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 (...) class='Hi'>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 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)

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)

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)

In an earlier paper by the author, Åqvist , I presented an approach to the logic of historical necessity, or inevitability, in the sense of a “two-dimensional” combination of tense and modal logic for worlds, or histories, with the same time order, known as T × W logic. Distinctive features of that approach were, apart from its two-dimensionality, its being based on discrete and finite time, and its use of so-called systematic frame constants in order to enable us (...) to indicate longitudes and latitudes of any points in the co-ordinate systems under consideration. This led us to study and axiomatize an infinite hierarchy HTWxy of two-dimensional modal tense logics with the characteristic operators for historical necessity and possibility added to the original basic vocabulary. The main purpose of the present paper is then twofold: to extend the logics HTWxy to the interesting branch of philosophical logic constituted by deontic logic as combined with tense logic; and to deal with a curious puzzle known as the so-called epistemic obligation paradox – a well known stumbling-block in this area of research in philosophical logic. We argue for a solution to both these problems, which appeals to a new infinite hierarchy DHTWxym of extensions of the HTWxy in the sense of logics combining dyadic deontic modalities with temporal ones such as those for historical necessity and other two-dimensional modalities. (shrink)

A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.

Imagination has recently attracted considerable attention from epistemologists and is recognized as a source of belief and even knowledge. One remarkable feature of imagination is that it is often and typically agentive: agents decide to imagine. In cases in which imagination results in a belief, the agentiveness of imagination may be taken to give rise to indirect doxastic control and epistemic responsibility. This observation calls for a proper understanding of agentive imagination. In particular, it calls for the development of a (...) semantics of imagination ascriptions. In the present paper an earlier suggestion by Ilkka Niiniluoto for a logic of imagination is considered. This proposal does not capture the agentive nature of imagination, and an alternative semantics is suggested. The new semantics combines the modal logic of agency with the neighbourhood semantics from alethic modal logic. (shrink)

There seems to be a minimal core that every theory wishing to accommodate the intuition that the future is open must contain: a denial of physical determinism (i.e. the thesis that what future states the universe will be in is implied by what states it has been in), and a denial of strong fatalism (i.e. the thesis that, at every time, what will subsequently be the case is metaphysically necessary).1 Those two requirements are often associated with the idea of (...) an objective temporal flow and the non-reality of the future. However, at least certain ways to frame the “openness” intuition do not rely on any of these. Branching Time Theory (BTT) is one such: it is compatible with the denial that time flow is objective and it is couched in a language with a (prima facie) commitment to an eternalist ontology. BTT, though, urges us to resist certain intuitions about the determinacy of future claims, which arguably do not lead either to physical determinism or to fatalism. Against BTT, supporters of the Thin Red Line Theory (TRL) argue that their position avoids determinism and fatalism, while also representing the fact that there is a future which is “special” because it is the one that will be the case. But starting with Belnap and Green 1994, some have objected to the tenability of TRL, mainly on metaphysical grounds. In particular, those argue that “positing a thin red line amounts to giving up objective indeterminism,”2 and that “has unacceptable consequences, ranging from a mistreatment of actuality to an inability to talk coherently about what would have happened had what is going to happen not taken place.”3 In this paper, we wish to reframe the.. (shrink)

In this paper we describe a novel approach to defining an ontologically fundamental notion of co-presentness that does not go against the tenets of relativity theory. We survey the possible reactions to the problem of the present in relativity theory, introducing a terminological distinction between a static role of the present, which is served by the relation of simultaneity, and a dynamic role of the present, with the corresponding relation of co-presentness. We argue that both of these relations need to (...) be equivalence relations, but they need not coincide. Simultaneity, the sharing of a temporal coordinate, need not have fundamental ontological import, so that a relativizing strategy with respect to simultaneity seems promising. The notion of co-presentness, on the other hand, does have ontological import, and can therefore not be relativized to an observer or to an arbitrarily chosen frame. We argue that a formal representation of indeterminism can provide the structure needed to anchor the relation of co-presentness, and that this addition is in fact congenial to the notion of dynamic time as requiring real change. The resulting picture is one of an extended dynamic present, implying a formal distinction between static simultaneity and dynamic co-presentness. After working out the basics of our approach in the simpler framework of branching time, we provide our full analysis in the framework of branching space-times, which allows for a formal definition of modal correlations. The spatial extension of the dynamic present can reach as far as the modal correlations do. In the limit, the dynamic present could extend across a maximal space-like hypersurface. (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)

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)

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)

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)

The paper looks into one branch of Ukrainian economy - the food industry. It is established that marketing activities of food industry companies have some specific features, namely mismatching of an agricultural performance period and production time; a perishable nature of products, which necessitates tight time frames of storage and sales; production focus on the direct consumer; a high level of materials consumption of products released, which requires a large quantity of feedstock as well as high qualification (...) skills and expertise from workers. The activity of a domestic bakery is described. It is determined that the complexity of its production processes and increased information flows requiring in-line processing for acquisition of appropriate data served as a basis for introduction of the special 'Marketing' software by its Marketing Department. The conducted analysis of the information product allowed to establish that the user of the above software maintains routine accounting and control of product supplies. To that end, information is processed, parameters related to production and supplies analyzed. The software significantly improves operational efficiency owing to an increased number of accountable factors and reduced decision making time. That bundled software however makes no provisions for development of a unified integrated management system, which reduces the company operating efficiency. It is established that to date there are many information systems available for food production automation, the Oracle E-Business Suite-based technology, developed by TopS BI, among them. It was offered for application at the food enterprise in question. The above system allows to automate production planning and management processes at various levels: from daily shop planning and management with step-by-step product quality control to scaled-up calendar planning of production, including that for a group of enterprises. (shrink)

