (...)
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  • Logical Anomalies of Quantum Objects. A Survey.G. Peruzzi - 1990 - Foundations of Physics 20 (3):337-352.
    We discuss some aspects of the concept of “object” and “objectuation” as suggested by the articulation of modern physics. In particular we analyze the new ontological thickness of the notion ofobject in quantum mechanics and in relativistic quantum mechanics.At the end we try to formulate some modifications of the logical approach to quantum theory in order to grasp the new situation connected with relativistic quantum theory.
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  • A Spinozistic Axiomatics in Story Semantics.Charles B. Daniels - 1988 - Philosophia 18 (4):347-356.
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  • Fatalism, Incompatibilism, and the Power to Do Otherwise.Penelope Mackie - 2003 - Noûs 37 (4):672-689.
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  • A Future for the Thin Red Line.Alex Malpass & Jacek Wawer - 2012 - Synthese 188 (1):117-142.
    The thin red line ( TRL ) is a theory about the semantics of future-contingents. The central idea is that there is such a thing as the ‘actual future’, even in the presence of indeterminism. It is inspired by a famous solution to the problem of divine foreknowledge associated with William of Ockham, in which the freedom of agents is argued to be compatible with God’s omniscience. In the modern branching time setting, the theory of the TRL is widely regarded (...)
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  • Temporal Reference in Linear Tense Logic.M. J. Cresswell - 2010 - Journal of Philosophical Logic 39 (2):173-200.
    The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.
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  • On the Puzzle of the Changing Past.Andrea Iacona - 2016 - Philosophia 44 (1):137-142.
    In the intriguing article The puzzle of the changing past, Barlassina and Del Prete argue that, if one grants a platitude about truth and accepts a simple story that they tell, one is forced to conclude that the past has changed. I will suggest that there is a coherent way to resist that conclusion. The platitude about truth is in fact a platitude, but the story is not exactly as they tell it.
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  • Combinations of Stit with Ought and Know.Ming Xu - 2015 - Journal of Philosophical Logic 44 (6):851-877.
    This paper presents a short survey of recent developments in stit theories, with an emphasis on combinations of stit and deontic logic, and those of stit and epistemic logic.
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  • A STIT Logic for Reasoning About Social Influence.Emiliano Lorini & Giovanni Sartor - 2016 - Studia Logica 104 (4):773-812.
    In this paper we propose a method for modeling social influence within the STIT approach to action. Our proposal consists in extending the STIT language with special operators that allow us to represent the consequences of an agent’s choices over the rational choices of another agent.
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  • Presentism, Non-Presentism and the Possibility of Time Travel.David Chico & Juan Colomina - 1st ed. 2015 - In Antonio Manuel Liz Gutiérrez & Margarita Vázquez Campos (eds.), Temporal Points of View. Springer Verlag.
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  • Rates of Passage.James van Cleve - 2011 - Analytic Philosophy 52 (3):141-170.
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  • A Temporal Logic for Reasoning About Processes and Plans.Drew McDermott - 1982 - Cognitive Science 6 (2):101-155.
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  • Worlds and Times: NS and the Master Argument.Peter K. Schotch & Gillman Payette - 2011 - Synthese 181 (2):295-315.
    In the fourteenth century, Duns Scotus suggested that the proper analysis of modality required not just moments of time but also “moments of nature”. In making this suggestion, he broke with an influential view first presented by Diodorus in the early Hellenistic period, and might even be said to have been the inventor of “possible worlds”. In this essay we take Scotus’ suggestion seriously devising first a double-index logic and then introducing the temporal order. Finally, using the temporal order, we (...)
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  • Two-Valued Logics of Intentionality: Temporality, Truth, Modality, and Identity.Gilbert T. Null - 2007 - Husserl Studies 23 (3):187-228.
    The essay introduces a non-Diodorean, non-Kantian temporal modal semantics based on part-whole, rather than class, theory. Formalizing Edmund Husserl’s theory of inner time consciousness, §3 uses his protention and retention concepts to define a relation of self-awareness on intentional events. §4 introduces a syntax and two-valued semantics for modal first-order predicate object-languages, defines semantic assignments for variables and predicates, and truth for formulae in terms of the axiomatic version of Edmund Husserl’s dependence ontology (viz. the Calculus [CU] of Urelements) introduced (...)
