SemOpenAlex |

SemOpenAlex

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2055113696> ?p ?o ?g. }

Showing items 1 to 64 of 64 with 100 items per page.

W2055113696 endingPage "696" @default.
W2055113696 startingPage "681" @default.
W2055113696 abstract "Previous article FreeDiscussionBranching with Uncertain Semantics Discussion Note on Saunders and Wallace, ‘Branching and Uncertainty’Nuel Belnap and Thomas MüllerNuel BelnapDepartment of Philosophy, University of Pittsburgh15232 Pittsburgh, PA, USA[email protected] Search for more articles by this author Email the corresponding author at [email protected] and Thomas MüllerDepartment of Philosophy, University of Utrecht3584 CS Utrecht, The Netherlands[email protected] Search for more articles by this author Email the corresponding author at [email protected]PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMore1. Identifying the Problem2. Unraveling the Discussion3. Branching Structures4. Identifying the Grammar5. Identifying an Adequate Semantics of Branching-Time6. Identifying the Saunders–Wallace Proposed Semantics7. ConclusionIn their paper ‘Branching and Uncertainty’, (Saunders and Wallace [2008]) aim to solve the so-called ‘incoherence problem’ commonly attributed to the Everett interpretation of quantum mechanics (EQM). The Everett interpretation posits a multiplicity of branching universes as a realistic reading of the evolution of the quantum state function. The ‘incoherence problem’ is, roughly, that our common talk of uncertainty of outcomes of quantum-mechanical experiments seems to have no foothold in EQM: Since all the facts about the branching are fully acknowledged, there seems to be nothing, on that interpretation, to be uncertain about.Saunders and Wallace point to non-epistemic approaches to the mentioned problem (e.g., Greaves [2004]; Greaves and Myrvold [2008]), but their own solution is instead to provide ‘a ready set of semantic rules according to which our actual extant, ordinary talk of ignorance and uncertainty comes out as true’ (pp. 293-4). Thus, there is no incoherence problem to begin with, just a question of getting the semantics right. This project, according to Saunders and Wallace, is not motivated by metaphysical considerations but by the hope of making sense of our ‘best physical theory’ along the lines of a naturalized metaphysics.We agree with much of what Saunders and Wallace are aiming at. Whether one’s goal is to understand EQM or everyday indeterminism, branching is a basic concept that is needed to make sense of objective uncertainty about the future.1We agree and indeed insist that branching gives a perfectly coherent account of objective uncertainty. We take issue, however, with the way Saunders and Wallace carry out their task. The point of this discussion note is therefore partly critical and partly reconstructive. Our criticism is based on our sustained but unsuccessful attempt at identifying the ‘ready set of semantic rules’ promised in the paper’s introduction. It isn’t just that such rules are nowhere explicitly given in the paper: The scant exposition provided in the text glosses over a number of crucial choices that need to be made to identify such semantics, as is clear from extant discussion in readily available literature. Thus, even implicitly no rigorous semantic rules—rules that at least in idealized cases measure up to the standard set by Tarski—can be identified. Our reconstruction is founded on a mathematically exact semantic framework that has been proposed to explain objective uncertainty in terms of branching, namely, branching time.2 We hold that this framework, which is completely rigorous, preserves enough of the authors’ central ideas to count as a friendly reconstruction serving their purpose of countering the incoherence problem of EQM.1. Identifying the ProblemThe problem of making sense of objective uncertainty has been discussed in at least two different areas of philosophy, both of them rather technical: the philosophy of physics and philosophical logic. There has not been much interaction between these two strands of discussion.The problem that Saunders and Wallace are facing arises in the context of the interpretation of quantum mechanics: Given EQM, we seem to be in a situation where everything there is to be known is known (because the evolution of the quantum state describes all the facts about future branchings exactly), and still there is something we don’t know (because intuitively, we are facing an uncertain future; cf. p. 301). This tension has suggested to many that either EQM must be dropped or our attitude toward the future will need to be redescribed in non-epistemic terms, accounting for what we do while denouncing our intuitive explanation of why we do what we do, which points to an objective uncertainty that EQM apparently disallows. Saunders and Wallace reject both these options: EQM is taken to be ‘our best physical theory’ (p. 294),3 and our stance toward the future is