Our aim in the present paper is to investigate, from the standpoint of truth-theoretic semantics, English tense, temporal designators and quantifiers, and other expressions we use to relate ourselves and other things to the temporal order. Truth-theoretic semantics provides a particularly illuminating standpoint from which to discuss issues about the semantics of tense, and their relation to thoughts at, and about, times. Tense, and temporal modifiers, contribute systematically to conditions under which sentences we utter (...) are true or false. A Tarski-style truth-theoretic semantics, by requiring explicitly represented truth conditions, helps to sharpen questions about the function of tense, and to deepen our insight into the contribution the tenses and temporal modifiers make to what we say by using them. (shrink)

This paper presents an approach to the elementary temporal semantics of the English tense system, the atoms of which are the present tense, the past tense, the progressive auxiliary, the perfective auxiliary, and the modal will as used for the future. It offers accounts of the forms of temporal semantics of core verb phrases of different categories and of the atoms of the tense system, using machinery that that yields appropriate compositional accounts of the (...) temporal semantics of compound, tensed verb phrases. This machinery also yields a novel account of the Kenny-Vendler classification of core verb phrases. (shrink)

The thesis is an attempt to give a precise formal semantics for various time-referential linguistic categories of English such as tense, perfect, progressive and Aktionsart or "action type", with the ultimate goal of explaining why with a verb phrase such as walk the inference from, for instance, John is walking to John has walked is intuitively valid, while with a verb phrase such as build a house the even weaker inference from John is building a house to John (...) will have built a house is intuitively invalid. The difference is seen as one of the Aktionsart of the sentences involved. ;Accordingly, a theory of Aktionsarten is developed in chapter 2. Four different Aktionsarten are formally distinguished. In chapter 3 a theory of the tenses and their interaction with temporal adverbials is worked out. Chapter 4 is about the perfect. The so-called "extended now" theory of the perfect is given a precise treatment. Finally, chapter 5 deals with some problems of the English progressive. Especially the so-called "imperfective paradox" is given a solution. ;The method I use is that of model-theoretic semantics applied to natural languages, as it was first developed by the logician, Richard Montague. (shrink)

Let us call “tense logic” the programme of explaining tense in natural languages by means of a model theory similar in structure to possible worlds semantics for modality. This programme would make the following claims.

Montague’s framework for semantic interpretation has always been less well adapted to the interpretation of words than of syntactic constructions. In the late 1970s, David Dowty addressed this problem, concentrating on the interpretation of tense, aspect, inchoatives, and causatives in an extension of Montague’s Intensional Logic. In this paper I will try to revive this project, conceiving it as part of a larger task aiming at the interpretation of derivational morphology. I will try to identity some obstacles arising in (...) Dowty’s approach, and will suggest an alternative approach that, while it does not provide a global interpretation of causality, seems to work well with a wide range of the causal constructions that are important in word formation. I try to relate these ideas to some themes in contemporary philosophy and in the formalization of commonsense reasoning. (shrink)

In this paper back-and-forth structures are applied to the semantics of natural language. Back-and-forth structures consist of an event structure and an interval structure communicating via a relational link; transitions in the one structure correspond to transitions in the other. Such entities enable us to view temporal constructions (such as tense, aspect, and temporal connectives) as methods of moving systematically between information sources. We illustrate this with a treatment of the English present perfect, and progressive aspect, that draws (...) on ideas developed in Moens & Steedman (1988), and discuss the role of rich ontologies in formal semantics. (shrink)

We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path axioms, and for bi-intuitionistic logic. These logics do not have straightforward formalisations in the traditional Gentzen-style sequent calculus, but have all been shown to have cut-free nested sequent calculi. The proof of the interpolation theorem uses these calculi and is purely syntactic, without resorting to (...) embeddings, semantic arguments, or interpreted connectives external to the underlying logical language. A novel feature of our proof includes an orthogonality condition for defining duality between interpolants. (shrink)