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  • On Behalf of a Mutable Future.Patrick Todd - 2016 - Synthese 193 (7):2077-2095.
    Everyone agrees that we can’t change the past. But what about the future? Though the thought that we can change the future is familiar from popular discourse, it enjoys virtually no support from philosophers, contemporary or otherwise. In this paper, I argue that the thesis that the future is mutable has far more going for it than anyone has yet realized. The view, I hope to show, gains support from the nature of prevention, can provide a new way of responding (...)
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  • On Individuals in Branching Histories.Tomasz Placek - 2012 - Synthese 188 (1):23-39.
    Against the background of the theory of branching space-times (BST), the paper sketches a concept of individuals. It discusses Kripkean modal intuitions concerning individuation, and, finally it addresses Lewis’s objections to branching individuals.
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  • The Fitch-Church Paradox and First Order Modal Logic.Carlo Proietti - 2016 - Erkenntnis 81 (1):87-104.
    Reformulation strategies for solving Fitch’s paradox of knowability date back to Edgington. Their core assumption is that the formula \, from which the paradox originates, does not correctly express the intended meaning of the verification thesis, which should concern possible knowledge of actual truths, and therefore the contradiction does not represent a logical refutation of verificationism. Supporters of these solutions claim that can be reformulated in a way that blocks the derivation of the paradox. Unfortunately, these reformulation proposals come with (...)
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  • A. N. Prior's Rediscovery of Tense Logic.Peter Øhrstrøm & Per Hasle - 1993 - Erkenntnis 39 (1):23 - 50.
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  • The Stoics on World-Conflagration and Everlasting Recurrence.A. A. Long - 1984 - Southern Journal of Philosophy 23 (S1):13-37.
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  • Moment/History Duality in Prior’s Logics of Branching-Time.Alberto Zanardo - 2006 - Synthese 150 (3):483-507.
    The basic notions in Prior's Ockhamist and Peircean logics of branching-time are the notion of moment and that of history. In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology on the set (...)
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  • A Formal Characterisation of Hamblin’s Action-State Semantics.Chris Reed & Timothy J. Norman - 2007 - Journal of Philosophical Logic 36 (4):415-448.
    Hamblin's Action-State Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic (...)
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  • No Future.Leon Horsten & Hannes Leitgeb - 2001 - Journal of Philosophical Logic 30 (3):259-265.
    The difficulties with formalizing the intensional notions necessity, knowability and omniscience, and rational belief are well-known. If these notions are formalized as predicates applying to (codes of) sentences, then from apparently weak and uncontroversial logical principles governing these notions, outright contradictions can be derived. Tense logic is one of the best understood and most extensively developed branches of intensional logic. In tense logic, the temporal notions future and past are formalized as sentential operators rather than as predicates. The question therefore (...)
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  • The Revival of Rejective Negation.Lloyd Humberstone - 2000 - Journal of Philosophical Logic 29 (4):331-381.
    Whether assent ("acceptance") and dissent ("rejection") are thought of as speech acts or as propositional attitudes, the leading idea of rejectivism is that a grasp of the distinction between them is prior to our understanding of negation as a sentence operator, this operator then being explicable as applying to A to yield something assent to which is tantamount to dissent from A. Widely thought to have been refuted by an argument of Frege's, rejectivism has undergone something of a revival in (...)
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  • A Gabbay-Rule Free Axiomatization of T X W Validity.Maria Concetta Di Maio & Alberto Zanardo - 1998 - Journal of Philosophical Logic 27 (5):435 - 487.
    The semantical structures called T x W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, $[Unrepresented Character]_{o}$ , which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator ◇. However, these structures are also suitable for interpreting an extended language, $[Unrepresented Character]_{so}$ , containing a further possibility operator $\lozenge^{s}$ which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history 'simultaneity' operator. (...)
