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)

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)

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts (...) of the original semantics. (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)

This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with (...) a modality for possible paths. We then consider a hierarchy of natural classes of trees and bundled trees arising from a given class of linear orders and show that in general they provide different semantics. We also discuss transfer of definability from linear orders to trees and introduce a uniform translation from Priorean to Peircean formulae which transfers definability of properties of linear orders to definability of properties of all paths in trees. (shrink)

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)

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)

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)

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)

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.

In the tree-like representation of Time, two histories are undivided at a moment t whenever they share a common moment in the future of t. In the present paper, it will first be proved that Ockhamist and Peircean branching-time logics are unable to express some important sentences in which the notion of undividedness is involved. Then, a new semantics for branching-time logic will be presented. The new semantics is based on trees endowed with (...) an indistinguishability function, a generalization of the notion of undividedness. It will be shown that Ockhamist and Peircean semantics can be viewed as limit cases of the semantics developed in this paper. (shrink)

Trees with indistinguishability relations provide a semantics for a temporal language “composed by” the Peircean tense operators and the Ockhamist modal operator. In this paper, a finite axiomatization with a non standard rule for this language interpreted over bundled trees with indistinguishability relations is given. This axiomatization is proved to be sound and strongly complete.

We introduce a natural deduction system for the until-free subsystem of the branching time logic Although we work with labelled formulas, our system differs conceptually from the usual labelled deduction systems because we have no relational formulas. Moreover, no deduction rule embodies semantic features such as properties of accessibility relation or similar algebraic properties. We provide a suitable semantics for our system and prove that it is sound and weakly complete with respect to such semantics.

It is argued that reconstructions of the so-called ‘Master Argument’ of Dideros Cronos to the effect that possibility should be understood as present or future truth, essentially relies on two axioms: i) that every true proposition concerning the past is necessary, and ii) that it follows necessarily from a proposition being true that it always has been the case that it would be true. It is furthermore argued that these two axioms are inconsistent in the sense that any tense/modal (...) class='Hi'>semantics which incorporates both collapses either modally (fails to distinguish between truth simpliciter and modalised truth) or temporally (fails to offer a plausible semantical account for propositions about the future). This finding is, furthermore, taken as indicator for the more generel claim that there are principled difficulties involved in construing semantics for combined tense/modal logical systems. (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)

Indicative conditionals with present tense antecedents can have ‘shifted’ readings that are unexpected given the semantic behavior of the tenses outside of conditionals. In this paper, we compare two accounts of this phenomenon due to Kaufmann (J Semant 22(3):231–280, 2005) and Schulz (SALT XVIII, pp. 694–710, 2008), by reconstructing them in the framework of branching time. We then propose a novel account of indicative conditionals based on the branching time semantics suggested in Rumberg (J Logic (...) Lang Inf 25(1):77–108, 2016), viz. transition semantics. We show that not only is the account of ‘shifted’ readings with present tense antecedents within this semantics very natural, but it also is empirically superior to its rivals in some respects. (shrink)

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted (...) with respect to a version of the bundle semantics. (shrink)

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted (...) with respect to a version of the bundle semantics. (shrink)

The basic notions in Prior’s Ockhamist and Peircean logics of branching-time are the notion of moment and that of history (or course of events). In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical (and ontological) dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank (...) 1 base of a non-Archimedean topology on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (shrink)

The basic notions in Prior's Ockhamist and Peircean logics of branching-time are the notion of moment and that of history. In the tree semantics, histories are defined as maximal linearly ordered sets of moments. In the geometrical approach, both moments and histories are primitive entities and there is no set theoretical dependency of the latter on the former. In the topological approach, moments can be defined as the elements of a rank 1 base of a non-Archimedean topology (...) on the set of histories. In this paper, it will be shown that the topological approach, and hence the other approaches, can be reconstructed in a framework in which the basic notions are those of history and of relative closeness relation among histories. (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)

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)

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)

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.

My aim in this paper is to investigate the notions of comparative similarity definable in the framework of branching space-times. A notion of this kind is required to give a rigorous Lewis-style semantics of space-time counterfactuals, which is the task undertaken by Thomas Muller (PITT-PHIL-SCI00000509, this archive). In turn, the semantical analysis is needed to decide whether the recently proposed proofs of the non-locality of quantum mechanics are correct. From among the three notions of comparative similarity I (...) select two which appear equally good as far as their intuitiveness and algebraic properties are concerned. However, the relations are not transitive, and thus cannot be used in the semantics proposed by (Lewis 1973), which requires transitivity. Yet they are adequate for the account of (Lewis 1981). (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.