viewed as robustly grounded in objective uncertainty, ruling out a non-epistemic reinterpretation. Thus, the challenge is to find a place for objective uncertainty in a branching framework. In other words, the incoherence problem discussed by Saunders and Wallace has the following form. How can we give a coherent view of what the world is like that incorporates two facts forced upon us by our best physical theory: (a) a realistic interpretation of QM via EQM shows that we need to give a branching account of the evolution of the universe, (b) as practicing physicists we face objective uncertainty, e.g., in connection with the outcomes of quantum-mechanical experiments.Worries about EQM were certainly not what motivated the logicians’ tense-logical theories of branching time. Instead, from Aristotle’s famous discussion of ‘the sea-battle tomorrow’ onward, the worry concerned the following. Given our everyday intuitions about objective uncertainty, how can we find an appropriate semantic framework for the future tense of natural language?Branching time is precisely such a framework. Viewed from this perspective, the challenge posed by EQM may sound somewhat surprising. After all, the incoherence problem would seem to vanish once one adopts the branching-time semantic framework. In fact, although they do not mention ‘branching time’, this is more or less what is said in Saunders and Wallace’s paper. It could, however, be said more clearly, rigorously, and with ready references to existing literature, thus enforcing rather than weakening the connection between philosophy of physics and formal logic. This is what we aim to do in the rest of this discussion note.2. Unraveling the DiscussionSaunders and Wallace start to discuss branching in the context of personal fission, taking up an argument between (Parfit [1976] and Lewis [1976]).Whatever the merits of such a discussion, it is clearly not pertinent to the matter at issue, which is the objective uncertainty of the outcome of, e.g., a physical experiment. The authors themselves come to this conclusion when they explicitly suggest shifting the discussion of branching from intra-world branching of persons to branching of ‘worlds as wholes’ (p. 297), where by ‘worlds’ they presumably mean possible courses of events, i.e., what we call ‘histories’.4 The move from persons branching to histories branching is good: Many examples of objective uncertainty discussed in the literature do not involve persons at all, and even though many do so, they are not needed for illustrating either objective uncertainty or EQM. Discussion of the mind-dependent features of persons facing an ‘open future’ brings in many difficult issues that are best dealt with after the notion of objective uncertainty has been clarified.5Saunders and Wallace’s next step is to address and dismiss Lewis’s arguments against branching. While we refrain from endorsing a number of details in their argumentation, their conclusion, which is that Lewis gives only faulty arguments against branching, agrees with ours.6 Before going on to discuss the merits of their proposal for the understanding and defense of EQM, Saunders and Wallace wrap up their analysis by discussing the example sentence, ‘Al Gore might have won the 2000 US presidential elections’ (p. 298). On their view, that sentence is true if Al Gore ‘has a temporal part which is part of a person who won’ (p. 298). They later stress that a temporal part is a part of many histories, each a single course of possible events, while a personal continuant occurs in only one history.7On our view, it is good that Saunders and Wallace stress the importance of small entities for clarifying the semantics of such modal talk, and it is also good to allow these entities to occur in many histories.8 Where we disagree is with respect to the analysis of continuants. Saunders and Wallace do not make it easy to distinguish a possible ‘life history’, which by definition does not contain incompatible events, from a person (who may on occasion face future possibilities that are incompatible). With respect to the example, we would like to say the following: Al Gore might have won the 2000 US presidential elections if and only if in his past life, there was an event such that at that event, it would have been true to say ‘It is possible that he will win’, i.e., if there is at least one history passing through that event on which he later wins the election.9 All the time, we are talking about the man Al Gore, whose possible life histories branch, even though it makes no sense to say of the person, Al Gore, that he branches.At any rate, for the basic point at issue, i.e., how to make sense of objective uncertainty against a branching background, an analysis of continuants would require an additional exploration, whereas examples employing just impersonal events appear to suffice. The first step in giving a semantic account suitable for EQM, which is the express purpose of the Saunders and Wallace