This paper delves into the temporal interpretation of fronting constructions in English, a topic that has received limited attention in the literature on tense semantics. It presents new empirical findings revealing that specific fronting configurations, involving present tense morphology in a complement CP under a matrix past tense, can yield a theoretically unexpected simultaneous interpretation. A novel theoretical framework for understanding English tense is proposed, which accounts for the temporal interpretation of both fronting and non-fronting (...) versions of attitude reports. The framework introduces a null simultaneous tense as a replacement for the conventional indexical present and the Sequence-of-Tense (SOT) _de se_ tense. It is argued that in complement CPs the null simultaneous tense, as well as past tense, can be anchored either to the attitude time or to the utterance time. In either case, each tense receives a _de re_ interpretation. Moreover, the paper contends that evidence from fronting constructions supports Kratzer’s (Proceedings of semantics and linguistic theory 8, pp. 92–110, 1998 ) proposal that the transmission of temporal features (as part of the mechanism of SOT) occurs at PF. Finally, the proposed revision of the English tense system contributes to a more unified cross-linguistic perspective on tense. It is demonstrated how the temporal readings of attitude reports arising in such non-SOT languages as Russian, Japanese, and Hebrew can be captured within the system developed for English, with known contrasts attributed to the absence of Feature Transmission in those languages. Further known and new data from English, Modern Greek, and German are examined, revealing variations in SOT effects across SOT languages. These data are used as additional evidence supporting the claim that cross-linguistic variation in the interpretation of complement tense stems solely from differences in Feature Transmission. Regarding the semantic profile of tenses, it can be considered largely invariant. (shrink)

Although we believe the results reported below to have direct philosophical import, we shall for the most part confine our remarks to the realm of mathematics. The reader is referred to [4] for a philosophically oriented discussion, comprehensible to mathematicians, of tense logic.The “minimal” tense logicT0is the system having connectives ∼, →,F(“at some future time”), andP(“at some past time”); the following axioms:(whereGandHabbreviate ∼F∼ and ∼P∼ respectively); and the following rules:(8) fromαandα → β, inferβ,(9) fromα, infer any substitution instance (...) ofα,(10) fromα, inferGα,(11) fromα, inferHα.A tense logic is a systemTwhose language is that ofT0and whose axioms and rules include (1)–(11). The axioms and rules ofTother than (1)–(11) are calledproperaxioms and rules.We shall investigate three systems of semantics for tense logics, i.e. three notions ofstructureand three relations ⊧ which stand between structures and formulas. One reads⊧αas “αis valid in.” A structureis amodelof a tense logicTif every formula provable inTis valid in. A semantics isadequateforTif the set of models ofTin the semantics is characteristic forT, i.e. if wheneverT ∀ αthen there is a modelofTin the semantics such that∀ α. Two structuresand, possibly from different semantics, are calledequivalent(∼) if exactly the same formulas are valid inas in. (shrink)

Tenseless theories of time entail that earlierthan, later than and simultaneous with (i.e.,McTaggart's `B-series') are the only temporalproperties exemplified by events. Such theories oftencome under attack for being unable to satisfactorilyaccount for tensed language. In this essay I arguethat tenseless theories of time are capable of twofeats that critics, such as Quentin Smith, argue arebeyond their grasp: (1) They can coherently explainthe impossibility of translating all tensed sentencesby tenseless counterparts; (2) They can account forcertain obviously valid entailment relations betweentensed sentence (...) types. In analyzing tensed entailmentrelations tenselessly, I favor a date analysis oftensed language over a token-reflexive theory. Theupshot is that tenseless theories of time are notundermined by the linguistic facts. (shrink)

Expressivism - the sophisticated contemporary incarnation of the noncognitivist research program of Ayer, Stevenson, and Hare - is no longer the province of metaethicists alone. Its comprehensive view about the nature of both normative language and normative thought has also recently been applied to many topics elsewhere in philosophy - including logic, probability, mental and linguistic content, knowledge, epistemic modals, belief, the a priori, and even quantifiers. Yet the semantic commitments of expressivism are still poorly understood and have not been (...) very far developed. As argued within, expressivists have not yet even managed to solve the "negation problem" - to explain why atomic normative sentences are inconsistent with their negations. As a result, it is far from clear that expressivism even could be true, let alone whether it is. Being For seeks to evaluate the semantic commitments of expressivism, by showing how an expressivist semantics would work, what it can do, and what kind of assumptions would be required, in order for it to do it. Building on a highly general understanding of the basic ideas of expressivism, it argues that expressivists can solve the negation problem - but only in one kind of way. It shows how this insight paves the way for an explanatorily powerful, constructive expressivist semantics, which solves many of what have been taken to be the deepest problems for expressivism. But it also argues that no account with these advantages can be generalized to deal with constructions like tense, modals, or binary quantifiers. Expressivism, the book argues, is coherent and interesting, but false. (shrink)

