The Joint International Conference on Logic Programming, sponsored by the Association for Logic Programming, is a major forum for presentations of research, applications, and implementations in this important area of computer science. Logic programming is one of the most promising steps toward declarative programming and forms the theoretical basis of the programming language Prolog and its various extensions. Logic programming is also fundamental to work in artificial intelligence, where it has been used for nonmonotonic and commonsense reasoning, expert systems implementation, (...) deductive databases, and applications such as computer-aided manufacturing. Krzysztof R. Apt is project leader at the Centre for Mathematics and Computer Science in Amsterdam and part-time Professor in Computer Science at the University of Amsterdam. Topics covered: Theory Foundations. Programming Languages. Implementation. Programming Methodologies and Tools. Applications. Deductive Databases. Artificial Intelligence. Parallelism. (shrink)

Since some time the metaphor of logical space has been used to open new approaches to Hegel’s “Science of Logic”. Frequently it is noticed that in such an interpretation logical space must be understood as dynamic. However, as far as I can see, nobody has done yet the step to introduce the concept of logical time into the discussion, even though this step seems to suggest itself. The following contribution seeks to develop this thought and (...) arrives at some new conceptions, such as the curvature of logical space, logical actuality and semantic present, which may seem strange at first sight, but which follow consistently from the explication of the fundamental idea. The first aim in doing this is to broaden our conceptual repertoire do deal with Hegel’s Logic. This may open new perspectives of interpretation which may prove inspiring. Secondarily, the article also defends a systematic thesis which stands on its own and lays claim to truth. This claim goes far beyond a mere interpretation of Hegel and implies a fundamental critique of his philosophy. The comprehension of logical time-space leads to the requirement of logical chance event – and not only real chance. This goes against Hegel claim to absolute necessity in the dialectical development of his Logic and leads to a new philosophic comprehension of logic as such. (shrink)

Abstract In this paper, I investigate the purported dilemma between a symmetrical conception of time and the denial of what I call Universal Logical Determinateness (ULD). According to the dilemma, the timeless and universal application of logical laws to all propositions necessitates either the view that the past and future are both open, or that they are both closed. My investigation proceeds by way of an assessment of Taylor's argument for fatalism, then of Dummet's presentation and refutation (...) of the fatalistic argument, and finally of Dummet's analogous argument which attempts to prove the possibility of an open past. In all cases, we find that the arguments implicitly rely upon the assumption that there exists a necessary connection between the truth aptness of propositions and the fixity (or non-fixity) of events. I question this assumption and conclude that any argument for the symmetry of time which relies upon it begs the question against the asymmetry of time. (shrink)

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 with considerations of how to represent indeterminism and of the adequacy of tensed logic in light of special relativity. The correspondence underpins the point that Prior's later development of branching time may be understood as a crucial part of his attempt at the formulating a conceptual framework integrating basic human notions of time and free choice. (shrink)

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

Le problème du temps tourmente et nourrit la philosophie depuis sa naissance. Dans ce cadre, une lecture métaphysique des textes de S. Leśniewski permet de développer un point de vue original sur certaines propriétés fondamentales du temps logique. En particulier, après une analyse minutieuse des œuvres philosophiques de jeunesse, et notamment de l’article « La vérité est-elle éternelle ou éternelle et sempiternelle? », nous montrons que le temps logique est, chez Leśniewski, inévitablement double : les propositions, dont la vérité doit (...) pouvoir être _éternelle_, sont des entités qui se développent dans un espace et dans un temps déterminés. De même, cette double temporalité apparaît dans l’Ontologie, un calcul logique des noms dont l’axiomatique est établie à partir du foncteur ε, connecteur logique à la fois inscrit dans un espace et dans un temps et néanmoins sans ancrage temporel. Ainsi, plusie... (shrink)

