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)

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)

Imagine a model of the universe that, if true and known to be true, would solve the following philosophical problems: the direction and flow of time, an ontology for laws of nature, the interpretation of quantum mechanics, the interpretation of probability, a semantics for counterfactuals, trans-world and trans-temporal identity, essentialism and natural kinds, and free will and responsibility. The successful solution to these problems would convince most of us that we should, at the very least, give this model serious (...) consideration. This is the argument of Storrs McCall's A Model of the Universe: Space-Time, Probability, and Decision. Assume that the branched-tree model of the universe is true, and all these problems are solved. Thus, the branched-tree model should at least be a plausible candidate for the true model of the universe. (shrink)

Branching time logics have been studied in computer science since the 1980s primarily to model the tree of computations for discrete transition systems. Inconsistency measures for propositional log...

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)

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)

To analyse contingent propositions, this paper investigates how branching time structures can be combined with probability theory. In particular, it considers assigning infinitesimal probabilities—available in non-Archimedean probability theory—to individual histories. This allows us to introduce the concept of ‘remote possibility’ as a new modal notion between ‘impossibility’ and ‘appreciable possibility’. The proposal is illustrated by applying it to a future contingent and a historical counterfactual concerning an infinite sequence of coin tosses. The latter is a toy model that (...) is used to illustrate the applicability of the proposal to more realistic physical models. (shrink)

This essay examines the case for relativism about future contingents in light of a distinction between two ways of interpreting the ‘branching time’ framework. Focussing on MacFarlane (2014), we break the argument for relativism down into two steps. The first step is an argument for something MacFarlane calls the "Non-Determination Thesis", which is essentially the view that there is no unique actual future. The second step is an argument from the Non-Determination Thesis to relativism. I first argue that (...) first step of this argument fails. But despite that result, the second step is still of interest, since many philosophers have maintained something like the Non-Determination Thesis on alternative grounds. I then argue that whether the second step of the argument suc- ceeds depends on how the Non-Determination Thesis is motivated, and how the ‘branching time’ framework is interpreted in light of that moti- vation. If the branches in an intended branching time model are ersatz possible worlds, then the argument for relativism might go through; but if, instead, the branches are concrete parts of a ‘branching multiverse’, then the argument for relativism turns out to make implausible assumptions about the nature of personal identity over time. That argument can thus be rejected by rejecting those assumptions. One upshot of this is that the case for relativism about future contingents is much weaker than has been appreciated; a broader lesson is that philosophers who invoke the branching time framework need to pay close attention to different ways of interpreting it. (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)

The paper gives a physicist's view on the framework of branching space-time, 385--434). Branching models are constructed from physical state assignments. The models are then employed to give a formal semantics for the modal operators ``possibly'' and ``necessarily'' and for the counterfactual conditional. The resulting formal language can be used to analyze quantum correlation experiments. As an application sketch, Stapp's premises LOC1 and LOC2 from his purported proof of non-locality, 300--304) are analyzed.

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 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)

"This book develops a rigorous theory of indeterminism as a local and modal concept. Its crucial insight is that our world contains events or processes with alternative, really possible outcomes. The theory aims at clarifying what this assumption involves, and it does it in two ways. First, it provides a mathematically rigorous framework for local and modal indeterminism. Second, we support that theory by spelling out the philosophically relevant consequences of this formulation and by showing its fruitful applications in metaphysics. (...) To this end, we offer a formal analysis of modal correlations and of causation, which is applicable in indeterministic and non-local contexts as well. We also propose a rigorous theory of objective single-case probabilities, intended to represent degrees of possibility. In a third step, we link our theory to current physics, investigating how local and modal indeterminism relates to issues in the foundations of physics, in particular, quantum non-locality and spatio-temporal relativity. The book also ventures into the philosophy of time, showing how the theory's resources can be used to explicate the dynamic concept of the past, present, and future based on local indeterminism"--. (shrink)

The theory of branching space-times is designed as a rigorous framework for modelling indeterminism in a relativistically sound way. In that framework there is room for "funny business", i.e., modal correlations such as occur through quantummechanical entanglement. This paper extends previous work by Belnap on notions of "funny business". We provide two generalized definitions of "funny business". Combinatorial funny business can be characterized as "absence of prima facie consistent scenarios", while explanatory funny business characterizes situations in which no localized (...) explanation of inconsistency can be given. These two definitions of funny business are proved to be equivalent, and we provide an example that shows them to be strictly more general than the previously available definitions of "funny business". (shrink)