We offer additional points that support a distributed semantic memory: the activation of representations that are modality-specific; patients with inferotemporal lesions fail to activate visual object representations in semantic tasks, although normal subjects do; direct activation of action systems from pictorial information, but not from words; patients who demonstrate superiority with abstract words fail to access perceptual representations.

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)

Branching theories are popular frameworks for modeling objective indeterminism in the form of a future of open possibilities. In such theories, the notion of a history plays a crucial role: it is both a basic ingredient in the axiomatic definition of the framework, and it is used as a parameter of truth in semantics for languages with a future tense. Furthermore, histories—complete possible courses of events—ground the notion of modal consistency: a set of events is modally consistent iff (...) there is a history containing that set. We will explain these roles of histories and highlight some critical aspects having to do with the fact that histories are global and, in a relevant sense, “big” objects. The notion of modal consistency, on the other hand, has both local and global aspects. We ask in how far a local notion of modal consistency can serve as an alternative to the common uses of histories, and work out two recent approaches to alternatives to histories. Combining these approaches, we develop a novel semantics for branching time. (shrink)

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)

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)

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.

Since there are independent reasons for associating the habitual reading of the imperfective, in Italian, to a logical form based on universal or generic quantification, the purpose of Part I is to see how this kind of semantical structure accounts for another important interpretation of the imperfective: the progressive reading. And since in some particular cases the imperfective can also have a marginal interpretation which can be assimilated to a perfective effect (it is the so-called “narrative” reading), a further problem (...) is how to provide a reasonable explanation for this phenomenon too. If one considers the co-occurrence of the imperfective with different event predicates (in particular, accomplishments and achievements) it is possible to show that, with some minimal assumptions, the theoretical framework under discussion correctly predicts the following facts, which represent a crucial, but puzzling, characteristic of the imperfective in Italian: (i) activities allow for the progressive reading of the imperfective, but not the “narrative” reading; (ii) with achievements we have the opposite situation; (iii) accomplishments are compatible with both these readings. From this point of view, the semantic properties of the progressive reading of the imperfective are quite distinct from those of the perifrasi progressiva, which is the specialized form used in Italian to express the progressive meaning. Part II, which addresses the issue of the intensional character of both forms of the progressive, is more problematic, in the sense that it takes into consideration a possible extension of the theoretical framework presented in Part I. First of all I discuss some examples which clearly show that the perifrasi progressiva calls for some sort of “branching” representation of time, for it crucially refers to future courses of events which are not realized in the real world. On the other hand, since similar examples can be found in the case of the progressive reading of the imperfective, the main problem is represented by the fact that the kind of logical form under discussion is not completely adequate to account for such intensional phenomena.. (shrink)