The subject of Time has a wide intellectual appeal across different dis ciplines. This has shown in the variety of reactions received from readers of the first edition of the present Book. Many have reacted to issues raised in its philosophical discussions, while some have even solved a number of the open technical questions raised in the logical elaboration of the latter. These results will be recorded below, at a more convenient place. In the seven years after the (...) first publication, there have been some noticeable newer developments in the logical study of Time and temporal expressions. As far as Temporal Logic proper is concerned, it seems fair to say that these amount to an increase in coverage and sophistication, rather than further break-through innovation. In fact, perhaps the most significant sources of new activity have been the applied areas of Linguistics and Computer Science (including Artificial Intelligence), where many intriguing new ideas have appeared presenting further challenges to temporal logic. Now, since this Book has a rather tight composition, it would have been difficult to interpolate this new material without endangering intelligibility. (shrink)

Sets out the basic theory of normal modal and temporal propositional logics; applies this theory to logics of discrete (integer), dense (rational), and continuous (real) time, to the temporal logic of henceforth, next, and until, and to the propositional dynamic logic of regular programs.

In Ockhamist branching-time logic [Prior 67], formulas are meant to be evaluated on a specified branch, or history, passing through the moment at hand. The linguistic counterpart of the manifoldness of future is a possibility operator which is read as `at some branch, or history (passing through the moment at hand)'. Both the bundled-trees semantics [Burgess 79] and the $\langle moment, history\rangle$ semantics [Thomason 84] for the possibility operator involve a quantification over sets of moments. The Ockhamist frames are (...) (3-modal) Kripke structures in which this second-order quantification is represented by a first-order quantification. The aim of the present paper is to investigate the notions of modal definability, validity, and axiomatizability concerning 3-modal frames which can be viewed as generalizations of Ockhamist frames. (shrink)

칸트 철학에서 시간 개념은 항상 중요하게 거론되지만 쉽게 논의의 대상으로 흡수되지 못해왔다. 본 연구는 경험적·주관적 측면에서의 시간 현상을 칸트의 시간론에 근거하여 분석한다. 구체적으로 본 논문은 칸트의 비경험적, 불연속적 시간 즉 “논리적 구성물로서”의 시간의 의미를 시적 반추를 통해 재해석한다. 첫째, ‘시간은 경험의 소여인가’라는 물음에서 출발한다. 만약 시간이 경험의 인과적 연속물이라면, 지난 과거의 경험내용에 대한 재의미화는 없다. 이러한 점에 의문을 제기한 롱펠로우의 시는, 시간이 결과로서의 경험으로부터 왜 구분되는지를 반증한다. 두 번째 물음은 시간에서 경험적 의미가 사라진다면, 시간은 무엇으로 구성되는가이다. 칸트와 마찬가지로 헤세는 자신의 (...) 시 〈한탄〉에서 시간을 ‘틀’이라고 지칭한다. 심지어 그는 시간에 그 어떤 도덕적 가치나 의미가 부여될 수 없다고 암시한다. 스톨베르크의 시는 다름 아닌 그 이유를 제공해주는 단초가 된다. 셋째, 한스 마이어호프의 경험적 시간에 대한 해명으로부터 본 연구는 칸트의 ‘경험’과 ‘현상’의 관계를 설정하고, 이로써 논리적이고 구성적인 시간의 의미가 시의 시간 개념에 내재해 있음을 밝힌다. 넷째, 본 논문은 쉼보르스카의 시를 통해 내면에 변화하고 상상되고 사라지는 시간의 모습들이 선형 구조로만 이해될 수 없음을 규명한다. 요컨대, 칸트의 시간론으로 분석한 시 속에 시간은 경험에 예속된 현상이 아니라, 경험적 사건 및 이야기와 생각들이 새롭게 기술되고 재해석될 수 있는 사유의 무한 지평이다. 시간은 경험의 근원적 조건이자 현상하는 모든 것의 가능 조건이다. (shrink)

