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  1. Thomas Ågotnes (2006). Action and Knowledge in Alternating-Time Temporal Logic. Synthese 149 (2):375 - 407.
    Alternating-time temporal logic (ATL) is a branching time temporal logic in which statements about what coalitions of agents can achieve by strategic cooperation can be expressed. Alternating-time temporal epistemic logic (ATEL) extends ATL by adding knowledge modalities, with the usual possible worlds interpretation. This paper investigates how properties of agents’ actions can be expressed in ATL in general, and how properties of the interaction between action and knowledge can be expressed in ATEL in particular. One commonly discussed property is that (...)
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  2. Seiki Akama, Yasunori Nagata & Chikatoshi Yamada (2008). Three-Valued Temporal Logic Q T and Future Contingents. Studia Logica 88 (2):215 - 231.
    Prior's three-valued modal logic Q was developed as a philosophically interesting modal logic. Thus, we should be able to modify Q as a temporal logic. Although a temporal version of Q was suggested by Prior, the subject has not been fully explored in the literature. In this paper, we develop a three-valued temporal logic $Q_t $ and give its axiomatization and semantics. We also argue that $Q_t $ provides a smooth solution to the problem of future contingents.
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  3. Krzysztof R. Apt & Robert van Rooij (eds.) (2008). New Perspectives on Games and Interactions. Amsterdam University Press.
    This volume is a collection of papers presented at the colloquium, and it testifies to the growing importance of game theory as a tool that can capture concepts ...
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  4. Lennart Åqvist (2010). Grades of Probability Modality in the Law of Evidence. Studia Logica 94 (3):307 - 330.
    The paper presents an infinite hierarchy PR m [ m = 1, 2, . . . ] of sound and complete axiomatic systems for modal logic with graded probabilistic modalities , which are to reflect what I have elsewhere called the Bolding-Ekelöf degrees of evidential strength as applied to the establishment of matters of fact in law-courts. Our present approach is seen to differ from earlier work by the author in that it treats the logic of these graded modalities not (...)
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  5. Lennart Åqvist (2002). Old Foundations for the Logic of Agency and Action. Studia Logica 72 (3):313-338.
    The paper presents an infinite hierarchy of sound and complete axiomatic systems for Two-Dimensional Modal Tense Logic with Historical Necessity, Agents and Acts. A main novelty of these logics is their capacity to represent formally (i) basic action-sentences asserting that such and such an act is performed/omitted by an agent, as well as (ii) causative action-sentences asserting that by performing/omitting a certain act, an agent causes that such and such a state-of-affairs is realized (e.g. comes about/ceases/remains/remains absent). We illustrate how (...)
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  6. Lennart Åqvist (1999). The Logic of Historical Necessity as Founded on Two-Dimensional Modal Tense Logic. Journal of Philosophical Logic 28 (4):329-369.
    We consider a version of so called T x W logic for historical necessity in the sense of R.H. Thomason (1984), which is somewhat special in three respects: (i) it is explicitly based on two-dimensional modal logic in the sense of Segerberg (1973); (ii) for reasons of applicability to interesting fields of philosophical logic, it conceives of time as being discrete and finite in the sense of having a beginning and an end; and (iii) it utilizes the technique of systematic (...)
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  7. Lennart Åqvist (1996). Discrete Tense Logic with Infinitary Inference Rules and Systematic Frame Constants: A Hilbert-Style Axiomatization. [REVIEW] 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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  8. Lennart Åqvist (1979). A Conjectured Axiomatization of Two-Dimensional Reichenbachian Tense Logic. Journal of Philosophical Logic 8 (1):1 - 45.
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  9. Miloš Arsenijević (2002). Determinism, Indeterminism and the Flow of Time. Erkenntnis 56 (2):123 - 150.
    A set of axioms implicitly defining the standard, though not instant-based but interval-based, time topology is used as a basis to build a temporal modal logic of events. The whole apparatus contains neither past, present, and future operators nor indexicals, but only B-series relations and modal operators interpreted in the standard way. Determinism and indeterminism are then introduced into the logic of events via corresponding axioms. It is shown that, if determinism and indeterminism are understood in accordance with their core (...)
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  10. S. Artemov, Dynamic Topological Logic.
    Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system be (...)
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  11. Zdzisław Augustynek (1976). Past, Present and Future in Relativity. Studia Logica 35 (1):45 - 53.