paper, should therefore avoid requiring consideration of persons and life histories. The point is to adhere to Tarskian standards of rigor, being explicit and mathematically precise about the semantic rules. That this is possible for an assemblage of branching histories, each taken as a maximally consistent course of events, is witnessed by a number of publications.10 Saunders and Wallace, however, while referring to ‘their semantics’ many times, are never explicit. This would be sufficiently unhappy if their purpose were to clarify natural language, but the lack of rigor stands out especially in the present case, in which the concern is to illuminate a physical theory that from the beginning is phrased in mathematical language.3. Branching StructuresThere is a variety of rigorous semantics for a language in which one can express objective uncertainty. Common to many of them is the reliance on branching structures. Formally, a branching structure is minimally a strict partial ordering 〈W, <〉 (i.e., W is a non-empty set and < is a transitive and irreflexive—and therefore asymmetric11—binary relation on W) that also satisfies the principle of no backward branching (i.e., for any m1, m2, and m3 ∈ W, if m1 < m3 and m2 < m3, then either m1 = m2 or m1 < m2 or m2 < m1). A history, h, is defined as a subset of W that is linearly ordered by < (so that any two elements of h are comparable) and that is maximal with respect to that property.The elements of W, which we call moments, can be taken to carry various sorts of event-like information. In line with Prior’s original idea of a branching-time framework for discussing indeterminism (Prior [1967], pp. 126–7), moments could carry information about the facts everywhere across a universe-wide possible course of events at a single point in time—what (Thomson [1977]) calls a (momentary) ‘super-event’. We use m to range over moments. For the ordering relation m1 < m2, a temporal‐modal‐causal interpretation is natural: m1 < m2 may faithfully be read as either ‘m1 is in the (settled) causal past of m2’ or ‘m2 is in the future of possibilities of m1.’ A history, h, is a concrete course of events, explicating the modal structure: Two moments are consistent if and only if there is a history to which they both belong.Example 1. Let there be four moments in all: W = {m0, m1, m′1, m2}, with m0 < m1 < m2, m0 < m′1, and two histories, h1 = {m0, m1, m2}and h′1 = {m0, m′1}.So m1 and m′1 are inconsistent, as are m2 and m′1.In short, the branching of histories gives a formal representation of the alternative possibilities that form the basis for objective uncertainty.It is consistent with the spirit of branching to suppose that each possible moment, m, can be assigned a unique positive real number as its date‐time, say date‐time(m) = ρ, in a partly conventional but also partly natural way. Using <R for the standard linear ordering of the reals, it is, e.g., a necessary (but not yet sufficient) condition on the function date‐time is that if m1 < m2, then date‐time(m1) <Rdate‐time(m2).12 Let T be the range of the date‐time function, and let <T be <R restricted to T. Call 〈W, <, T, <T, date‐time〉 a ‘BTDT’ structure (branching times with date‐times). If one takes this route, one must be careful to distinguish date‐times in T from moments in W. We may enrich Example 1 by adding some date‐time information.Example 2. Add to Example 1 the following: T = {t0, t1, t2} with t0 <R< t1 <Rt2 and date‐time(m0) = t0, date‐time(m1) = date‐time(m′1) = t1 and date‐time(m2) = t2.Two easy and relevant remarks that are, however, also easy to forget: (i) Although the ordering of W is tree-like, it is natural that the set, T, of date‐times admits a linear order such as <R. (ii) That date‐time(m1) = date‐time(m′1), even though m1 is inconsistent with m′1, is nothing special. It is, however, misleading to report this situation by saying that ‘even though they are inconsistent, m1 and m′1 occur at the same time.’ That recipe neglects that we are speaking of individually possible but jointly inconsistent moments, whereas ‘occurs at the same time’ wrongly suggests joint consistency. Better instead to endure the cumbersome ‘m1 and m′1 are alternative possibilities for the same time.’With respect to EQM, a BTDT structure, 〈W, <, T, <T, date‐time〉 would most probably correspond to a branching tree of quantum states of the universe, even though the idea of continuous branching that is sometimes evoked in connection with EQM (e.g., Wallace [2008], p. 26) might pose formal challenges (we’ll leave these considerations by the wayside).13Based on a branching structure, semantical rules for interpreting sentences of a given language may be formulated. In what follows, we will only consider formal languages.144. Identifying the GrammarWhich (formal) language is appropriate for discussing and possibly resolving the incoherence problem for EQM?Given the basic branching-time structure 〈W, <〉, it is possible to specify a number of different semantics