This paper explains how to obtain quantification over times in a tense logic in which all temporal distinctions are ultimately spelled out in terms of the two simple tense operators “it was the case that” and “it will be the case that.” The account of times defended here is similar to what is known as “linguistic ersatzism” about possible worlds, but there are noteworthy differences between these two cases. For example, while linguistic ersatzism would support actualism, the view of times (...) defended here does not support presentism. (shrink)

J. M. E. McTaggart famously divided time into two time series, which he entitled A-series and B-series. Although he was proponent of neither of them, his division initiated a discussion as to which of the series is prior or real. This paper follows Clifford Williams’s claim that these series are not as distant as their proponents argue they are. It demonstrates their translatability in the case of examples from temporal logic and natural language. It argues that, if there (...) are any deep-rooted differences between these two series, they are only metaphysical. These metaphysical differences could be overcome by focusing on logic or natural language. These two series of time are also used in computer science and in the development of Artificial Intelligence. However, no attempt at unifying them has been suggested in these fields of study. J. M. E. McTaggart rozdělil čas na dvě časové série, A-série a B-série. Třebaže nebyl zastáncem žádné z nich, jeho rozdělení podnítilo diskuzi, která z těchto časových sérií je přednější nebo jediná skutečně reálná. Tento článek navazuje na názor Clifforda Williamse, že tyto časové série nejsou tak rozdílné, jak tvrdí jejich zastánci. V článku je demonstrována jejich přeložitelnost na příkladech z temporální logiky a přirozeného jazyka. Článek dále tvrdí, že jestliže je zde nějaký hluboce zakořeněný rozdíl mezi těmito dvěma sériemi, pak je pouze metafyzický. Tyto metafyzické rozdíly mohou být překonány, zaměříme-li se na logiku a přirozený jazyk. Tyto dvě časové série jsou také použity v informatice a rozvoji umělé inteligence, třebaže v těchto oborech dosud nebyly navrženy žádné pokusy o jejich propojení. (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)

We propose a distinction between two different concepts of time that play a role in physics: geometric time and creative time. The former is the time of deterministic physics and merely parametrizes a given evolution. The latter is instead characterized by real change, i.e. novel information that gets created when a non-necessary event becomes determined in a fundamentally indeterministic physics. This allows us to give a naturalistic characterization of the present as the moment that separates the (...) potential future from the determined past. We discuss how these two concepts find natural applications in classical and intuitionistic mathematics, respectively, and in classical and multivalued tensed logic, as well as how they relate to the well-known A- and B-theories in the philosophy of time. (shrink)

While classical temporal logics lose track of a state as soon as a temporal operator is applied, several branching-time logics able to repeatedly refer to a state have been introduced in the literature. We study such logics by introducing a new formalism, hybrid branching-time logics, subsuming the other approaches and making the ability to refer to a state more explicit by assigning a name to it. We analyze the expressive power of hybrid branching-time logics and the complexity (...) of their satisfiability problem. As main result, the satisfiability problem for the hybrid versions of several branching-time logics is proved to be 2EXPTIME -complete. To prove the upper bound, the automata-theoretic approach to branching-time logics is extended to hybrid logics. As a result of independent interest, the nonemptiness problem for alternating one-pebble Büchi tree automata is shown to be 2EXPTIME -complete. A common property of the logics studied is that they refer to only one state. This restriction is crucial: The ability to refer to more than one state causes a nonelementary blow-up in complexity. In particular, we prove that satisfiability for NCTL * has nonelementary complexity. (shrink)

An experiment is reported examining dual-process models of belief bias in syllogistic reasoning using a problem complexity manipulation and an inspection-time method to monitor processing latencies for premises and conclusions. Endorsement rates indicated increased belief bias on complex problems, a finding that runs counter to the “belief-first” selective scrutiny model, but which is consistent with other theories, including “reasoning-first” and “parallel-process” models. Inspection-time data revealed a number of effects that, again, arbitrated against the selective scrutiny model. The most (...) striking inspection-time result was an interaction between logic and belief on premise-processing times, whereby belief - logic conflict problems promoted increased latencies relative to non-conflict problems. This finding challenges belief-first and reasoning-first models, but is directly predicted by parallel-process models, which assume that the outputs of simultaneous heuristic and analytic processing streams lead to an awareness of belief - logic conflicts than then require time-consuming resolution. (shrink)