The future is different from the past. What is past is fixed and set in stone. The future, on the other hand, is open insofar as it holds numerous possibilities. Branching-tree models of time account for this asymmetry by positing an ontological difference between the past and the future. Given a time t, a unique unified past lies behind t, whereas multiple alternative existing futures lie ahead of t. My goal in this paper is to show (...) that there is an incompatibility between the way branching-tree models account for the open future and the possibility of time travel. That is, I argue that once time travel enters the picture, branching time fails to model the openness of the future by means of alternative future branches. I show how this holds independently of whether branching-time models are cashed out in A-theoretic or B-theoretic terms. (shrink)

The seventeenth century Muslim philosopher Muhammad Sadr al-Din Shirazi, known as Mulla Sadra, introduced the idea of substantial motion in Islamic philosophy. This view is characterized by a continuity criterion for diachronic identity, a four-dimensional view of individual substances, the notion that possibilities change, and the continual creation of all creatures. Modern philosophical logic provides means to model a variety of claims about individuals, substances, modality and time. In this paper, the semantics of formal systems discussed by Carnap, Bressan (...) and Gupta are reviewed with regard to the issue of substance and identity. Next a model introduced by Storrs McCall is described that is able to build upon and yet resolve some of the issues about substance and identity as characterized by Bressan and others. McCall’s model is also shown to be able to provide an illustration of Mulla Sadra’s doctrine of substantial motion. (shrink)

The paper extends the framework of outcomes in branching space-time (Kowalski and Placek [1999]) by assigning probabilities to outcomes of events, where these probabilities are interpreted either epistemically or as weighted possibilities. In resulting models I define the notion of common cause of correlated outcomes of a single event, and investigate which setups allow for the introduction of common causes. It turns out that a deterministic common cause can always be introduced, but (surprisingly) only special setups permit (...) the introduction of truly stochastic common causes. I analyse next the Bell-Aspect experiment and derive the Bell-CH inequalities. I observe that we postulate there not a common cause for outcomes of a single event but rather a common common cause that accounts for outcomes of many events, where 'events' mean 'measurements with (different) directions of polarization'. Since the inequalities are violated, I claim that no causal story can be told about the Bell correlations, where causality is subliminal and restricted by screening-off condition. Similarly, given certain intuitive principles, no deterministic story can be told about these correlations. (shrink)

Branching space-times (BST; Belnap, Synthese 92:385–434, 1992 ) is the most advanced formal framework for representing indeterminism. BST is however based on continuous partial orderings, while our natural way of describing indeterministic scenarios may be called discrete. This paper establishes a theorem providing a discrete data format for BST: it is proved that a discrete representation of indeterministic scenarios leading to BST models is possible in an important subclass of cases. This result enables the representation of limited indeterminism (...) in BST and hopefully paves the way for the representation of substances with capacities in that framework. (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)

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)

First the Branching Space-time and Branching Continuations mod-els are briefly presented. We compare their properties with the traditional definition of a Flow of Time from physics and we point out the difficulties of it in relativistic time. A solution of a Flow of Time in the given models is then proposed.

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)

In most cases, we think that what settles what act it is right to perform is sensitive to what we take the facts about the world to be. But those facts include many controversial metaphysical claims about the world. I argue that depending on what metaphysical model we take to be correct, we will have very different views about what the right actions are. In particular, I argue that if a particular metaphysical model — the branching universe model — (...) is correct, then many of our ethical intuitions are false. We need to think carefully about the relation between ethical and metaphysical intuitions, and ethical and metaphysical theories. (shrink)