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  12. Philippe Balbiani, Andreas Herzig & Nicolas Troquard (2008). Alternative Axiomatics and Complexity of Deliberative Stit Theories. Journal of Philosophical Logic 37 (4):387 - 406.
    We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of Chellas’s STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators (...)
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  13. Robert F. Barnes (1981). Interval Temporal Logic: A Note. [REVIEW] Journal of Philosophical Logic 10 (4):395 - 397.
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  14. Rainer Bäuerle (1979). Tense Logics and Natural Language. Synthese 40 (2):225 - 230.
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  15. Donald L. M. Baxter (2000). A Humean Temporal Logic. The Proceedings of the Twentieth World Congress of Philosophy 2000 (Analytic Philosophy and Logic):209-216.
    Hume argues that the idea of duration is just the idea of the manner in which several things in succession are arrayed. In other words, the idea of duration is the idea of successiveness. He concludes that all and only successions have duration. Hume also argues that there is such a thing as a steadfast object—something which co-exists with many things in succession, but which is not itself a succession. Thus, it seems that Hume has committed himself to a contradiction: (...)
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  16. Jc Beall (2012). Future Contradictions. Australasian Journal of Philosophy 90 (3):547-557.
    A common and much-explored thought is ?ukasiewicz's idea that the future is ?indeterminate??i.e., ?gappy? with respect to some claims?and that such indeterminacy bleeds back into the present in the form of gappy ?future contingent? claims. What is uncommon, and to my knowledge unexplored, is the dual idea of an overdeterminate future?one which is ?glutty? with respect to some claims. While the direct dual, with future gluts bleeding back into the present, is worth noting, my central aim is simply to sketch (...)
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  17. Susanne Bobzien (1993). Chrysippus' Modal Logic and Its Relation to Philo and Diodorus. In K. Doering & Th Ebert (eds.), Dialektiker und Stoiker. Franz Steiner. 63--84.
    ABSTRACT: The modal systems of the Stoic logician Chrysippus and the two Hellenistic logicians Philo and Diodorus Cronus have survived in a fragmentary state in several sources. From these it is clear that Chrysippus was acquainted with Philo’s and Diodorus’ modal notions, and also that he developed his own in contrast of Diodorus’ and in some way incorporated Philo’s. The goal of this paper is to reconstruct the three modal systems, including their modal definitions and modal theorems, and to make (...)
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  18. Giacomo Bonanno (2008). Belief Revision in a Temporal Framework. In Krzysztof Apt & Robert van Rooij (eds.), New Perspectives on Games and Interaction. Amsterdam University Press.
    The theory of belief revision deals with (rational) changes in beliefs in response to new information. In the literature a distinction has been drawn between belief revision and belief update (see [6]). The former deals with situations where the objective facts describing the world do not change (so that only the beliefs of the agent change over time), while the letter allows for situations where both the facts and the doxastic state of the agent change over time. We focus on (...)
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  19. Giacomo Bonanno (2007). Axiomatic Characterization of the AGM Theory of Belief Revision in a Temporal Logic. Artificial Intelligence 171 (2-3):144-160.
    Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the (...)
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  20. Craig Bourne (2004). Future Contingents, Non-Contradiction, and the Law of Excluded Middle Muddle. Analysis 64 (2):122–128.
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  21. David Bresolin, Joanna Golinska-Pilarek & Ewa Orlowska (2006). Relational Dual Tableaux for Interval Temporal Logics. Journal of Applied Non-Classical Logics 16 (3-4):251–277.
    Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems enable us to verify validity and entailment of these temporal logics. We show how to incorporate in the systems various relations between intervals and/or (...)
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  22. Rachael Briggs & Graeme A. Forbes (2012). The Real Truth About the Unreal Future. In Karen Bennett & Dean Zimmerman (eds.), Oxford Studies in Metaphysics, volume 7.
    Growing-Block theorists hold that past and present things are real, while future things do not yet exist. This generates a puzzle: how can Growing-Block theorists explain the fact that some sentences about the future appear to be true? Briggs and Forbes develop a modal ersatzist framework, on which the concrete actual world is associated with a branching-time structure of ersatz possible worlds. They then show how this branching structure might be used to determine the truth values of future contingents. They (...)
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  23. Eric M. Brown, Logic II: The Theory of Propositions.