In this paper, a timed modal logic L c is presented for the specification and verification of real-time systems. Several important results for L c are discussed. First we address the model checking problem and we show that it is an EXPTIME-complete problem. Secondly we consider expressiveness and we explain how to express strong timed bisimilarity and how to build characteristic formulas for timed automata. We also propose a compositional algorithm for L c model checking. Finally we consider several (...) control problems for which L c can be used to check controllability. (shrink)

: Usually, when studying schematism we devote almost exclusive attention to the study of the modifications that the categories suffer when combined with time. Instead, we have focused our attention on the determinations that time receives when combined with the categories. Departing from the definition of the transcendental schemata as “determinations of time”, an attempt is made to establish the various determinations that time receives from each one of the categories, as these perform the determination of (...) time in schematism. The categories of quantity allow us to think of time as a series of homogeneous unities; the categories of quality show each instant of time as a receptacle able to receive the different intensities of the real; the categories of relation establish a rule-dependent order on the flow of time; finally, the categories of modality determine the whole of time forming a collective unity that gathers or embraces each one of the instants of time preserving its specificity. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...) on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

There are two ways of thinking about instants of time: "spatial" accounts emphasize the similarities between instants and places; "modal" accounts focus on the parallels between times and possible worlds. My aim in this paper is to draw attention to one respect in which times are more similar to possible worlds than they are to places.

Recent theories of agency (sees to it that) of Nuel Belnap and Michael Perloff are examined, particularly in the context of an early proposal of the author.

In the Logic of Being: Realism, Truth, and Time, the influential philosopher Paul M. Livingston explores and illuminates truth, time, and their relationship by employing methods from both Continental and analytic philosophy.

The subject of time travel has been receiving increasing attention in the recent philosophical literature. Most of the articles that deal with it have been concerned to defend the logical consistency of time travel against those who claim that it entails one or more contradictions. Two sorts of defences have been offered. The first sort of defence involves showing that time travel does not entail those consequences which other philosophers allege it does entail. The second sort (...) of defence involves an admission that time travel does indeed involve that which its opponents allege it does involve, e.g., being in more than one place at a time, but arguing that such consequences in no way vitiate the logical consistency of this notion.My first aim in this paper is to provide a defence of time travel of the second sort. More specifically, I want to cut the ground from under an argument which might run thus:Time travel entails that certain effects can precede their causes.It is logically impossible for an effect to precede its cause. (shrink)

Epistemic logic in the tradition of Hintikka provides, as one of its many applications, a toolkit for the precise analysis of certain epistemological problems. In recent years, dynamic epistemic logic has expanded this toolkit. Dynamic epistemic logic has been used in analyses of well-known epistemic “paradoxes”, such as the Paradox of the Surprise Examination and Fitch’s Paradox of Knowability, and related epistemic phenomena, such as what Hintikka called the “anti-performatory effect” of Moorean announcements. In this paper, we explore a variation (...) on basic dynamic epistemic logic—what we call sequential epistemic logic—and argue that it allows more faithful and fine-grained analyses of those epistemological topics. (shrink)

In some systems of Legniewskian Ontology were introduced as a toolkit for Husserl's and Meinong's theory of objects. Here such consi- deration is extended to Brentano-Husserl's theory of time. So-called antidiodo- rean logics are used as the foundations of the approach undertaken.