Conversation is one of the main contexts in which we are conducting inquiries. Yet, little attention has been paid so far in pragmatics or epistemology to the process of inquiry in conversation. In this paper, we propose to trigger such an investigation through the development of a formal modelling based on inquisitive pragmatics—a framework offering a semantic representation of questions and answers, along with an analysis of the pragmatic principles that govern questioning and answering moves in conversations geared towards information (...) exchange. Our starting observation is that an interrogative inquiry in a conversation takes the form of a finite sequence of questioning and answering steps, and appears thereby as an inherently temporal process. The central notion of interrogative protocol introduced in this paper precisely aims to capture the temporal dimension of inquiry. Interrogative protocols are defined as branching-time tree structures encoding all the possible sequences of questioning and answering steps—i.e., all the possible inquiry paths—that can subsequently occur in a starting conversational situation in accordance with the principles of inquisitive pragmatics. They provide us with a formal environment to define and investigate the epistemological notions of interrogative inquiry and interrogative consequence in conversational contexts. One of the main interests of the resulting framework is to enable a formal investigation of central epistemological issues relative to interrogative inquiry under the form of computational problems. We frame three key inquiry problems along this line, and we then propose an algorithmic procedure for solving them in the restricted case where the inquirer has at her disposal a finite number of questions in her inquiry. We conclude by relating our approach to Wiśniewski’s Erotetic Search Scenarios and Hintikka’s Interrogative Model of Inquiry. (shrink)

Lewis (Noûs 13:455–476, 1979) claimed that branching-time(-like) models can be derived from his sphere models. However, he did not present any specific construction of branching-time(-like) models from his sphere models formally. Meanwhile, Hosokawa (in: Modern logic of modality and its philosophical range: counterfactuals, Gettier problem, and information flow, Tokyo Metropolitan University, 2018) presented a logico-mathematically strict manner in which sphere models can be reconstructed from branching-time models. Subsequently, Hosokawa (...) (J Logic Lang Inf 32:677–706, 2023) presented a proof-theoretically refined version of hybrid tense logic for a certain type of conditionals, which is referred to as hybrid tense logic for temporal conditionals ( $$\textbf{HTL}_{TC}$$ ). In this paper, we interpret a hybrid version $${\textbf{V}}_{\mathcal {HC(@, \downarrow )}}$$ of Lewis’s counterfactual logic $${\textbf{V}}$$ into $$\textbf{HTL}_{TC}$$, and then prove that $$\textbf{HTL}_{TC}$$ is more expressive than $${\textbf{V}}_{\mathcal {HC(@, \downarrow )}}$$ on the class of temporal sphere models, i.e., sphere models derived from a type of branching-time models. (shrink)

This book discusses fundamental topics on contemporary Ockhamism. The collected essays show how contemporary Ockhamism can impact areas of research such as semantics, metaphysics and also the philosophy of science. In addition, the volume hosts one historian of Medieval philosophy who investigates the way in which William of Ockham “in flesh and bone” construed time and, more generally, future contingency. The essays explore the different meanings of this theory. They cover three main topics, in particular. The first examines the (...) thesis that sentences and propositions about the future have a definite truth value, without any ensuing commitment to determinism or fatalism. The second topic looks at the problem whether the branching-time model needs to countenance a privileged branch (the so-called Thin Red Line). Finally, the third topic considers the idea that there are so-called soft facts. These would be the subject matter of sentences and propositions verbally about the present or the past, but metaphysically about a later time, and which might change in the future. Overall, the book provides an updated and rigorous idea of the debate about Ockhamism. It gives readers a deeper understanding into this philosophical approach influenced by William of Ockham, characterized by the rejection of the Aristotelian idea that, in order to preserve the contingency of the future, future contingents must be deemed neither true nor false. (shrink)

The basic principles of Cipra's metaphysics (according to his book "Metamorphoses of Metaphysics") are analyzed with respect to Cipra's request for the revision of classical logical principles (of identity, excluded middle and contradiction). In Cipra's metaphysics, the principle of identity holds for being, necessity and past only, the principle of excluded middle does not hold for coming-to-be, possibility and present, and the principle of contradiction does not hold for the actuality, reality (freedom) and future. A propositional and first-order temporal model (...) and semantics are defined for such a concept of metaphysical time. The propositional ockhamistic branching time model is extended, in a first-order model, with a non-empty set of object shapes and an equivalence relation between object shapes in time, so that, for example, different, previously equivalent object shapes can in future contradict one another. (shrink)

The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of (...) tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world. (shrink)

Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, (...) such as the question of how actuality can be understood and formally represented in a branching framework. The present volume is intended to be a 360 degree reflection on the tree model. The contributions is gathers concern the model and its alternatives, both from a semantic and from a metaphysical point of view. ​. (shrink)

Mereotopology is the discipline obtained from combining topology with the formal study of parts and their relation to wholes, or mereology. This article develops a mereotopological theory of time, illustrating how different temporal topologies can be effectively discriminated on this basis. Specifically, we demonstrate how the three principal types of temporal models—namely, the linear ones, the forking ones, and the circular ones—can be characterized by differently combining two sole mereotopological constraints: one to denote the absence of closed loops, (...) and the other one to denote the absence of branches. (shrink)

Alternating-time temporal logic (ATL) is a branching time temporal logic in which statements about what coalitions of agents can achieve by strategic cooperation can be expressed. Alternating-time temporal epistemic logic (ATEL) extends ATL by adding knowledge modalities, with the usual possible worlds interpretation. This paper investigates how properties of agents’ actions can be expressed in ATL in general, and how properties of the interaction between action and knowledge can be expressed in ATEL in particular. One commonly (...) discussed property is that an agent should know about all available actions, i.e., that the same actions should be available in indiscernible states. Van der Hoek and Wooldridge suggest a syntactic expression of this semantic property. This paper shows that this correspondence in fact does not hold. Furthermore, it is shown that the semantic property is not expressible in ATEL at all. In order to be able to express common and interesting properties of action in general and of the interaction between action and knowledge in particular, a generalization of the coalition modalities of ATL is proposed. The resulting logics, ATL-A and ATEL-A, have increased expressiveness without loosing ATL’s and ATEL’s tractability of model checking. (shrink)

In addressing the problem of the (in)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 ( $$\mathsf {TRL}$$ ) seem to imply that conditionals of freedom are true or false, as Molinists maintain. (...) Noting the resemblance between Molinism and $$\mathsf {TRL}$$ models, Restall (Molinism and the thin red line. In: Perszyk K (ed) Molinism: the contemporary debate, pp 227–239, 2011) has advanced some criticisms of Molinism that have also been leveled against $$\mathsf {TRL}$$ models. In particular, Restall believes that the implication $$p \rightarrow \mathbf {HF}p$$ is not true in $$\mathsf {TRL}$$ 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 (not just $$\mathsf {TRL}$$ ) the implication $$p \rightarrow \mathbf {HF}p$$ 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 $$\mathsf {TRL}$$ 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 (not just for Molinists) or can be accounted for by these models and so is not a problem for Molinists either. (shrink)

From the nineteen sixties onwards a branch of philosophy of science has come to development, called history-oriented philosophy of science. This development constitutes a reaction on the then prevailing logical empiricist conception of scientific knowledge. The latter was increasingly seen as suffering from insurmountable internal problems, like e. g. the problems with the particular "observational-theoretical distinction" on which it drew. In addition the logical empiricists' general approach was increasingly criticized for two external shortcomings. Firstly, the examples of scientific knowledge that (...) the logical empiricists were focusing on were con sidered as too simplistic to be informative on the nature of real life science. Secondly, it was felt that the attention of these philosophers of science was restricted to the static aspects of scientific knowledge, while neglecting its developmental aspects. History-oriented philosophy of science has taken up the challenge implicit in the latter two criticisms, i. e. to develop accounts of science that would be more adequate for understanding the development 1 of real life science. One of the more successful products of this branch of philosophy of science is Lakatos's theory of scientific development, sometimes called the "methodology of scientific research programmes". This theory conceives science as consisting of so called research program mes developing in time, and competing with each other over the issue which one generates the best explan~tions of the phenomena that they address. (shrink)

The paper develops models of statistical experiments that combine propensities with frequencies, the underlying theory being the branching space-times (BST) of Belnap (1992). The models are then applied to analyze Bell's theorem. We prove the so-called Bell-CH inequality via the assumptions of a BST version of Outcome Independence and of (non-probabilistic) No Conspiracy. Notably, neither the condition of probabilistic No Conspiracy nor the condition of Parameter Independence is needed in the proof. As the Bell-CH inequality is most (...) likely experimentally falsified, the choice is this: contrary to the appearances, experimenters cannot choose some measurement settings, or some transitions, with spacelike related initial events, are correlated; or both. (shrink)