According to a number of authors it is possible to give tenseless (B-series) truth conditions for tensed sentences by utilizing token indexicals in something like the following fashion. (1a) An utterance u of 'Past S' is true iff at some time earlier than u, S is true (1b) An utterance u of 'Pres S' is true iff at some time overlapping u, S is true This strategy has been challenged on the grounds that it will break down in cases like (...) (2). (2) There was no spoken language A number of strategies have been attempted to circumvent this difficult, including the introduction of possible utterances, etc. In this paper I argue that such moves are unnecessary — that the problem turns on scope interactions with hidden modals in the theorems of the T-theory. (shrink)

In recent years combinations of tense and modality have moved intothe focus of logical research. From a philosophical point of view, logical systems combining tense and modality are of interest because these logics have a wide field of application in original philosophical issues, for example in the theory of causation, of action, etc. But until now only methods yielding completeness results for propositional languages have been developed. In view of philosophical applications, analogous results with respect to languages of (...) predicate logic are desirable, and in this paper I present two such results. The main developments in this area can be split into two directions, differing in the question whether the ordering of time is world-independent or not. Semantically, this difference appears in the discussion whether T x W-frames or Kamp-frames (resp. Ockham-frames) provide a suitable semantics for combinations of tense and modality. Here, two calculi are presented, the first adequate with respect to Kamp-semantics, the second to T x Wsemantics. (Both calculi contain an appropriate version of Gabbay's irreflexivity rule.) Furthermore, the proposed constructions of canonical frames simplify some of those which have hitherto been discussed. (shrink)

Standard rigid designator accounts of a name’s meaning have trouble accommodating what I will call a descriptive name’s “shifty” character -- its tendency to shift its referent over time in response to a discovery that the conventional referent of that name does not satisfy the description with which that name was introduced. I offer a variant of Kripke’s historical semantic theory of how names function, a variant that can accommodate the character of descriptive names while maintaining rigidity for proper names. (...) A descriptive name’s shiftiness calls for a semantic account of names that makes their semantic values bipartite, containing both traditional semantic contents and what I call "modes of introduction." Both parts of a name's semantic value are derived from the way a name gets introduced into discourse -- from what I refer to as its "context of introduction." Making a name's semantic value bipartite in this way allows for a definite description to be a part of proper name's meaning without thereby sacrificing that name’s status as a rigid designator. On my view, a definite description is part of descriptive name’s mode of introduction. That is, it is part of what determines the content assigned to that name. As it turns out, making a definite description part of a descriptive name’s mode of introduction allows for that definite description to play the role of a mere reference-fixer regarding that name’s content, as Kripke would have it. However, my account allows a definite description to fix a descriptive name’s content actively over time, thereby explaining its inherent shiftiness. (shrink)

The semantics of tense has received a great deal of attention in the contemporary linguistics, philosophy and logic literatures. This is probably due partly to a renewed appreciation for the fact that issues involving tense touch on certain issues of philosophical importance (viz., determinism, causality, and the nature of events, of time and of change). It may also be due partly to neglect. Tense was noticeably omitted from the theories of meaning advanced in previous generations. In (...) the writings of both Russell and Frege there is the suggestion that tense would be absent altogether from an ideal or scientifically adequate language. (Tense was not the only blemish of natural language to be removed, of course, but tense is a more serious omission than, say, pronouns because it is present in every sentence of the language.) Finally, in recent years there has been a greater recognition of the important role that all of the so-called “indexical” expressions must play in an explanation of mental states and human behavior. Tense is no exception. Knowing that our friend died is cause for mourning, knowing that he dies is just another confirmation of a familiar syllogism. (shrink)