for a basic propositional temporal–modal language, i.e., a language containing propositional constants (p, q, r,…), propositional connectives (not, and, or, if…then, often symbolized as ¬, ∧, ∨, →), temporal operators it was the case that and it will be the case that (symbolized by Prior as P and F, and by FF as Was: and Will:), and the modalities of settledness (‘historical necessity’) and historical possibility (symbolized by FF as Sett: (short for ‘settled true’) and Poss:). It is this simple grammar that we will take as our principal target in making a case that branching time, when properly understood, supports the coherence of EQM. Given a full BTDT structure, 〈W, <, T, <T, date‐time〉, it is also enlightening to include forms Att:A, where A is a sentence and t is an individual constant that ‘rigidly’ denotes a member of T, i.e., a date‐time. Att:A is given the informal reading, ‘that A is true at date‐time t’.15 For a richer language, typically only a subset of its expressions will admit of semantic interpretation given just a branching structure with date‐times.Saunders and Wallace evidently have in mind a language whose grammar allows one to talk about individuals (e.g., events, persons, and so on) such as the language of predicate logic; such a language obviously needs additional information to allow for semantic interpretation. Formally, this points to the many issues of quantified modal logic, for the illumination of which a number of widely different semantic approaches have been proposed. A useful summary of such options is given by (Garson [2006]). An especially delicate issue in this area is the formal representation of individuals. Even deciding on an underlying branching structure still allows for many options in this respect.16 We will not consider individuals in what follows, for the reasons given at the end of Section 2.5. Identifying an Adequate Semantics of Branching‐TimeWe think that the semantics of FF (Chapter 8) and DTR is of major help in understanding EQM. Here, we give a relaxed account of the semantics, trusting the reader to consult the mentioned sources for mathematically exact formulations. A critical requirement in giving a semantics based on a branching structure is to identify the index ofevaluation, i.e., the suite of parameters with respect to which truth values of utterances are to be assessed. Following the ideas of (Kaplan [1989], pp. 591–3), such an index usually comprises both context parameters, such as moment, place, and speaker of the context of utterance, and auxiliary parameters that may be shifted by, for example, the modal and tense operators.17 For simplicity, we omit every element of context, except the moment of utterance.18 Even in non-branching tense logic, the index of evaluation needs at least two parameters: one context parameter, ‘the moment of the context of utterance’, mC, and one auxiliary parameter, ‘the moment of evaluation’, m.19 Each must be an element of W. The former pertains to the moment at which a stand-alone sentence is uttered, presumably as the vehicle of some speech act. The auxiliary parameter, m, identifies a ‘moment of evaluation’, that is, an element of W with respect to which embedded parts of uttered sentences are evaluated and which is shifted up and down a single history by tenses or by an Att: operator. For example, the Was: operator shifts that parameter backwards in time so that for the sentence ‘it was the case that p’, the embedded p is evaluated, as it should be, not at the moment of evaluation of the whole sentence but at some moment before that. The truth value of a stand-alone sentence must not depend on the value of auxiliary parameters: Such parameters must in effect eventually be ‘canceled’ either by quantifying over them or with the help of some element of the context. (This is nothing specific to modal languages: Standard first-order logic treats the quantificational auxiliary, ‘assignment of values to the variables’, α, as something that needs to be canceled by quantification.) Given a stand-alone sentence of our language, the auxiliary moment of evaluation, m, is canceled in the second way, by identification with the moment of utterance, mC. That is to say, a stand-alone sentence is to be evaluated at a suite of parameters such that the moment of evaluation is identical to the moment of utterance: m = mC. We may say that the auxiliary moment parameter is ‘canceled by initialization by context’. When there is no branching, there is no point in distinguishing moments and times. So much for non-branching: The required suite of parameters must be 〈mC, m〉.In giving semantics for the future tense based on branching structures, there is no getting around the idea of a history, h, namely, a maximal linear chain within W representing one complete possible course of events. The literature reveals several ways in which histories can play a role in the semantics.1.