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 often involved in conditional obligations makes possible a sensitive way of expressing some kinds of general prohibitions, which in turn makes it possible to account for the special role of explicit permission. (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)

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)

Past public announcement operators have been defined in Hoshi and Yap :259–281, 2009) and Yap, to describe an agent’s knowledge before an announcement occurs. These operators rely on branching-time structures that do not mirror the traditional, relativization-based semantics of public announcement logic, and favor a historical reading of past announcements. In this paper, we introduce reverse public announcement operators that are interpreted on expanded models. Our model expansion adds accessibility links from an epistemic model \ to a (...) filtrated submodel of the canonical model for \. Here \ is the minimal normal modal logic together with \ axioms for the universal operator U. This yields a highly general pre-announcement version of \ that makes our operators potentially useful for studying non-standard interpretations of rescinded announcements in PAL. Indeed, we find that our reverse announcement operators cannot be represented by product update, and that they have an intimate connection with the knowledge forgetting of Zhang and Zhou :1525–1537, 2009). We show that the logic resulting from adding reverse announcements to PAL is sound and complete. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in (...) terms of epistemic event models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall , No Miracles , and Bisimulation Invariance . We then focus on new issues of completeness . One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (shrink)

A variety of logical frameworks have been developed to study rational agents interacting over time. This paper takes a closer look at one particular interface, between two systems that both address the dynamics of knowledge and information flow. The first is Epistemic Temporal Logic (ETL) which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. The second framework is Dynamic Epistemic Logic (DEL) that describes interactive processes in (...) terms of epistemic event models which may occur inside modalities of the language. This paper systematically and rigorously relates the DEL framework with the ETL framework. The precise relationship between DEL and ETL is explored via a new representation theorem characterizing the largest class of ETL models corresponding to DEL protocols in terms of notions of Perfect Recall, No Miracles, and Bisimulation Invariance. We then focus on new issues of completeness. One contribution is an axiomatization for the dynamic logic of public announcements constrained by protocols, which has been an open problem for some years, as it does not fit the usual ‘reduction axiom’ format of DEL. Finally, we provide a number of examples that show how DEL suggests an interesting fine-structure inside ETL. (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)

The paper offers an explanation of the intuitive appeal of Saul Kripke's necessity of origin thesis, exhibiting it as the consequence of a temporally asymmetrical 'branching model' of possibilities which, in turn, rests on two plausible principles concerning possibility, time, and identity. Unlike some other accounts, my explanation dissociates the necessity of origin thesis from a commitment to individual essences or other sufficient conditions for identity across possible worlds. I conclude that although the branching model is not (...) irresistible, its rejection may necessitate the denial of a plausible principle that requires possibilities for actual individuals to be 'anchored' to their actual characteristics. (shrink)

The paper defends the thesis that future tensed statements have truth values that can change over time. In relativistic approaches to the evaluation of future contingents (MacFarlane, 2003, 2007), only changes in the truth status of such statements from neither-true-nor-false to definitely true (or definitely false) are taken into consideration. More precisely, given the monotonicity property of the model of historical possibilities, for which historical alternatives to a world w at a time t increase moving backward and shrink (...) moving forward in time with respect to t (Thomason, 1984), only such changes are predicted to be possible. I will consider the theoretical possibility of truth value transitions for future contingents from true to false and from false to true, as well as some potential linguistic evidence for such transitions - drawn from certain uses of phase adverbs like still, no longer, and always in English and Romance. To deal with the natural language data, I will propose a situation-based version of Branching Time which accommodates partiality of information, and a revision of the Kaplanian notion of truth-in-context. (shrink)