This paper is predicated on the idea that some modal operators are better understood as quantificational expressions over worlds that determine not only first-order facts but modal facts also. In what follows, we will present a framework in which these two types of facts are brought closer together. Structural features will be located in the worlds themselves. This result will be achieved by decomposing worlds into parts, where some of these parts will have “modal import” in the sense that they (...) will determine structure on other worldly parts. The main upshot of this will be a clearer grasp of the interaction between modal notions. (shrink)

Many languages allow for “fake” uses of their past tense marker: the marker: can occur in certain contexts without conveying temporal pastness. Instead it appears to bear a modal meaning. Iatridou :231–270, 2000) has dubbed this phenomenon Fake Tense. Fake Tense is particularly common to conditional constructions. This paper analyzes Fake Tense in English conditional sentences as a certain kind of ambiguity: the past tense morphology can mark the presence of a temporal operator, but it (...) can also signal a specific modal operator. The ambiguity is proposed to be the result of recategorization: the Simple Past develops a second, modal meaning because of structural similarities between the temporal and the modal/epistemic domain. The proposal is spelled out in the generative semantics framework, using the restrictor approach to conditionals Semantics from different points of view, 1979; in: A. von Stechow and D. Wunderlich Semantics: an international handbook of contemporary research, 1991), and building on von Stechows et al.’s recent work on the English tense system The expression of time in language, 2010; Romero and von Stechow, Tense: introduction, 2008). (shrink)

This study shows that the Turkish expression _hani_ exhibits interesting properties for the study of the semantics and pragmatics interface, because, on the one hand, its function is merely pragmatic, but on the other hand, it is subject to the truth-conditional effect of other constituents at LF. This notwithstanding, studies on this expression are remarkably scarce. The only attempts to describe its properties are Erguvanlı-Taylan (Studies on Turkish and Turkic languages; proceedings of the ninth international conference on Turkish linguistics, (...) 133–143, 2000 ), Akar et al. (Discourse meaning, 57–78, 2020 ), and Akar and Öztürk (Information-structural perspectives on discourse particles, 251–276, 2020 ). In the present study, we introduce the first formal semantic and pragmatic treatment of clauses containing _hani_. Unlike previous accounts, we claim that _hani_ can have one of the following two major pragmatic functions: making salient a proposition in the Common Ground or challenging one in a past Common Ground, therefore requiring a Common Ground revision. Despite its variety of occurrences, we argue that _hani_ has a uniform interpretation and provide a compositional analysis of the different construals that it is associated with. Furthermore, we show that a formally explicit and accurate characterization of _hani_ clauses requires operating on indexical parameters, in particular the context time. Therefore, if our proposal is on the right track, _hani_ clauses may provide indirect empirical evidence in favour of the existence of “monstrous” phenomena, adding to the accumulating cross-linguistic evidence in this domain (see Schlenker in Linguistics and Philosophy 26(1):29–120, 2003 and much work since then). The definition of monsters is intended as in Kaplan (Themes from Kaplan, 481–563, 1989 ). (shrink)

This paper investigates the semantics of tense and aspect in Romance languages. Its goal is to develop a compositional, model-theoretic semantics for tense and temporal adverbs which is sensitive to aspectual distinctions. I will consider durative adverbial distributions and aspectual contrasts across different morphological tense forms. I will examine tense selection under habitual meanings, generic meanings and state of result constructions. In order to account for these facts I will argue that temporal homogeneity plays (...) a fundamental role in tense selection in Romance languages. (shrink)

