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

In this paper I analyze the temporal structures that are appropriate to study the notion of point of view. When we analyze the points of view and their structure, it seems clear that we must take into account the time t in which a point of view is attributed to a subject. A two-dimensional temporal logic which combines a modal dimension for possibilities and a temporal one for the flow of time, offers a clear view of the (...) temporary location of a point of view. In this logic, we have histories, thanks to the temporal dimension, and evaluation is in two indices, time and history. These stories can be seen as different scenarios, providing a clear advantage when applying to the analysis of the notion of point of view. The conclusion is that, in order to give a proper approach for the notion of point of view, all these aspects should be combined. (shrink)

Branching time is a popular theory of time that is intended to account for the openness of the future. Generally, branching-time models the openness of the future by positing a multiplicity of concrete alternative futures mirroring all the possible ways the future could unfold. A distinction is drawn in the literature among branching-time theories: those that make use of moment-based structures and those that employ history-based ones. In this paper, I introduce and (...) discuss a particular kind of openness relative to the possibility that time ends (doomsday). I then show that whereas moment-based branching structures cannot represent this kind of openness, history-based structures can account for it. The conclusion is that history-based structures have an advantage over moment-based ones. (shrink)

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)

In this paper we develop a novel propositional semantics based on the framework of branching time. The basic idea is to replace the moment-history pairs employed as parameters of truth in the standard Ockhamist semantics by pairs consisting of a moment and a consistent, downward closed set of so-called transitions. Whereas histories represent complete possible courses of events, sets of transitions can represent incomplete parts thereof as well. Each transition captures one of the alternative immediate future possibilities open (...) at a branching point. The transition semantics exploits the structural resources a branching time structure has to offer and provides a fine-grained picture of the interrelation of modality and time. In addition to temporal and modal operators, a so-called stability operator becomes interpretable as a universal quantifier over the possible future extensions of a given transition set. The stability operator allows us to specify how and how far time has to unfold for the truth value of a sentence at a moment to become settled and enables a perspicuous treatment of future contingents. We show that the semantics developed along those lines generalizes and extends extant approaches: both Peirceanism and Ockhamism can be viewed as limiting cases of the transition approach that build on restricted resources only, and on both accounts, stability collapses into truth. (shrink)

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

We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies (...) the AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007 ). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically. (shrink)

The concept of event is one of the key notions of many theories dealing with causality or agency. In this paper we study different approaches to events that share the basic assumption that events can be analyzed fruitfully in branching-time structures. The terminological framework developed thereby may be helpful for further analyses in the fields of causality and agency and also in those fields of computational semantics, where similar concepts are considered.

The aim of this paper is to present a new perspective under which branching-time semantics can be viewed. The set of histories (maximal linearly ordered sets) in a tree structure can be endowed in a natural way with a topological structure. Properties of trees and of bundled trees can be expressed in topological terms. In particular, we can consider the new notion of topological validity for Ockhamist temporal formulae. It will be proved that this notion of validity is (...) equivalent to validity with respect to bundled trees. (shrink)

Branching is a set-theoretical model of reality that is in accord with contemporary physics. This structure is also a model for some logical calculi. However, if the formal language defined on the basis of branching is to correspond to our ways of speaking about possible events, a number of issues must be clarified. All of them are connected with the notion of possibility that is employed in this language. Yet the apparent need to supplement this language with an (...) additional notion of possibility means that branching ceases to be attractive as a candidate for a model of physical reality, as it contains considerably more elements than we would like to see in reality. Thus, the connection between this logical tool and ontology becomes questionable. (shrink)

Replacing the value-free ideal (VFI) for science requires attention to the broader understanding of how science in society should function. In public spaces, science needed to project the VFI in norms for science advising, science education, and science communication. This resulted in the independent science advisor model and a focus on science literacy for science education and communication. Attending to these broader implications of the VFI which structure science and society relationships is crucial if we are to properly replace the (...) VFI with a better ideal. (shrink)

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

In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching space-time models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract space-time structures based on the real numbers and the integers, considering (...) three different accessibility relations between spatio-temporal points. (shrink)