The statistics-based method ignores the semantic constraints in the English grammar area branch training model and is unable to identify the orientation information effectively. This paper systematically discusses the close relationship between English grammar area branch training model filtering, English grammar area branch training model retrieval, and machine learning. By analyzing the role of the situation in the understanding of the English grammar area branch training model, the relationship between the English grammar area branch training model and situation model and (...) the correlation between the features of the English grammar area branch training model and situation model are determined, and then, a set of filtering methods for the English grammar area branch training model are proposed. At present, there are few research studies on bias filtering, and the method of thematic filtering is generally used, which has poor effect. This paper makes full use of the domain knowledge and adopts the semantic pattern analysis technology to establish a wealth of semantic analysis resources, including various dictionaries, rules, and weight representation, so as to effectively filter the inclined English grammar area branch training model. The introduction of semantic data sources solves the problem of data sparsity and cold start in the traditional collaborative filtering system. In addition, in order to improve the scalability and real-time performance of the recommendation system, the data mining method is used to perform fuzzy clustering for users and projects in the offline data preprocessing stage. This paper proposes a search and filter scheme based on the orientation of the training model in English grammar area, elaborates on the details, constructs a whole set of function structure from representation to weight, and gives the experimental results, which prove that the system has a good filtering effect and is fast. Compared with the traditional statistical methods, the results are satisfactory. (shrink)

The paper defends an Aristotelian notion of indeterminism, as rigorously formulated in the framework of branching space-times (BST) of Belnap (1992), against the model-theoretic characterization of indeterminism that Montague (1962) introduced into the philosophy of science. It delineates BST branching against the background provided by Earman's (2008) distinction between individual vs. ensemble branching. It describes a construction of physically-motivated BST models, in which histories are isomorphic to Minkowski spacetime. Finally it responds to criticism leveled against BST (...) by addressing some semantical questions, a topological issue, and the past/future asymmetry. (shrink)

In ‘A New Route to the Necessity of Origin’, Rohbraugh and deRosset offer an argument for the Necessity of Origin appealing neither to Suffciency of Origin nor to a branching-times model of necessity. What is doing the crucial work in their argument is instead the thesis they name ‘Locality of Prevention’. In this response, we object that their argument is question-begging by showing, first, that the locality of prevention thesis is not strong enough to satisfactorily derive from it the (...) intended conclusion, and, second, that the argument is not sound unless the Necessity of Origin is operating as an implicit premiss. (shrink)

In the dissertation we study the complexity of generalized quantifiers in natural language. Our perspective is interdisciplinary: we combine philosophical insights with theoretical computer science, experimental cognitive science and linguistic theories. -/- In Chapter 1 we argue for identifying a part of meaning, the so-called referential meaning (model-checking), with algorithms. Moreover, we discuss the influence of computational complexity theory on cognitive tasks. We give some arguments to treat as cognitively tractable only those problems which can be computed in polynomial (...) class='Hi'>time. Additionally, we suggest that plausible semantic theories of the everyday fragment of natural language can be formulated in the existential fragment of second-order logic. -/- In Chapter 2 we give an overview of the basic notions of generalized quantifier theory, computability theory, and descriptive complexity theory. -/- In Chapter 3 we prove that PTIME quantifiers are closed under iteration, cumulation and resumption. Next, we discuss the NP-completeness of branching quantifiers. Finally, we show that some Ramsey quantifiers define NP-complete classes of finite models while others stay in PTIME. We also give a sufficient condition for a Ramsey quantifier to be computable in polynomial time. -/- In Chapter 4 we investigate the computational complexity of polyadic lifts expressing various readings of reciprocal sentences with quantified antecedents. We show a dichotomy between these readings: the strong reciprocal reading can create NP-complete constructions, while the weak and the intermediate reciprocal readings do not. Additionally, we argue that this difference should be acknowledged in the Strong Meaning hypothesis. -/- In Chapter 5 we study the definability and complexity of the type-shifting approach to collective quantification in natural language. We show that under reasonable complexity assumptions it is not general enough to cover the semantics of all collective quantifiers in natural language. The type-shifting approach cannot lead outside second-order logic and arguably some collective quantifiers are not expressible in second-order logic. As a result, we argue that algebraic (many-sorted) formalisms dealing with collectivity are more plausible than the type-shifting approach. Moreover, we suggest that some collective quantifiers might not be realized in everyday language due to their high computational complexity. Additionally, we introduce the so-called second-order generalized quantifiers to the study of collective semantics. -/- In Chapter 6 we study the statement known as Hintikka's thesis: that the semantics of sentences like ``Most boys and most girls hate each other'' is not expressible by linear formulae and one needs to use branching quantification. We discuss possible readings of such sentences and come to the conclusion that they are expressible by linear formulae, as opposed to what Hintikka states. Next, we propose empirical evidence confirming our theoretical predictions that these sentences are sometimes interpreted by people as having the conjunctional reading. -/- In Chapter 7 we discuss a computational semantics for monadic quantifiers in natural language. We recall that it can be expressed in terms of finite-state and push-down automata. Then we present and criticize the neurological research building on this model. The discussion leads to a new experimental set-up which provides empirical evidence confirming the complexity predictions of the computational model. We show that the differences in reaction time needed for comprehension of sentences with monadic quantifiers are consistent with the complexity differences predicted by the model. -/- In Chapter 8 we discuss some general open questions and possible directions for future research, e.g., using different measures of complexity, involving game-theory and so on. -/- In general, our research explores, from different perspectives, the advantages of identifying meaning with algorithms and applying computational complexity analysis to semantic issues. It shows the fruitfulness of such an abstract computational approach for linguistics and cognitive science. (shrink)