The author's motivation for constructing the calculi of this paper\nis so that time and tense can be "discussed together in the same\nlanguage" (p. 282). Two types of enriched propositional caluli for\ntense logic are considered, both containing ordinary propositional\nvariables for which any proposition may be substituted. One type\nalso contains "clock-propositional" variables, a,b,c, etc., for\nwhich only clock-propositional variables may be substituted and that\ncorrespond to instants or moments in the semantics. The other type\nalso contains "history-propositional" variables, u,v,w, etc., for\nwhich only history-propositional (...) variables may be substituted and\nthat correspond to maximally linearly ordered subsets of instants.\nThis second type is for tense logics in which time is not linear\nand where at any moment there may exist alternative future courses\nof events. Quantifiers are included in both types but only for clock-\nand history-propositional variables. However, these quantifiers are\ngiven an essentially substitutional interpretation. In addition,\nbesides each clock-propositional variable being true at exactly one\ninstant, the semantics requires that for each instant there be at\nleast one clock-propositional variable true at that instant, which\nin effect amounts to having each instant of the model "denoted" in\nthe formalism by some clock-propositional variable. Thus it is not\nsurprising that quantification over clock-propositional variables\nturns out to have a "well behaved first-order semantics" (p. 284).\n{One axiom relating history- with clock-propositions seems to need\nrevision: CKTauTbuAUabUba. Since the clock-propositional variables\nmight be true at the same instant the consequent should include an\nalternative, namely, LCab.} Besides the standard truth-functional\nand tense operators G,H,F,P, the author includes L for "it is\nalways the case that". The model-theoretic earlier-than relation\nordering instants and the semantic truth-at (an instant) relation\nare formalized by Uab and Taα (for a wff α) which\nare defined respectively as LCbPa (whenever the clock-proposition\nb is the case the clock-proposition a was the case) and LCaα\n(α is the case whenever the clock-proposition a is the case).\nBecause the future tense operators are definable in terms of U\nand T and the latter are definable in terms of L and P, the\ndual of H, the author notes that his completeness proofs can be\nrestricted to L and H as primitive and with the future tense\noperators used for other interpretations, especially Prior, A.'s\nindeterminist "it will be the case that", where time is not linear.\nThe author concludes with some rather technical observations showing\nthat "in ordinary tense logics the instants are nonstandard elements\nof the models. This provides", according to the author, "a semantic\npressure to build the instants into tense logic, so that they will\nappear as standard elements in the models" (p. 283). (shrink)

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking (...) about partitions of general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. (shrink)

We take the well-known intuitionistic modal logic of Fischer Servi with semantics in bi-relational Kripke frames, and give the natural extension to topological Kripke frames. Fischer Servi’s two interaction conditions relating the intuitionistic pre-order with the modal accessibility relation generalize to the requirement that the relation and its inverse be lower semi-continuous with respect to the topology. We then investigate the notion of topological bisimulation relations between topological Kripke frames, as introduced by Aiello and van Benthem, and show that (...) their topology-preserving conditions are equivalent to the properties that the inverse relation and the relation are lower semi-continuous with respect to the topologies on the two models. The first main result is that this notion of topological bisimulation yields semantic preservation w.r.t. topological Kripke models for both intuitionistic tense logics, and for their classical companion multi-modal logics in the setting of the Gödel translation. After giving canonical topological Kripke models for the Hilbert-style axiomatizations of the Fischer Servi logic and its classical companion logic, we use the canonical model in a second main result to characterize a Hennessy–Milner class of topological models between any pair of which there is a maximal topological bisimulation that preserve the intuitionistic semantics. (shrink)

The essays in this collection are the outgrowth of a workshop, held in June 1976, on formal approaches to the semantics and pragmatics of natural languages. They document in an astoundingly uniform way the develop ments in the formal analysis of natural languages since the late sixties. The avowed aim of the' workshop was in fact to assess the progress made in the application of formal methods to semantics, to confront different approaches to essentially the same problems on (...) the one hand, and, on the other, to show the way in relating semantic and pragmatic explanations of linguistic phenomena. Several of these papers can in fact be regarded as attempts to close the 'semiotic circle' by bringing together the syntactic, semantic and pragmatic properties of certain constructions in an explanatory framework thereby making it more than obvious that these three components of an integrated linguistic theory cannot be as neatly separated as one would have liked to believe. In other words, not only can we not elaborate a syntactic description of (a fragment of) a language and then proceed to the semantics (as Montague pointed out already forcefully in 1968), we cannot hope to achieve an adequate integrated syntax and semantics without paying heed to the pragmatic aspects of the constructions involved. The behavior of polarity items, 'quantifiers' like any, conditionals or even logical particles like and and or in non-indicative sentences is clear-cut evidence for the need to let each component of the grammar inform the other. (shrink)