    This is part two of a complete exposition of Logic, in which there is a radically new synthesis of Aristotelian-Scholastic Logic with modern Logic. Part II is the presentation of the theory of propositions. Simple, composite, atomic, compound, modal, and tensed propositions are all examined. Valid consequences and propositional logical identities are rigorously proven. Modal logic is rigorously defined and proven. This is the first work of Logic known to unite Aristotelian logic and modern logic using scholastic logic as the (...)
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  24. Mark Brown & Valentin Goranko (1999). An Extended Branching-Time Ockhamist Temporal Logic. Journal of Logic, Language and Information 8 (2):143-166.
    For branching-time temporal logic based on an Ockhamist semantics, we explore a temporal language extended with two additional syntactic tools. For reference to the set of all possible futures at a moment of time we use syntactically designated restricted variables called fan-names. For reference to all possible futures alternative to the actual one we use a modification of a difference modality, localized to the set of all possible futures at the actual moment of time.We construct an axiomatic system for this (...)
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  25. Robert S. Brumbaugh (1965). Logic and Time. Review of Metaphysics 18 (4):647 - 656.
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  26. R. A. Bull (1970). An Approach to Tense Logic. Theoria 36 (3):282-300.
    The author's motivation for constructing the calculi of this paper\nis so that time and tense can be "discussed together in the same\nlanguage" (p. 282). Two types of enriched propositional caluli for\ntense logic are considered, both containing ordinary propositional\nvariables for which any proposition may be substituted. One type\nalso contains "clock-propositional" variables, a,b,c, etc., for\nwhich only clock-propositional variables may be substituted and that\ncorrespond to instants or moments in the semantics. The other type\nalso contains "history-propositional" variables, u,v,w, etc., for\nwhich only history-propositional variables may (...)
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  27. John P. Burgess (1984). Review: Beyond Tense Logic. [REVIEW] Journal of Philosophical Logic 13 (3):235 - 248.
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  28. John P. Burgess & Yuri Gurevich (1985). The Decision Problem for Linear Temporal Logic. Notre Dame Journal of Formal Logic 26 (2):115-128.
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  29. Richard N. Burnor (2000). Modal Models of Time. Southern Journal of Philosophy 38 (1):19-37.
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  30. Jeremy Butterfield (1984). The Logic of Time. Philosophical Books 25 (1):53-55.
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  31. Carlos Caleiro, Luca Viganò & Marco Volpe (2013). On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators. [REVIEW] Logica Universalis 7 (1):33-69.
    We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness (...)
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  32. Hector-Neri Castañeda (1977). Ought, Time, and the Deontic Paradoxes. Journal of Philosophy 74 (12):775-791.
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  33. M. J. Cresswell (2006). Now is the Time. Australasian Journal of Philosophy 84 (3):311 – 332.
    The aim of this paper is to consider some logical aspects of the debate between the view that the present is the only 'real' time, and the view that the present is not in any way metaphysically privileged. In particular I shall set out a language of first-order predicate tense logic with a now predicate, and a first order (extensional) language with an abstraction operator, in such a way that each language can be shewn to be exactly translatable into the (...)
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  34. Anatoli Degtyarev, Michael Fisher & Alexei Lisitsa (2002). Equality and Monodic First-Order Temporal Logic. Studia Logica 72 (2):147-156.
    It has been shown recently that monodic first-order temporal logic without functional symbols but with equality is incomplete, i.e., the set of the valid formulae of this logic is not recursively enumerable. In this paper we show that an even simpler fragment consisting of monodic monadic two-variable formulae is not recursively enumerable.
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  35. Joeri Engelfriet & Jan Treur (2002). Linear, Branching Time and Joint Closure Semantics for Temporal Logic. Journal of Logic, Language and Information 11 (4):389-425.
    Temporal logic can be used to describe processes: their behaviour ischaracterized by a set of temporal models axiomatized by a temporaltheory. Two types of models are most often used for this purpose: linearand branching time models. In this paper a third approach, based onsocalled joint closure models, is studied using models which incorporateall possible behaviour in one model. Relations between this approach andthe other two are studied. In order to define constructions needed torelate branching time models, appropriate algebraic notions are (...)
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  36. Matt Farr (2012). On A- and B-Theoretic Elements of Branching Spacetimes. Synthese 188 (1):85-116.
    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 (...)
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  37. Marcelo Finger & Dov Gabbay (1996). Combining Temporal Logic Systems. Notre Dame Journal of Formal Logic 37 (2):204-232.
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  38. Rohan French (2008). A Note on the Logic of Eventual Permanence for Linear Time. Notre Dame Journal of Formal Logic 49 (2):137-142.