The article discusses the relation between two intuitive properties of time, namely its flow and branching. Both properties are introduced first in an informal way and compared. The conclusion of this informal analysis is that the two properties do not entail each other nor are they in contradiction. In order to verify this, we briefly introduced the branching temporal structures called branching space-time, branching continuation and their versions Minkowski branching structure and (...) class='Hi'>branching time with Instants. Two possible ways how to formalize flow of time are given, one based on the definition of flow of time from temporal logics and the other based on relativistic physics. The latter is used to define flow of time with the use of linearly ordered points on worldines while respecting the ontological definiteness given by the difference of the past and the future. This is formalized in each of the branching models and it is concluded by comparing the resulting properties that branching and flow, even in the formal sense, do not entail each other. However, notions connected with flow of time represent a useful basis for semantics of the branching models. (shrink)

In this paper we show that properties of non-linear time structures have not been studied enough. Axioms forcing the existence of a branching point in a branching area of a structure are presented for various classes of structures. We show also that the classical Dedekind continuity axiom does not work well in non-linear structures and we suggest stronger versions. Finally, some interdependencies between the axioms presented are proved.

There is a remarkable similarity between some mathematical objects used in the Branching Space-Times framework and those appearing in computer science in the fields of event structures for concurrent processing and Chu spaces. This paper introduces the similarities and formulates a few open questions for further research, hoping that both BST theorists and computer scientists can benefit from the project.

The theory of branching space-times, put forward by Belnap, considers indeterminism as local in space and time. In the axiomatic foundations of that theory, so-called choice points mark the points at which the possible future can turn out in different ways. Working under the assumption of choice points is suitable for many applications, but has an unwelcome topological consequence that makes it difficult to employ branching space-times to represent a range of possible physical space-times. Therefore it is (...) interesting to develop a branching space-times theory without choice points. This is what we set out to do in this paper, providing new foundations for branching space-times in terms of choice sets rather than choice points. After motivating and developing the resulting theory in formal detail, we show that it is possible to translate structures of one style into structures of the other style and vice versa. This result shows that the underlying idea of indeterminism as the branching of spatio-temporal histories is robust with respect to different implementations, making a choice between them a matter of expediency rather than of principle. (shrink)

The paper intends to provide an algebraic framework in which subluminal causation can be analysed. The framework merges Belnap's 'outcomes in branching time' with his 'branching space-time' (BST). it is shown that an important structure in BST, called 'family of outcomes of an event', is a boolean algebra. We define next non-stochastic common cause and analyse GHZ-Bell theorems. We prove that there is no common cause that accounts for results of GHZ-Bell experiment but construct common causes (...) for two other quantum mechanical setups. Finally, we investigate why some setups allow for common causes whereas other setups do not. (shrink)

Originally published in 1980. What is time? How is its structure determined? The enduring controversy about the nature and structure of time has traditionally been a diametrical argument between those who see time as a container into which events are placed, and those for whom time cannot exist without events. This controversy between the absolutist and the relativist theories of time is a central theme of this study. The author's impressive arguments provide grounds for rejecting (...) both these theories, firstly by establishing that 'empty' time is possible, and secondly by showing, through a discussion of the structure of time which involves considering whether time might be cyclical, branching, beginning or non-beginning, that the absolutist theory of time is untenable. This book then advances two new theories, and succeeds in shifting the traditional debate about time to a consideration of time as a theoretical structure and as a theoretical framework. (shrink)

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 w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language L_t by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

Contemporary architecture is increasingly grounded in science and mathematics. Architectural discourse has shifted radically from the sometimes disorienting Derridean deconstruction, to engaging scientific terms such as fractals, chaos, complexity, nonlinearity, and evolving systems. That's where the architectural action is -- at least for cutting-edge architects and thinkers -- and every practicing architect and student needs to become conversant with these terms and know what they mean. Unfortunately, the vast majority of architecture faculty are unprepared to explain them to students, not (...) having had a scientific education themselves. Here is an architecture book by an architect/scientist, just in time to help architects in the new millennium. Alexander discusses many of the scientific terms arising in cutting-edge architecture, and explains them to those who don't have scientific training or advanced mathematical knowledge. We find discussions of the evolution of forms; the importance of process in design; iteration; genetic algorithms; sequences of transformations; different levels of scale (i.e. fractals); etc. They are explained here by an architect who is also a scientist, because he wants to change the way architects think and build. Alexander is not merely popularizing other scientists' results and making them accessible to architects: he is in fact presenting new and original scientific work that ties many of these concepts together in a way that will be useful to architects. (shrink)