(Prior [1967], pp. 128–36) describes the so-called ‘Peircean’ semantics, in which the future operator is taken to quantify over all histories, h, passing through the moment of evaluation, m, thus reading ‘it will be the case that’ as ‘it is unpreventable that it will be the case that’, or, to use the (Thomason [1970]) terminology, ‘it is settled that it will be the case that’. On the Peircean semantics, there is quantification over histories, but there is no history parameter: Truth is relative simply to the pair, 〈mC, m〉. Although simple, Peircean semantics will do neither for EQM nor for our ordinary employment of the future tense in the context of indeterminism. With regard to the latter, ‘I now bet that the outcome of the measurement will be spin-up’ is not plausibly construed as a bet that it isnow a settled matter that the outcome will be spin-up.2. ‘Occamist’ semantics, also mentioned by (Prior [1967], pp. 121–7), employs an auxiliary history parameter, the ‘history of evaluation’, and takes truth to be relative to a triple 〈mC, m, h〉 (moment of utterance, moment of evaluation, and history of evaluation), where h must contain m; Was: and Will: shoot existentially, respectively, backward and forward along h. This turns out to allow for a more natural reading of the future tense in both ordinary and EQM employment. Being auxiliary, the history of evaluation parameter must eventually be canceled.20 The literature has considered various possibilities.2a. In the triple 〈mC, m, h〉, one might be tempted to take the auxiliary, h, to be canceled through unique determination by the moment of utterance, mC, or (which comes to the same thing) one might simply take h itself to be a context-of-utterance parameter, or one may take the history, h, to be uniquely determined by the moment of evaluation, m. Each of these alternatives amounts to postulating that there is the actual future which is uniquely determined by a single momentary event. Each of these alternatives must be dropped because each is really just determinism in sheep’s clothing. These views are discussed and criticized in Chapter 6 of FF under the heading, ‘the thin red line’.212b. If the history of evaluation parameter, h, is not determined by context, then it is an auxiliary parameter and as such must eventually be canceled. There are many possibilities (see DTR); we mention just two.2b1.(Thomason [1970]) cancels the history parameter in the service of a supervaluational theory of truth. Thus, leaving out mC for the nonce, a sentence is said to be true [false] at a moment, m, just in case it is true [false] at every moment‐history pair 〈m, h〉; with m∈ h, that is, just in case it is settled true [false] at m. This supervaluational lapse from bivalence answers to the idea that a sentence in the future tense may be neither settled true nor settled false when uttered. We recommend keeping the idea, which goes back to Aristotle, but not keeping the shortening of ‘settled true’ to plain ‘true,’ a shortening that makes it almost impossible to avoid confusion. Think of the confusion in modal logic were one to uniformly shorten ‘necessarily true’ to plain ‘true’. To fail to make the modality explicit in either case invites wholly unnecessary confusion.222b2. A more sophisticated use of the supervaluational idea is to distinguish the moment of evaluation of a future tense sentence from the moment defining the set of histories required for settledness. The intuition is that an utterance of a sentence at mC (paradigmatically in the future tense) may well not have a settled truth value at mC, when it is uttered, even though it will be settled one way or the other later, a phenomenon labeled a ‘double time reference’ in DTR. This application of the semantics for branching time can make sense of our ordinary employment of predictions, as well as of promises, bets, and so forth, as subject to normative assessment. The key idea is that the auxiliary moment of evaluation, m, is canceled by identification with the moment of utterance, mC, whereas the auxiliary history of evaluation, h, is canceled by quantification with respect to all histories passing through a later ‘moment of assessment’ (the phrase is due to MacFarlane, ibid.). This makes it easy to see a rigorous and coherent semantic underpinning for sentences such as the following, which in English are almost hopelessly confusing to those lacking a firm grasp of the semantics required by indeterminism:Example 3. 