    In a paper from the 1980s, Byrd claims that the logic of "eventual permanence" for linear time is KD5. In this note we take up Byrd's novel argument for this and, treating the problem as one concerning translational embeddings, show that rather than KD5 the correct logic of "eventual permanence" is KD45.
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  39. Max A. Freund (2001). A Temporal Logic for Sortals. Studia Logica 69 (3):351-380.
    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.
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  40. D. M. Gabbay & G. Malod (2002). Naming Worlds in Modal and Temporal Logic. Journal of Logic, Language and Information 11 (1):29-65.
    In this paper we suggest adding to predicate modal and temporal logic a locality predicate W which gives names to worlds (or time points). We also study an equal time predicate D(x, y)which states that two time points are at the same distance from the root. We provide the systems studied with complete axiomatizations and illustrate the expressive power gained for modal logic by simulating other logics. The completeness proofs rely on the fairly intuitive notion of a configuration in order (...)
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  41. Haim Gaifman (2008). Contextual Logic with Modalities for Time and Space. Review of Symbolic Logic 1 (4):433-458.
    Contextuality is trivially pervasive: all human experience takes place in endlessly changing environments and inexorably moving time frames. In order to have any meaning, the changing items must be placed within a more stable setting, a framework that is not subject to the same kind of contextual change. Total contextuality collapses into chaos, or becomes ineffable. While basic learning is highly contextual (one learns by example), what is learned transcends the examples used in the learning. Perhaps, in a similar manner, (...)
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  42. Antony Galton, Temporal Logic. Stanford Encyclopedia of Philosophy.
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  43. Joanna Golinska-Pilarek & Emilio Munoz Velasco (2009). Relational Approach for a Logic for Order of Magnitude Qualitative Reasoning with Negligibility Non-Closeness and Distance. Logic Journal of Igpl 17 (4):375–394.
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  44. Joanna Golinska-Pilarek & Emilio Munoz-Velasco (2009). Dual Tableau for a Multimodal Logic for Order of Magnitude Qualitative Reasoning with Bidirectional Negligibility. International Journal of Computer Mathematics 86 (10-11):1707–1718.
  45. James Harrington, Tense Logic in Einstein-Minkowski Space-Time.
    This paper argues that the Einstein-Minkowski space-time of special relativity provides an adequate model for classical tense logic, including rigorous definitions of tensed becoming and of the logical priority of proper time. In addition, the extension of classical tense logic with an operator for predicate-term negation provides us with a framework for interpreting and defending the significance of future contingency in special relativity. The framework for future contingents developed here involves the dual falsehood of non-logical contraries, only one of which (...)
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  46. Wiebe van Der Hoek & Michael Wooldridge (2003). Cooperation, Knowledge, and Time: Alternating-Time Temporal Epistemic Logic and Its Applications. Studia Logica 75 (1):125 - 157.
    Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic CTL, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in CTL. Recently, CTL was generalised by Alur, Henzinger, and Kupferman in a logic known as "Alternating-time Temporal Logic" (ATL). The key (...)
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  47. Paul Hovda (2013). Tensed Mereology. Journal of Philosophical Logic 42 (2):241-283.
    Classical mereology (CM) is usually taken to be formulated in a tenseless language, and is therefore associated with a four-dimensionalist metaphysics. This paper presents three ways one might integrate the core idea of flat plenitude, i.e., that every suitable condition or property has exactly one mereological fusion, with a tensed logical setting. All require a revised notion of mereological fusion. The candidates differ over how they conceive parthood to interact with existence in time, which connects to the distinction between endurance (...)
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  48. G. E. Hughes & M. J. Cresswell (1975). Omnitemporal Logic and Converging Time. Theoria 41 (1):11-34.
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  49. Martha Hurst (1934). Can the Law of Contradiction Be Stated Without Reference to Time? Journal of Philosophy 31 (19):518-525.
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  50. Walter Hussak (2008). Decidable Cases of First-Order Temporal Logic with Functions. Studia Logica 88 (2):247 - 261.
    We consider the decision problem for cases of first-order temporal logic with function symbols and without equality. The monadic monodic fragment with flexible functions can be decided with EXPSPACE-complete complexity. A single rigid function is sufficient to make the logic not recursively enumerable. However, the monadic monodic fragment with rigid functions, where no two distinct terms have variables bound by the same quantifier, is decidable and EXPSPACE-complete.
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