permits a sound and rigorously definable notion of ‘originating cause’ or causa causans—a type of transition event—of an outcome event. Mackie has famously suggested that causes form a family of ‘inus’ conditions, where an inus condition is ‘an insufficient but non-redundant part of an unnecessary but sufficient condition’. In this essay the needed concepts of BST theory are developed in detail, and it is then proved that the causae causantes of a given outcome event have exactly the structure of a (...) set of Mackie inus conditions. The proof requires the assumption that there is no EPR-like ‘funny business’. This seems enough to constitute a theory of ‘causation’ in at least one of its many senses. Introduction The cement of the universe Preliminaries 3.1 First definitions and postulates 3.2 Ontology: propositions 3.3 Ontology: initial events 3.4 Ontology: outcome events 3.5 Ontology: transition events 3.6 Propositional language applied to events Causae causantes 4.1 Causae causantes are basic primary transition events 4.2 Causae causantes of an outcome chain 4.3 No funny business Causae causantes and inns and inus conditions 5.1 Inns conditions of outcome chains: not quite 5.2 Inns conditions of outcome chains 5.3 Inns conditions of scattered outcome events 5.4 Inus conditions for disjunctive outcome events 5.5 Inns and inus conditions of transition events Counterfactual conditionals Appendix: Tense and modal connectives in BST. (shrink)

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

This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational universe can be referred—which is (...) quite necessary for assigning them a probability distribution. The “historical” state of a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed. An age operator computes the informational depth of historical states and its standard deviation can be used to provide a universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence of the subject’s activity of measuring, which defines the flow of time-information. (shrink)

I investigate the consequences for semantics, and in particular for the semantics of tense, if time is assumed to have a branching structure not out of metaphysical necessity (to solve some philosophical problem) but just as a contingent physical fact, as is suggested by a currently-popular approach to the interpretation of quantum mechanics.

The transition semantics presented in Rumberg :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 \ 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 \-validity w.r.t. transition structures. As a consequence, for a certain fragment (...) of \, validity w.r.t. transition structures turns out to be axiomatizable. The result is then extended to the entire language \ by means of a quite natural ‘Henkin move’, i.e. by relaxing the notion of validity to bundled structures. (shrink)

Stephen Jay Gould’s monumental The Structure of Evolutionary Theory ‘‘attempts to expand and alter the premises of Darwinism, in order to build an enlarged and distinctive evolutionary theory . . . while remaining within the tradition, and under the logic, of Darwinian argument.’’ The three branches or ‘‘fundamental principles of Darwinian logic’’ are, according to Gould: agency (natural selection acting on individual organisms), efficacy (producing new species adapted to their environments), and scope (accumulation of changes that through geological time (...) yield the living world’s panoply of diversity and morphological complexity). Gould’s efforts to contribute something important to each of these three fundamental components of Darwinian Theory are far from successful. (shrink)

A theory of temporal passage is put forward which is "objective" in the sense that time flow characterizes the universe independently of the existence of conscious beings. The theory differs from Grunbaum's "mind-dependence" theory, and is designed to avoid Grunbaum's criticisms of an earlier theory of Reichenbach's. The representation of temporal becoming is accomplished by the introduction of indeterministic universe-models; each model representing the universe at a time. The models depict the past as a single four-dimensional manifold, and (...) the future as a branched structure of such manifolds. Time flow is relativistic in that it manifests itself in a frame-dependent (but not observer-dependent) way. The indeterministic character of the universe-models is mirrored in a "temporal" theory of truth which rejects the principle of bivalence, and suitable semantics are provided for this theory. Finally, an account of physical law is given which defines it in terms of physical possibility, rather than vice versa. (shrink)

Most of the descriptions of interval time structures in the first order predicate calculus are based on linear time. However, in the case of intervals, abandoning the condition oflinearity (e.g.LIN in van Benthem's systems) is not sufficient. In this paper, some properties of non-linear time structures are discussed. The most important one is the characterization of location of intervals in a fork of branches. This is connected with the fact that an interval can contain non-collinear (...) subintervals. As a result of non-linearity, some basic properties of interval structures must be formulated in a weaker form. Moreover, time must be filled by intervals to indicate that time cannot pass without events occurring in it. Finally, it is shown that when intervals cannot contain non-collinear subintervals, most of the conditions described in the paper are satisfied. (shrink)