In this investigation we analyze, from the point of view of glottopolitics, the metalinguistics discourses published on “El Boletín” of the Chilean Academy of the Spanish Language between 1915 and 1931, the period of the institution’s reactivation. This phase has special significance because the Chilean Academy strives to reposition itself in the Chilean cultural field after a long recess in which relevant changes developed in the country. At the same time the hispanist cultural trend acts with great force, represented (...) by the Spanish Royal Academy and its American branches. Our frame of reference is historical glottopolitics, and our main analytical concept is language ideology. From this background we apply a discursive analysis oriented toward the contents of academic discourses published on the Academy’s official magazine in the already indicated period. Our conclusion is that the language ideology contained in the corpus corresponds in general terms to the standard language ideology but permeated by local specific context as well as global. (shrink)

The concept of branching time is widely utilized to counter fatalistic arguments to the conclusion that whatever will happen is already unavoidable. The most common semantics for branching time, such as Ockhamism, Peirceanism, and Supervaluationism, offer a formal explanation for why fatalistic arguments are flawed. This paper explores a different type of argument, one that borders on fatalism and is concerned with what might possibly happen in the future. In the paper, I show how this type (...) of argument poses a new fatalistic threat to branching time. (shrink)

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

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)

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)

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

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

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

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

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

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)

The semantical structures called T x W frames were introduced in (Thomason, 1984) for the Ockhamist temporal-modal language, $[Unrepresented Character]_{o}$ , which consists of the usual propositional language augmented with the Priorean operators P and F and with a possibility operator ◇. However, these structures are also suitable for interpreting an extended language, $[Unrepresented Character]_{so}$ , containing a further possibility operator $\lozenge^{s}$ which expresses synchronism among possibly incompatible histories and which can thus be thought of as a cross-history 'simultaneity' (...) operator. In the present paper we provide an infinite set of axioms in $[Unrepresented Character]_{so}$ , which is shown to be strongly complete for T x W-validity. Von Kutschera (1997) contains a finite axiomatization of T x W-validity which however makes use of the Gabbay Irreflexivity Rule (Gabbay, 1981). In order to avoid using this rule, the proof presented here develops a new technique to deal with reflexive maximal consistent sets in Henkin-style constructions. (shrink)

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

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)

The 1968 My Lai Massacre in South Vietnam and shocking events at Abu Graibh prison in Iraq in 2003 show that the behaviour of some in the American military has descended into barbarism. How strong is the military's commitment to avoiding misconduct and atrocity? This timely and compelling book asks critical questions and raises sobering issues the Australian Army can't ignore. Leading military personnel, aid workers, commentators and scholars discuss the Australian Army's commitment to behaving ethically and the challenges associated (...) with contemporary warfare. With chapters on social media and inciting violence, cyberweapons, and special operations and humanitarian deployments, 'Ethics Under Fire' offers a rare insight into the key issues facing the modern army, from technology and tactics to terrorism"--Back cover. (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)

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)

When we make a prediction we select, among the conceivable future descriptions of the world, those that appear to us to be most plausible. We capture this by means of two binary relations, ≺c and ≺p: if t1 and t2 are points in time, we interpret t1 ≺ct2 as sayingthat t2 is in the conceivable future of t1, while t1 ≺pt2 is interpreted to mean that t2 isin the predicted future of t1. Within a branching-time framework we (...) propose the following notion of “consistency of prediction”. Suppose that at t1 some future moment t2 is predicted to occur, then every moment t on the unique path from t1 to t2 should also be predicted at t1 and the prediction of t2 should continue to hold at every such t. A sound and complete axiomatization is provided. (shrink)

The branching-time logic called Peircean by Arthur Prior is considered and given an infinite axiomatization. The axiomatization uses only the standard deduction rules for tense logic.

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...

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

The theory of trees with additional unary predicates and quantification over nodes and branches embraces a rich branching time logic. This theory was reduced in the companion paper to the first-order theory of binary, bounded, well-founded trees with additional unary predicates. Here we prove the decidability of the latter theory.

We propose a theory of events and causes against the background of branching time. Notions discussed include possibility based on reality, transitions, events, determinacy, contingency, causes and effects. The main idea in defining causal relations is to introduce a certain preconditioning circumstance under which one event follows another. We also briefly compare this theory with some other theories.

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)

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

Miller (2005) and Miller (2008) argue that the branching picture of time is incompatible with the possibility of backwards time travel. In this paper I show that Miller’s conclusion is based on a hidden assumption which, while generally plausible, is unwarranted if time travel is possible. Branching time is, after all, compatible with time travel as Miller characterises it.

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.

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.

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)

An important branch of environmental theory frames the climate crisis as a moral problem in need of a moral solution: human hubris is responsible for environmental degradation and must be atoned for through humility. Politically indeterminate, however, such argumentation is vulnerable to de-politicizing and mal-politicizing capture. In an effort to fend off the threat of either, this paper turns to the history of political thought and Jean-Jacques Rousseau, who theorized the environment as both a moral and a political domain. (...) I examine how Rousseau understood the availability of republican self-rule to be contingent both on the natural environment and on the relationship we construct with it such that freedom, in his words, is not automatically ‘a fruit of every Clime.’ This is the case, he suggests, because of the environment’s intersection with political economy and political culture. At the same time, Rousseau contends, republican self-rule is also a moral practice; republican polities afford citizens a public means of achieving and exercising moral agency. Triangulating the relationship between polity, morality, and environment, Rousseau’s thought offers an integrative logic through which to imbue the environment with both moral and political salience, thereby circumventing the dangers of mere moralization alone. (shrink)

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal (...) class='Hi'>frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting. (shrink)

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)

In this article we discuss the validity of previous preferences and advance directives in cases of severe mental illness.