Still, some may still want to say it. If so, my replies may gain nothing better than a stalemate against such persistence, though I can hope that earlier revelations will discourage others from persisting. But two replies are possible. Both come down, one circuitously, to an issue with us from the beginning: whether the language of the right side of (10) is suspect. For if (10) is to support instances for (6) which are about objects, that clause must itself be (...) about objects. (These would be ones assigned by variants of I it mentions to constants it mentions.) Yet Barwise and I would call it implicitly about functions. Ironically, the discussion surrounding (10), hoping to settle that issue, could only do so if the issue were already settled, revealing decisively the ontology of (10). If irritating, this is also inevitable, given the Tarskian spirit of the ensivioned semantics for QLB.A second reply begins by noting that a QLB semantics which implies (10) cannot simply be assumed. Even a QL semantics augmented to imply (11) is not trivial to frame, as I will let readers confirm. On the QLB project, Barwise comments thus:It is not possible to explain the meaning of an essential use of branching quantification ... inductively, by treating one quantifier at a time in a first-order fashion. Some use of higher-type abstract objects is essential. (BQE75)But believers in a modest ontology for QLB can claim a non sequitur here. For (10), as they read it, succeeds without mentioning abstract objects, though not in the “one quantifier at a time” way which Barwise rightly finds impossible. This is not yet to say the same about a QLB semantics implying (10). But that too can be said, as it happens, with as good a conscience as with (10). A suitable treatment can begin by somehow linearizing non QL sentences like (6). Still assuming prefixes whose rows each consist, speaking loosely, of n universal quantifiers followed by a single existential, we could simply line up these rows in any order, with unique deconcatenatability being assured. From then on, it gets both tedious and complex. A full syntax is essential, and some surprising categories arose in mine. I will spare readers all details, except to say that one can indeed “treat one quantifier at a time”, if not “in first-order fashion”: schematic rules for treating n quantifiers at once can be eschewed. Unsurprisingly, heavy use is made of the “depending only on” idiom seen in (10). Nor does it surprise me that this semantics can succeed, with that idiom available. Roughly, if open talk about functions works in a semantics for QLF, what I read as implicit talk about them should work in a semantics for QLB See [6] for a start on a semantics aspiring to handle sentences like (6) without invoking abstract objects. See also my comments on its notion of dependence, in [9]. . So even from a bare sketch, we can see that this new semantics settles nothing. It just leads back to the stalemate. Barwise and I will read crucial clauses as talking implicitly about functions, but this general charge against an idiom is equally deniable wherever the idiom occurs: in a reading for (6), say, or in the metalanguage can hardly repress a motherhood slogan: better dead than obscurely read. But that just denies the denial, unhelpfully. A better comment is the reminder that the claim stays alive only in a form which no one has ever imagined for it. The QLB quantifiers that cannot be shown not to range over objects are not the items anyone would ever have pointed to in illustrating the unkillable claim. (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)

According to a common opinion, the word ‘semantics’ , derived from the Greek word semantikos , appeared for the first time, at least in modern times, in the book Essai de semantique, science de significations by M. J. A. Bréal . However, Quine says in his lectures on Carnap:As used by C. S. Peirce, “semantic” is the study of the modes of denotation of signs: whether a sign denotes its object through causal or symptomatic connection, or through imagery, (...) or through arbitrary convention and so on. This sense of semantic, namely a theory of meaning, is used also in empirical philology: empirical semantic is the study of historical changes of meanings of words.1For Bréal, semantics was a branch of general linguistics. In particular, semantics was occupied with so-called lexical meaning and its changes through time. Thus, semantics in this sense belonged to what was called “the diachronic treatment of language”. This tradition is fairly alive in contemporary linguistic theory. Quine’s description of the word ‘semantic’ in Peirce corresponds, which Quine explicitly states, to its use in philology. However, some linguists ascribe a more theoretical role to lingustic semantics. Karl Bühler is an example. In his Sprachtheorie he says that a theory of semantic functions of language is a part of theory of language.2 This account is to be found also among philosophers. It is also rather obvious that Peirce did not limit his semantic only to empirical studies. Linguists also use the word ‘semasiology’ instead of ‘semantics’; Bühler proposed the term ‘sematology’ for a general theory of symbols. (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 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 the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL (...) formulas can be interpreted as modal formulas over a flow of time, where the logic of each instant is Łukasiewicz, with a finite or infinite number of truth values. As a main result, we obtain validity with respect to all flows of times that are non-branching to the future, and completeness with respect to all finite linear flows of time, or to an appropriate single infinite linear flow of time. It may be argued that this reduces the problem of establishing a meaningful interpretation of the truth values in BL logic to the analogous problem for Łukasiewicz logic. (shrink)

McCall (1984) offered a semantics of counterfactual conditionals based on “real possible worlds” that avoids using the vague notion of similarity between possible worlds. I will propose an interpretation of McCall’s counterfactuals in a formal framework based on Baltag-Moss-Solecki events and protocols. Moreover, I will argue that using this interpretation one can avoid an objection raised by Otte (1987).

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)

“Counterfactual” readings of might/could have were previously analyzed using metaphysical modal bases. This paper presents examples and scenarios where the assumptions of such a branching-time semantics are not met, because there are facts at the base world that preclude the complement of the modal becoming true. Additional arguments show that counterfactual readings are context dependent. These data motivate a semantics using a circumstantial (or factual) modal base, which refers to context-dependent facts about a world and (...) class='Hi'>time. The analysis is formulated in a version of premise semantics for modality. (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)

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)