With the innovation of computer, virtual clothing has also emerged. This research mainly discusses the real-time animation complex of interactive clothing design based on computer simulation. In the process of realizing virtual clothing, the sample interpolation synthesis method is used, and the human body sample library is constructed using the above two methods first, and then, the human body model is obtained by interpolation calculation according to the personalized parameters. Building a clothing model is particularly important for the effect (...) of trying on. The clothing that needs to be displayed can be scanned and then input into the computer to build the model. The model can be directly built in 3DMAX and other software and then its surface texture can be mapped, or the clothing model can be directly built. The 3D model in the 3ds file is loaded by the loop body nested switch branch selection structure. Correspondingly, the write-back operation of 3ds files is similar. Just follow the general structure of the 3ds file and write the root block, version information block, edit information block, key frame information block, etc. to a brand new file in sequence. The main reason for this article to perform the 3ds file write-back operation is that, after the clothing model is dynamically simulated through the dynamic principle, the deformed key animation frame needs to be saved as a 3ds file so that it can be further imported into the 3DSMAX software and generated by the renderer, form high-quality picture information, and finally get high-definition animation video. In the CPU-GPU hybrid method, modules such as force calculation, collision processing, and position update use the GPU method, while overstretching is processed by the CPU method, making the overall performance 10 times higher than the pure CPU method. This research helps to promote the development of 3D virtual clothing design. (shrink)

The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.

In addressing the problem of the compatibility of divine foreknowledge and human freedom, philosophers of religion encounter problems regarding the metaphysics and structure of time. Some models of temporal logic developed for completely independent reasons have proved especially appropriate for representing the temporal structure of the world as Molinism conceives it. In particular, some models of the Thin Red Line ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. Noting the resemblance between Molinism (...) and \ models, Restall Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against \ models. In particular, Restall believes that the implication \ is not true in \ models. Because Molinists must also accept that this implication is not true, this is a problem for them. We will show that Restall’s criticism is wide of the mark. Firstly, it will be demonstrated that in many open future models ) the implication \ is invalid. Secondly, while it is possible to account for this implication, some modifications are required in respect of the branching time semantics. In proposing one such modification, we show that this new semantics can be adopted by advocates of the \ and, as a consequence, by Molinists as well. We conclude that the principle stated by Restall is either a problem for many open future models or can be accounted for by these models and so is not a problem for Molinists either. (shrink)

Some very good arguments can be given in favor of the Augustinean wisdom, according to which it is impossible to provide a satisfactory definition of the concept of time. However, even in the absence of a proper definition, it is possible to deal with conceptual problems regarding time. It can be done in terms of analogies and metaphors. In particular, it is attractive to make use of Peirce's diagrams by means of which various kinds of conceptual experimentation can (...) be carried out. This paper investigates how Peircean diagrams can be used within the study of time. In particular, we discuss 1) the topological properties of time, 2) the implicative structure in tense logic, 3) the notions of open future and branching time models, and finally 4) tenselogical alternatives to branching time models. (shrink)

The majority of the Sufi orders, which have their own special ezkar, evrâd, etiquette, and erkan and have survived until today, particularly VI/XII. They were formed over centuries and spread to many parts of the world by dividing into different branches in the historical process. Sufi personalities who belonged to these sufi orders established structures such as dervish lodges and dervish lodges in the regions they reached with great efforts, and they were instrumental in the conversion of many people (...) to Islam. Attributed to its founder, Abdulqadir Geylani, Qadiriyya is one of the most famous of these sufi orders. From the Middle East, especially from Iraq, to Afkaya; It spread over a wide area from Anatolia to the Balkans and China in the east and carried out convent activities with more than fifty branches. The Reshidiyya Sufi Order, which is attributed to Ahmed Reshidi and whose center is in Mosul, is a sect that operates in a wide region from Turkey to India and still has followers in these regions. It can be said that the Reshidiyya Sufi Order, which has its principles and manners, is one of the largest branches of the Qadiriyya. This Sufi order also has relations with the Rifaiyya, Bedewiyya, Desûqiyya, and Suhrawardiyya Sufi Order. Because Ahmed ar-Reshidi, the founder of the sect, is a Sufi figure who received the caliphate from all these sects. Although it is a Sufi order that has spread to this extent in Islamic lands and continues its dervish activities until today, the name of the Reshidiyya sect is not encountered even in the encyclopedic studies conducted in our country on the branches of the Qadiriyya Sufi Order. However, a scholar such as Mollâ Khalil Siirdî, who was mentioned as the "ser ring" in the ijazah ceremonies held in classical madrasahs that continued to be active in Anatolia until today, is one of the caliphs of this order. This humble study has been prepared by making use of the sources obtained through Ahmed ar-Reshidi's last-generation grandchildren after reaching them. With this study, we have been trained in recent times like Ahmed ar-Reshidi, Hz. We will try to introduce a great Sufi figure, who came from the progeny of the Prophet, who devoted his whole life to the task of guidance and who was referred to as the "pole", as well as the principles and manners of the Sufi order he was the founder of. (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)