In his 1966 paper “The Strategy of model-building in Population Biology”, Richard Levins argues that no single model in population biology can be maximally realistic, precise and general at the same time. This is because these desirable model properties trade-off against one another. Recently, philosophers have developed Levins’ claims, arguing that trade-offs between these desiderata are generated by practical limitations on scientists, or due to formal aspects of models and how they represent the world. However this project is (...) not complete. The trade-offs discussed by Levins had a noticeable effect on modelling in population biology, but not on other sciences. This raises questions regarding why such a difference holds. I claim that in order to explain this finding, we must pay due attention to the properties of the systems, or targets modelled by the different branches of science.Keywords: Trade-offs; Population biology; Scientific models; Generality; Precision. (shrink)

Many logical systems today describe intelligent interacting agents over time. Frameworks include Interpreted Systems (IS, Fagin et al. [8]), Epistemic-Temporal Logic (ETL, Parikh & Ramanujam [22]), STIT (Belnap et al. [5]), Process Algebra and Game Semantics (Abramsky [1]). This variety is an asset, as different modeling tools can be fine-tuned to specific applications. But it may also be an obstacle, when barriers between paradigms and schools go up. This paper takes a closer look at one particular interface, between two (...) systems that both address the dynamics of knowledge and information flow in multi-agent systems. One is IS/ETL (IS and ETL are, from a technical point of view, the same up to model transformations, cf. [20]), which uses linear or branching time models with added epistemic structure induced by agents’ different capabilities for observing events. These models provide a Grand Stage where histories of some process unfold constrained by a protocol, and a matching epistemic-temporal language describes what happens. The other framework is Dynamic Epistemic Logic (DEL, [10, 4, 34]) that describes interactive processes in terms of epistemic event models which may occur inside modalities of the language. Temporal evolution is then computed from some initial epistemic model through a process of successive ‘product updates’. It has long been unclear how to best compare IS/ETL and DEL. Various aspects have been investigated in [10, 30, 32], but in this paper, we study the interface in a more systematic way. Often, DEL and ETL are presented as alternative ways of adding dynamics to multi-agent epistemic models. In this paper, we rather focus on how merging the two different modeling choices leads to interesting new questions. Our leading interest here will be a view of informational processes as evolving over time. To see what we mean, consider the simplest version of DEL, viz. the logic of public announcements PAL ([23]) which adds a very specific type of communicative 1 action to epistemic models: a public announcement.. (shrink)

I argue that Deutsch’s model for the behavior of systems traveling around closed timelike curves relies implicitly on a substantive metaphysical assumption. Deutsch is employing a version of quantum theory with a significantly supplemented ontology of parallel existent worlds, which differ in kind from the many worlds of the Everett interpretation. Standard Everett does not support the existence of multiple identical copies of the world, which the D-CTC model requires. This has been obscured because he often refers to the (...) class='Hi'>branching structure of Everett as a “multiverse”, and describes quantum interference by reference to parallel interacting definite worlds. But he admits that this is only an approximation to Everett. The D-CTC model, however, relies crucially on the existence of a multiverse of parallel interacting worlds. Since his model is supplemented by structures that go significantly beyond quantum theory, and play an ineliminable role in its predictions and explanations, it does not represent a quantum solution to the paradoxes of time travel. (shrink)