Is what could have happened but never did as real as what did happen? What did happen, but isn't happening now, happened at another time. Analogously, one can say that what could have happened happens in another possible world. Whatever their views about the reality of such things as possible worlds, philosophers need to take this analogy seriously. Adriane Rini and Max Cresswell exhibit, in an easy step-by-step manner, the logical structure of temporal and modal discourse, and show (...) that every temporal construction has an exact parallel that requires a language that can refer to worlds, and vice versa. They make precise, in a way which can be articulated and tested, the claim that the parallel is at work behind even ordinary talk about time and modality. The book gives metaphysicians a sturdy framework for the investigation of time and modality - one that does not presuppose any particular metaphysical view. (shrink)

Weak ontic necessity is the ontic necessity expressed by “should” or “ought to”. An example of it is “I should be dead by now”. A feature of this necessity is that whether it holds is irrelevant to whether its underlying proposition holds. This necessity essentially involves time. This paper presents a logic for conditional weak ontic necessity in branching time. The logic’s language includes the next instant operator, the last instant operator, and the operator for conditional weak ontic (...) necessity. Formulas are evaluated at tuples consisting of a tree-based model, a context, a timeline, and an instant. A context is a set of ordered ontic laws determining expected timelines. When evaluating conditional weak ontic necessity, we first update the context with the antecedent, then check whether the consequent holds with respect to the updated context. We discuss some consequences of the formalization and compare it to some related work. We study the logic’s expressivity and axiomatize a special validity of it. (shrink)

We aim to show that Kant’s theory of time is consistent by providing axioms whose models validate all synthetic a priori principles for time proposed in the Critique of Pure Reason. In this paper we focus on the distinction between time as form of intuition and time as formal intuition, for which Kant’s own explanations are all too brief. We provide axioms that allow us to construct ‘time as formal intuition’ as a pair of continua, (...) corresponding to time as ‘inner sense’ and the external representation of time as a line Both continua are replete with infinitesimals, which we use to elucidate an enigmatic discussion of ‘rest’ in the Metaphysical foundations of natural science. Our main formal tools are Alexandroff topologies, inverse systems and the ring of dual numbers. (shrink)

Is what could have happened but never did as real as what did happen? What did happen, but isn't happening now, happened at another time. Analogously, one can say that what could have happened happens in another possible world. Whatever their views about the reality of such things as possible worlds, philosophers need to take this analogy seriously. Adriane Rini and Max Cresswell exhibit, in an easy step-by-step manner, the logical structure of temporal and modal discourse, and show (...) that every temporal construction has an exact parallel that requires a language that can refer to worlds, and vice versa. They make precise, in a way which can be articulated and tested, the claim that the parallel is at work behind even ordinary talk about time and modality. The book gives metaphysicians a sturdy framework for the investigation of time and modality - one that does not presuppose any particular metaphysical view. (shrink)

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 insight in ATL is that the path quantifiers of CTL could be replaced by cooperation modalities, of the form , where is a set of agents. The intended interpretation of an ATL formula is that the agents can cooperate to ensure that holds (equivalently, that have a winning strategy for ). In this paper, we extend ATL with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with ATL, it becomes possible to express such properties as group can cooperate to bring about iff it is common knowledge in that . The resulting logic — Alternating-time Temporal Epistemic Logic (ATEL) — shares the tractability of model checking with its ATL parent, and is a succinct and expressive language for reasoning about game-like multiagent systems. (shrink)

The intuition guiding the de…nition of computation has shifted over time, a process that is re‡ected in the changing formulations of the Church-Turing thesis. The theory of computation began with logic and gradually moved to the capacity of …nite automata. Consequently, modern computer models rely on general physical principles, with quantum computers representing the extreme case. The paper discusses this development, and the challenges to the Church-Turing thesis in its physical form, in particular, Kieu’s quantum computer and relativistic hyper-computation. (...) Finally, the robustness of the boundary between polynomial and exponential time complexity is considered in connection with quantum computers and quantum information theory. (shrink)