Since 1970 the United Kingdom, like the United States, has developed a “winner-take-all” political economy characterized by widening inequality and spectacular income growth at the top of the distribution. However, Britain’s centralized executive branch and relatively insulated policymaking process are less amenable to the kind of “organized combat” that Hacker and Pierson describe for the United States. Britain’s winner-take-all politics is better explained by the rise of political ideas favoring unfettered markets that, over time, produce a self-perpetuating structural advantage (...) for the richest. That advantage is, in turn, justified and sustained by reference to the same ideas. Inequality growth in the United Kingdom has been primarily driven by the financialization of the economy that began under the Thatcher government and continued under New Labour. The survival of pro-finance policies through the financial crisis provides further evidence that lobbying by a weakened City of London was less decisive in shaping policy than the financial sector’s continuing structural advantage and the tenacity of its supporting political consensus. (shrink)

If r is a reducibility between sets of numbers, a natural question to ask about the structure ? r of the r-degrees containing computably enumerable sets is whether every element not equal to the greatest one is branching (i.e., the meet of two elements strictly above it). For the commonly studied reducibilities, the answer to this question is known except for the case of truth-table (tt) reducibility. In this paper, we answer the question in the tt case by showing (...) that every tt-incomplete computably enumerable truth-table degree a is branching in ? tt . The fact that every Turing-incomplete computably enumerable truth-table degree is branching has been known for some time. This fact can be shown using a technique of Ambos-Spies and, as noticed by Nies, also follows from a relativization of a result of Degtev. We give a proof here using the Ambos-Spies technique because it has not yet appeared in the literature. The proof uses an infinite injury argument. Our main result is the proof when a is Turing-complete but tt-incomplete. Here we are able to exploit the Turing-completeness of a in a novel way to give a finite injury proof. (shrink)

The logical foundations of game-theoretic solution concepts have so far been explored within the con¯nes of epistemic logic. In this paper we turn to a di®erent branch of modal logic, namely temporal logic, and propose to view the solution of a game as a complete prediction about future play. The branching time framework is extended by adding agents and by de¯ning the notion of prediction. A syntactic characterization of backward induction in terms of the property of internal consistency (...) of prediction is given. (shrink)

Some fictions seem to involve branching time, where one time series ‘splits’ into two or two time series ‘fuse’ into one. We provide a new framework for thinking about these fictional representations: not as representations of branching time series but rather as branching representations of linear time series. We explain how branching at the level of the representation creates a false impression that the story describes a branching of the (...) class='Hi'>time series in the fictional world itself. This involves explaining away the illusion of various causal connections which may at first appear essential to understanding the story as a unified whole. This provides a more accurate account of the relationship between the representation and what is represented, which in turn reveals the extent to which it is legitimate to draw conclusions about actual time from fictional representations. (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)

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 defined(in a category theoretical manner) and exploited. In particular, thenotion of joint closure is used to construct one model subsuming a setof models. Using this universal algebraic construction we show that aset of linear models can be merged to a unique branching time model.Logical properties of the described algebraic constructions are studied.The proposed approach has been successfully aplied to obtain anappropriate semantics for non-monotonic reasoning processes based ondefault logic. References are discussed that show the details of theseapplications. (shrink)