23 As a matter of settled fact, it is (at m2) false that ‘The electron will be measured spin up’ was (at m0) settled (i.e., on both h1 and h′1) true at any moment (i.e., m0) prior to the moment of measurement (m1). But now (at m2), it is a settled fact (i.e., on h1, which is the only history through m2) that ‘The electron will be measured spin up’ was true at each moment (i.e., m0) prior to the moment of measurement (m1).In accord with the treatment of ‘double time references’ in BTDT semantics (we’ll call the whole package ‘BTDT‐DTR semantics’), what must be done is to distinguish the following two, when asserted at some moment of assessment (m2) after the measurement came out ‘spin up’ (at m1), with reference to a past moment of utterance (m0) of ‘Will:Up’ that is prior to the measurement:Was:Sett:Will:Up (false) from Sett:Was:Will:Up (true).24 We could describe the situation as follows as a repetition and enrichment of previously displayed examples.Example 4. Assume, as in Examples 1 and 2, that there are just four moments, two histories, and three date‐times. The ‘spin’ facts are that the electron is measured spin-up at the possible moment m1, but ‘spin down’ at m′1, which we encode by assuming that Up is settled true at m1, but settled false at m′1. We can envision three speech acts.At m0 (whose date‐time is t0), Sarah, with the date‐time, t1, in mind, predicts spin-up by uttering Will:Up. Bill, at m2, thinking of m0, utters Was:Sett:Will:Up as a way, perhaps, of trying to trivialize Sarah’s speech act by claiming that what Sarah said was settled true when she said it, at m0. Bill speaks falsely: Since Up is (timelessly) settled false at m′1, it follows that Will:Up was not settled true at m0, thus making Bill’s utterance settled false at the moment, m2, of his utterance. Jack, however, also speaking at m2, utters Sett:Was:Will:Up as a way of positively assessing the prediction Sarah made: It is now, at m2, settled true that what Sarah said was indeed (plain) true when she said it, at m0. Jack speaks the settled truth: Since Up is (timelessly) settled true at m1, it follows that Will:Up is true at m0 on every history passing through (not m0 but) m2, even though it is false that Will:Up is true at m0 on every history passing through m0 itself. So Was:Will:Up is settled true at Jack’s moment of speech, m2, and he would be right in crediting Sarah with having spoken truly. (It turned out that she spoke the truth.)(We refuse to take the blame for the complications revealed by disentangling this example. Blame them instead on the situation, not the reporters.)Note, incidentally, that when ‘Was:’ in the above passages is evaluated at m2, it takes us back via ‘<’ to some moment in the causal past of m2 (either m1 or m0), not just to some moment such as m′1 whose date‐time is in the past of the date‐time of m2 (‘the temporal past’, as we might say).We can also use Att: to speak of contemporaneous ‘might-have-beens’, for example Att1:Up, but also Was:Poss:Att1:¬Up. Or even, using date‐times exclusively, with m2 as moment of context (and moment of evaluation), Att1:Up, but also Att0:Poss:Att1:¬Up.The often misunderstood point is that one cannot escape dealing with indeterminism by substituting pure date‐time language for tenses.6. Identifying the Saunders–Wallace Proposed SemanticsUnfolding all of the above may be belaboring the obvious, but it seems necessary as a background for becoming clear on the semantics that Saunders and Wallace say they propose since their presentation is extremely condensed.Here are a number of short passages that hint at something like semantic rules. If persons are continuants [which Saunders and Wallace endorse], we do better to attribute thoughts and utterances at t to continuants C at t. That is, thoughts or utterances are attributed to ordered pairs 〈C, t 〉 or slices of persons 〈C, S〉, S ∈ C, not to temporal parts S. (p. 295)Here one might make a case for a variety of different semantic rules, but the one we are interested in is this: the word ‘I’ refers to the speaker of any sentence in which it occurs. (pp. 295f.)[The authors understand this in such a way that] the referent of ‘I myself’, thought or uttered at time t (at temporal part S) is the continuant who thinks or utters the phrase [in question]. (p. 296)To conclude: if—as Lewis proposes [and Saunders and Wallace seem to endorse]—in cases of personal branching we say there are two persons present even before the branch, it is at least somewhat natural to attribute two sets of thoughts to those persons; in the case of worlds branching, it becomes entirely natural. (p. 303)If this is depersonalized, or if branching-time theory is personalized, this sounds rather like our understanding of branching time. In particular, the attribution of utterances to continuant–slice pairs 〈C, S〉 seems just like our attribution of truth to moment‐history pairs 〈m, h〉 as the index of evaluation.25 In further analogy to (or endorsement of) the Saunders and Wallace scheme, we allow that even before a branch point m, the various histories h containing m must be kept distinct.When one is semantically precise, however, it becomes obvious that in contrast to Saunders and Wallace, one must distinguish (plain) truth at a moment‐history pair 〈m, h〉 from settled truth at a moment (the histories having been canceled by universal quantification). The next step is one of application (or metaphysics?): We submit that an utterance is, when properly idealized, a momentary event, so that Abigail uttered ‘I will survive’is either settled true at a mome" @default.
