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  1. B-Theory and Time Biases.Sayid Bnefsi - 2019 - In Patrick Blackburn, Per Hasle & Peter Øhrstrøm (eds.), Logic and Philosophy of Time: Further Themes from Prior. Aalborg, Denmark: Aalborg University Press. pp. 41-52.
    We care not only about what experiences we have, but when we have them too. However, on the B-theory of time, something’s timing isn’t an intrinsic way for that thing to be or become. Given B-theory, should we be rationally indifferent about the timing per se of an experience? In this paper, I argue that B-theorists can justify time-biased preferences for pains to be past rather than present and for pleasures to be present rather than past. In support of this (...)
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  • Computation Tree Logics and Temporal Logics with Reference Pointers.Valentin Goranko - 2000 - Journal of Applied Non-Classical Logics 10 (3-4):221-242.
    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 (...)
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  • First-Order Definability of Transition Structures.Antje Rumberg & Alberto Zanardo - 2019 - Journal of Logic, Language and Information 28 (3):459-488.
    The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...)
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  • The Truth About the Future.Jacek Wawer - 2014 - Erkenntnis 79 (S3):365-401.
    There is a long-standing disagreement among Branching-Time theorists. Even though they all believe that the branching representation accurately grasps the idea that the future, contrary to the past, is open, they argue whether this representation is compatible with the claim that one among many possible futures is distinguished—the single future that will come to be. This disagreement is paralleled in an argument about the bivalence of future contingents. The single, privileged future is often called the Thin Red Line. I reconstruct (...)
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  • Combinations of Tense and Modality for Predicate Logic.Stefan Wölfl - 1999 - Journal of Philosophical Logic 28 (4):371-398.
    In recent years combinations of tense and modality have moved intothe focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of predicate logic (...)
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  • BH-CIFOL: Case-Intensional First Order Logic.Nuel Belnap & Thomas Müller - 2013 - Journal of Philosophical Logic (2-3):1-32.
    This paper follows Part I of our essay on case-intensional first-order logic (CIFOL; Belnap and Müller (2013)). We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events (extending all the way into the future) that that moment (...)
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  • Conditional Obligation and Positive Permission for Agents in Time.Mark A. Brown - 2000 - Nordic Journal of Philosophical Logic 5 (2):83-111.
    This paper investigates the semantic treatment of conditional obligation, explicit permission (often called positive permission), and prohibition based on models with agents and branched time. In such models branches (rather than moments) are taken as basic, and the branching provides a way to represent the indeterminism which is normally presupposed by talk of free will, responsibility, action and ability. Careful treatment of the relation between ability and responsibility avoids many common problems with accounts of conditional obligation. Recognition of the generality (...)
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  • Temporal Logic and its Application to Normative Reasoning.Emiliano Lorini - 2013 - Journal of Applied Non-Classical Logics 23 (4):372-399.
    I present a variant of with time, called, interpreted in standard Kripke semantics. On the syntactic level, is nothing but the extension of atemporal individual by: the future tense and past tense operators, and the operator of group agency for the grand coalition. A sound and complete axiomatisation for is given. Moreover, it is shown that supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment.
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  • Temporal Logics with Reference Pointers and Computation Tree Logics.Valentin Goranko - 2000 - Journal of Applied Non-Classical Logics 10 (3):221-242.
    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 (...)
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  • BH-CIFOL: Case-Intensional First Order Logic. Branching Histories.Nuel Belnap & Thomas Müller - unknown
    This paper follows Part I of our essay on case-intensional first-order logic. We introduce a framework of branching histories to take account of indeterminism. Our system BH-CIFOL adds structure to the cases, which in Part I formed just a set: a case in BH-CIFOL is a moment/history pair, specifying both an element of a partial ordering of moments and one of the total courses of events that that moment is part of. This framework allows us to define the familiar Ockhamist (...)
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  • Finding One's Way in the Labyrinth of Forking Paths. (The Semantics of the Future Tense: Part I.).Andrea Bonomi - unknown
    unified treatment of both (families of) interpretations is based on a revised notion of settledness. The main features of this approach are the following: (i) in branching structures, a world can be represented not by a single course of events, but by a node u in the tree, where u itself is seen as the cluster of courses of events passing through it; (ii) the utterance time is uniquely fixed; (iii) the utterance world is not uniquely fixed; (iv) because of (...)
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  • On Possible Worlds with Modal Parts.Neil Kennedy - 2014 - Journal of Philosophical Logic 43 (6):1129-1152.
    This paper is predicated on the idea that some modal operators are better understood as quantificational expressions over worlds that determine not only first-order facts but modal facts also. In what follows, we will present a framework in which these two types of facts are brought closer together. Structural features will be located in the worlds themselves. This result will be achieved by decomposing worlds into parts, where some of these parts will have “modal import” in the sense that they (...)
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  • Indistinguishability, Choices, and Logics of Agency.Alberto Zanardo - 2013 - Studia Logica 101 (6):1215-1236.
    This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set of indistinguishability (...)
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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 (or course of events). 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 (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of (...)
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  • Quantification Over Sets of Possible Worlds in Branching-Time Semantics.Alberto Zanardo - 2006 - Studia Logica 82 (3):379-400.
    Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.
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  • Temporal Alethic–Deontic Logic and Semantic Tableaux.Daniel Rönnedal - 2012 - Journal of Applied Logic 10 (3):219-237.
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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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  • Decidability of Logics Based on an Indeterministic Metric Tense Logic.Yan Zhang & Kai Li - 2015 - Studia Logica 103 (6):1123-1162.
    This paper presents two general results of decidability concerning logics based on an indeterministic metric tense logic, which can be applied to, among others, logics combining knowledge, time and agency. We provide a general Kripke semantics based on a variation of the notion of synchronized Ockhamist frames. Our proof of the decidability is by way of the finite frame property, applying subframe transformations and a variant of the filtration technique.
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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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  • 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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  • 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 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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  • On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators. [REVIEW]Carlos Caleiro, Luca Viganò & Marco Volpe - 2013 - 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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