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  • Book Reviews: Thomas Müller: Arthur Priors Zeitlogik, Paderborn: Mentis, 2002, S. 319 ISBN 3-89785-257-8; 46 Euro. [REVIEW]Niko Strobach - 2004 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (2):403-411.
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  • A Completeness Proof of Kiczuk’s Logic of Physical Change.Robert Trypuz - 2010 - Studia Logica 95 (1-2):139-159.
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  • All Finitely Axiomatizable Tense Logics of Linear Time Flows Are CoNP-Complete.Tadeusz Litak & Frank Wolter - 2005 - Studia Logica 81 (2):153-165.
    We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■n+1F p → nF p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural (...)
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  • Tense Logic.Ulrich Meyer - 2015 - Philosophy Compass 10 (6):406-419.
    This article surveys some of the key issues that arise when one tries to use tense logic as a metaphysical theory of the nature of time. Topics discussed include basic tense logic, tense logic and verb tense, the structure of the time series, instants of time, quantified tense logic, and the expressive resources of tense logic.
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  • Truth Values, Neither-True-nor-False, and Supervaluations.Nuel Belnap - 2009 - Studia Logica 91 (3):305 - 334.
    The first section (§1) of this essay defends reliance on truth values against those who, on nominalistic grounds, would uniformly substitute a truth predicate. I rehearse some practical, Carnapian advantages of working with truth values in logic. In the second section (§2), after introducing the key idea of auxiliary parameters (§2.1), I look at several cases in which logics involve, as part of their semantics, an extra auxiliary parameter to which truth is relativized, a parameter that caters to special kinds (...)
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  • The Open Future: Bivalence, Determinism and Ontology.Elizabeth Barnes & Ross Cameron - 2009 - Philosophical Studies 146 (2):291-309.
    In this paper we aim to disentangle the thesis that the future is open from theses that often get associated or even conflated with it. In particular, we argue that the open future thesis is compatible with both the unrestricted principle of bivalence and determinism with respect to the laws of nature. We also argue that whether or not the future (and indeed the past) is open has no consequences as to the existence of (past and) future ontology.
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  • Ockhamism Without Thin Red Lines.Andrea Iacona - 2014 - Synthese 191 (12):2633-2652.
    This paper investigates the logic of Ockhamism, a view according to which future contingents are either true or false. Several attempts have been made to give rigorous shape to this view by defining a suitable formal semantics, but arguably none of them is fully satisfactory. The paper draws attention to some problems that beset such attempts, and suggests that these problems are different symptoms of the same initial confusion, in that they stem from the unjustified assumption that the actual course (...)
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  • Actions as Events.Ming Xu - 2012 - Journal of Philosophical Logic 41 (4):765 - 809.
    We present a theory of actions based on a theory of events in branching time, in which "particular" or "token" actions are taken to be sets of transitions from their initial states to the outcomes. We also present a simple theory of composition of events by which composite events can be formed out of other events. Various kinds of actions, including instantaneous group actions and sequential group actions, are introduced by way of composition, and an extended stit theory of agency (...)
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  • Presentism and Truthmaking.Ben Caplan & David Sanson - 2011 - Philosophy Compass 6 (3):196-208.
    Three plausible views—Presentism, Truthmaking, and Independence—form an inconsistent triad. By Presentism, all being is present being. By Truthmaking, all truth supervenes on, and is explained in terms of, being. By Independence, some past truths do not supervene on, or are not explained in terms of, present being. We survey and assess some responses to this.
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  • The Modal Logic of Continuous Functions on Cantor Space.Philip Kremer - 2006 - Archive for Mathematical Logic 45 (8):1021-1032.
    Let $\mathcal{L}$ be a propositional language with standard Boolean connectives plus two modalities: an S4-ish topological modality $\square$ and a temporal modality $\bigcirc$ , understood as ‘next’. We extend the topological semantic for S4 to a semantics for the language $\mathcal{L}$ by interpreting $\mathcal{L}$ in dynamic topological systems, i.e. ordered pairs $\langle X, f\rangle$ , where X is a topological space and f is a continuous function on X. Artemov, Davoren and Nerode have axiomatized a logic S4C, and have shown (...)
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