The supervaluationist approach to branching time (‘SBT-theory’) appears to be threatened by the puzzle of retrospective determinacy: if yesterday I uttered the sentence ‘It will be sunny tomorrow’ and only in some worlds overlapping at the context of utterance it is sunny the next day, my utterance is to be assessed as neither true nor false even if today is indeed a sunny day. John MacFarlane (“Truth in the Garden of Forking Paths” 81) has recently criticized a promising (...) solution to this puzzle for falling short of an adequate account of ‘actually’. In this paper, I aim to rebut MacFarlane's criticism. To this effect, I argue that: (i) ‘actually’ can be construed either as an indexical or as a nonindexical operator; (ii) if ‘actually’ is nonindexical, MacFarlane's criticism is invalid; (iii) there appear to be independent reasons for SBT-theorists to claim that ‘actually’ is a nonindexical expression. (shrink)

We present a temporal logic of branching time with four primitive operators: |$\exists {\mathcal {C}}$| – it may change whether; |$\forall {\mathcal {C}} $| – it must change whether; |$\exists \Box $| – it may be endlessly unchangeable that; and |$\forall \Box $| – it must be endlessly unchangeable that. Semantically, operator |$\forall {\mathcal {C}}$| expresses a change in the logical value of the given formula in every state that may be an immediate successor of the one considered, (...) while |$\exists {\mathcal {C}}$| expresses a change in the logical value of the given formula in some state that is a possible immediate successor. |$\forall {\mathcal {C}} $| and |$\exists {\mathcal {C}}$| are not normal operators, they are not mutually definable and have unusual properties: |$\forall {\mathcal {C}} A\leftrightarrow \forall {\mathcal {C}} \neg A$| and |$\exists {\mathcal {C}} A \leftrightarrow \exists {\mathcal {C}} \neg A$| are axioms. Operators |$\exists \Box $| and |$\forall \Box $| express endless unchangeability in some and all paths, respectively. Our axiomatization contains two infinitary rules that allow one to obtain |$\exists \Box A$| from infinitely many combinations of formulas with |$A, \neg, \forall {\mathcal {C}}, \land $|⁠, and to get |$\forall \Box A$| from infinitely many combinations of formulas with |$A, \neg, \exists {\mathcal {C}}, \land $|⁠. We show that our formalism is complete by presenting a bridge between our logic and logic |$\textsf {UB}$|⁠, which is a fragment of |$\textsf {CTL}$| in which until operators does not occur. (shrink)

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 extended branching-time logic and prove its soundness and completeness with respect to bundle tree semantics. Finally, we show how our axiomatic system can be extended with a variety of important additional operators, such as Since and Until, a global difference operator, operators for undivided and divided histories, reference pointers, etc. (shrink)

Since it is desirable to be able to talk about rational agents forming attitudes toward their concrete agency, we suggest an introduction of doxastic, volitional, and intentional modalities into the multi-agent logic of deliberatively seeing to it that, dstit logic. These modalities are borrowed from the well-known BDI (belief-desire-intention) logic. We change the semantics of the belief and desire operators from a relational one to a monotonic neighbourhood semantic in order to handle ascriptions of conflicting but not inconsistent beliefs and (...) desires as being satisfiable. The proposed bdi-stit logic is defined with respect to branching time frames, and it is shown that this logic is a generalization of a bdi logic based on branching time possible worlds frames (but without temporal operators) and dstit logic. The new bdi-stit logic generalizes bdi and dstit logic in the sense that for any model of bdi or dstit logic, there is an equivalent bdi-stit model. (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- (...) class='Hi'>time, as for instance Stit Logics. (shrink)

In this paper I assess the prospects for combining contemporary Everettian quantum mechanics (EQM) with branching-time semantics in the tradition of Kripke, Prior, Thomason and Belnap. I begin by outlining the salient features of ‘decoherence-based’ EQM, and of the ‘consistent histories’ formalism that is particularly apt for conceptual discussions in EQM. This formalism permits of both ‘branching worlds’ and ‘parallel worlds’ interpretations; the metaphysics of EQM is in this sense underdetermined by the physics. A prominent argument due (...) to Lewis (On the Plurality of Worlds, 1986 ) supports the non-branching interpretation. Belnap et al. (Facing the Future: Agents and Choices in Our Indeterministic World, 2001 ) refer to Lewis’ argument as the ‘Assertion problem’, and propose a pragmatic response to it. I argue that their response is unattractively ad hoc and complex, and that it prevents an Everettian who adopts branching-time semantics from making clear sense of objective probability. The upshot is that Everettians are better off without branching-time semantics. I conclude by discussing and rejecting an alternative possible motivation for branching time. (shrink)