W2055113696 created "2016-06-24" @default.
W2055113696 creator A5036317806 @default.
W2055113696 creator A5073884439 @default.
W2055113696 date "2010-09-01" @default.
W2055113696 modified "2023-10-03" @default.
W2055113696 title "Branching with Uncertain Semantics" @default.
W2055113696 cites W2047179354 @default.
W2055113696 cites W2054686020 @default.
W2055113696 cites W2106084809 @default.
W2055113696 cites W2165758916 @default.
W2055113696 cites W2167496701 @default.
W2055113696 cites W4255970744 @default.
W2055113696 doi "https://doi.org/10.1093/bjps/axq001" @default.
W2055113696 hasPublicationYear "2010" @default.
W2055113696 type Work @default.
W2055113696 sameAs 2055113696 @default.
W2055113696 citedByCount "6" @default.
W2055113696 countsByYear W20551136962012 @default.
W2055113696 countsByYear W20551136962013 @default.
W2055113696 countsByYear W20551136962019 @default.
W2055113696 countsByYear W20551136962022 @default.
W2055113696 crossrefType "journal-article" @default.
W2055113696 hasAuthorship W2055113696A5036317806 @default.
W2055113696 hasAuthorship W2055113696A5073884439 @default.
W2055113696 hasBestOaLocation W20551136961 @default.
W2055113696 hasConcept C111472728 @default.
W2055113696 hasConcept C138885662 @default.
W2055113696 hasConcept C178790620 @default.
W2055113696 hasConcept C184337299 @default.
W2055113696 hasConcept C185592680 @default.
W2055113696 hasConcept C199360897 @default.
W2055113696 hasConcept C206175624 @default.
W2055113696 hasConcept C41008148 @default.
W2055113696 hasConceptScore W2055113696C111472728 @default.
W2055113696 hasConceptScore W2055113696C138885662 @default.
W2055113696 hasConceptScore W2055113696C178790620 @default.
W2055113696 hasConceptScore W2055113696C184337299 @default.
W2055113696 hasConceptScore W2055113696C185592680 @default.
W2055113696 hasConceptScore W2055113696C199360897 @default.
W2055113696 hasConceptScore W2055113696C206175624 @default.
W2055113696 hasConceptScore W2055113696C41008148 @default.
W2055113696 hasIssue "3" @default.
W2055113696 hasLocation W20551136961 @default.
W2055113696 hasLocation W20551136962 @default.
W2055113696 hasOpenAccess W2055113696 @default.
W2055113696 hasPrimaryLocation W20551136961 @default.
W2055113696 hasRelatedWork W1587224678 @default.
W2055113696 hasRelatedWork W2104078272 @default.
W2055113696 hasRelatedWork W2112962394 @default.
W2055113696 hasRelatedWork W2118300983 @default.
W2055113696 hasRelatedWork W2166247150 @default.
W2055113696 hasRelatedWork W2748952813 @default.
W2055113696 hasRelatedWork W2899084033 @default.
W2055113696 hasRelatedWork W3137189469 @default.
W2055113696 hasRelatedWork W4235530921 @default.
W2055113696 hasRelatedWork W4243252198 @default.
W2055113696 hasVolume "61" @default.
W2055113696 isParatext "false" @default.
W2055113696 isRetracted "false" @default.
W2055113696 magId "2055113696" @default.
W2055113696 workType "article" @default.