Compound propositions which can successfully be defended in a quantumdialogue independent of the elementary propositions contained in it, must have this property also independent of the mutual elementary commensur-abilities. On the other hand, formal commensurabilities must be taken into account. Therefore, for propositions which can be proved by P, irrespective of both the elementary propositions and of the elementary commensur-abilities, there exists a formal strategy of success. The totality of propositions with a formal strategy of success in a quantum dialogue (...) form the effective quantum logic. The propositions of the effective quantum logic can be derived from a calculus Q eff which is — on the other hand — equivalent to a lattice L qi.Propositions about measuring results are above all time dependent propositions A(S;t). In a dialogue, different partial propositions will have in general different time values. If one can (accidentally) win a material dialogue, this dialogue can be related to a single time value. For the propositions of the effective quantum logic there exist formal strategies of success, independent of the elementary propositions contained in it. All partial propositions appearing in the dialogue are formally commensurable. Therefore the propositions of effective quantum logic which can be proved by formal dialogues can always be related to a single time. They present a description of the system S considered in which all partial propositions can be related jointly to the state of S.Therefore in the effective quantum logic we have — in the limit of equal time values — a situation which corresponds conceptually to the description of the system (S; ψ) in Hilbert space. Consequently, one would expect that also the lattice L qi — except from the tertium non datur 8 — agrees with the lattice L q of subspaces of Hilbert space. It has been shown that these lattices are in fact isomorphic. (shrink)

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e. as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than (...) others. We introduce the time-stamped claim logic including a sound and complete sequent calculus. In order to show how time-stamped claim logic can be used in practice, we consider a concrete cyber-attribution case study. (shrink)

Active time reversal in the sense of “object reversal” and passive time reversal in the sense of a frame reversal of time are discussed separately and then together so as to bring out their dual nature. An understanding of that duality makes it unavoidable to contrast symmetry properties of matter with symmetry properties to be assigned to antimatter. Only frame reversal of time can “see” all conceivable active time reversals relevant to physical objects. Only frame (...) reversal of time can be used for a meaningful extension of the Neumann principle to the time domain. (shrink)

We present an overview of linear-time temporal logics with Presburger constraints whose models are sequences of tuples of integers. Such formal specification languages are well-designed to specify and verify systems that can be modelled with counter systems. The paper recalls the general framework of LTL over concrete domains and presents the main decidability and complexity results related to fragments of Presburger LTL. Related formalisms are also briefly presented.

Prior has conjectured that the tense-logical system Gli obtained by adding to a complete basis for the classical propositional calculus the primitive symbolG, the definitionsDf. F:Fα=NGNαDf. L:Lα=KαGα,and the postulatesis complete for the logic of linear, infinite, transitive, discrete future time. In this paper it is demonstrated that that conjecture is correct and it is shown that Gli has the finite model property: see [4]. The techniques used are in part suggested by those used in Bull [2] and [3]:Gli (...) can be shown to be complete for the logic of linear, infinite, transitive, discrete future time in the sense that every formula of Gli which is true of such time can be proved as a theorem of Gli. For this purpose the notion of truth needs to be formalized. This formalization is effected by the construction of a model for linear, infinite, transitive, discrete future time. (shrink)

Ulrich Meyer's book The Nature of Time uses tense logic to argue for a `modal' view of time, which replaces substantial times with `ersatz times' constructed using conceptually basic tense operators. He also argues against Bertrand Russell's relationist theory, in which times are classes of events, and against the idea that relativity compels the integration of time and space. I find fault with each of these negative arguments, as well as with Meyer's purported reconstruction of empty spacetime (...) from tense operators and substantial spatial points. I suggest that Meyer's positive project is best conceived as an elimination of time in the mode of Julian Barbour's The End of Time. (shrink)

Despite some talk of ‘erotetic logic’ and ‘the logic of interrogatives’, logicians have hitherto completely overlooked the peculiar logical form of questions, also shared by interrogative clauses generally. Of relevance to an understanding of time are those interrogative clauses that are janus-like: sometimes raising a question, sometimes answering it—which can then no longer arise. Since a closed question can no longer arise, it might seem that simply the passing of time turns an open into a closed question. (...) Instead, the passing of time itself can be understood as the closing or resolution of open questions, of the determination of what is not fixed but as yet in question. (shrink)

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)