In this article I defend the view that many central aspects of the semantics of tense are determined by independently-motivated principles of syntactic theory. I begin by decomposing tenses syntactically into a temporal ordering predicate (the true tense, on this approach) and two time-denoting arguments corresponding to covert a reference time (RT) argument and an eventuality time (ET) argument containing the verb phrase. Control theory accounts for the denotation of the RT argument, deriving the distinction between main (...) clause and subordinate clause tenses. The theory of covert movement is used to account for the independent/indexical interpretation of relative clause tenses, and for the correlation between independent tense interpretation and a de re construal of the relative clause. A theory of “past polarity”, based on traditional negative polarity theory, accounts both for the simultaneous “sequence of tense” construal of past tenses in subordinate clauses embedded within past tense contexts, and for the obligatory indexical/independent interpretation of present tense in a relative clause embedded within a past tense context. Combined with the copy theory of movement, the polarity theory also provides an account of the semantics of double access sentences, treating them as involving a special kind of reconstruction effect. (shrink)

In chapter 1, I begin the task of giving a semantical theory which is appropriate for the general indeterministic context and which can profitably be applied to the special context of quantum mechanics. I treat the notion of indeterminism, and discuss tree structures. In the second chapter, I consider several theories of tense meant for the indeterministic context. All presuppose tree structures. I defend one of these as the best rendering of simple English future tense. ;In the third (...) chapter, I begin discussing counterfactual conditionals. It is the burden of this chapter to show that one well known analysis of counterfactuals, Stalnaker's theory, is not appropriate for the context of quantum mechanics. I show that his analysis leads all too easily to a contradiction of experimental evidence. Stalnaker's analysis--like many theories of counterfactuals--is based on the relation of comparative similarity between worlds. Recently this basis has been questioned. In chapter 4, I step back a bit from the project of analyzing counterfactuals and consider the foundations for any such analysis. I first argue that the similarity approach is still a promising one. But I go on to argue that a similarity approach requires a non-ordinary notion of 'similarity'. So 'similarity' is in need of explication. This, I argue, is something that should be done on a piecemeal basis. ;In the fifth chapter, I attempt to unify the results of earlier chapters by relating them to the quantum mechanical context. I begin by defending an analysis of counterfactuals which is given in terms of similarity between worlds. I try to show that this theory is a natural one for the quantum mechanical context. And I discuss how, for purposes of the analysis of counterfactuals, 'similarity' is to be understood in the quantum mechanical context. Also, I consider the logical form of quantum mechanical attribution of probability. These attributions, I argue, involve counterfactuals and tense in interesting ways. Utilizing the results of chapters 1 and 2, I argue for a somewhat novel rendering of these quantum mechanical attributions. (shrink)

The revolution in semantics in the late 1960s and 1970s overturned an earlier competing paradigm, ‘translational’ semantics. I revive and defend Prior’s translational semantics for modals and tense-modals. I also show how to extend Prior’s propositional modal semantics to quantificational modal logic, and use the resulting semantics to formalize Prior’s own counterexample to the Barcan Formula.

A remarkable thing about natural language is that we can use it to share our beliefs and thoughts about the world with other speakers of our language. In cases of successful communication, beliefs seem to be transferred from speakers to hearers by means of the hearer recovering the contents of the speaker’s utterances. This is so natural to us that we take it for granted in our everyday life, and rarely stop to think about how it's is possible. Nevertheless, it's (...) a phenomenon that calls for explanation. It is natural to expect that natural language semantics has a key explanatory role to play here. In order to understand this role, we must relate the semantic values assigned to sentences by semantic theory with the content of our speech acts. The simplest possible relation would be identity; the meaning of a sentence is simply the belief expressed by an assertion of the sentence in a given context of utterance. However, a number of problem cases in the literature suggest that this cannot be the case. This dissertation offers a critical assessment of the arguments for distinguishing the semantic value of a sentence from it's so called assertoric content, focusing on problems arising from the analysis of tense and temporal expressions. I conclude that they are indeed distinct, and offer a constructive account of how they must be related in order to allow for an explanation of communicative success. (shrink)

The forward convergence constraint is important to time analysis. Without it, given two future moments to the same point, the time branches. This is unacceptable if one assumes that time is linear. Nevertheless, one may wish to consider time-branching in order to discuss future possibilities. One can have both a linear order for the time and branching through the combination of the tense logic semantics with those of an alethic logic which allows the evaluation of the timelines of (...) other possible worlds. In this paper, I give the semantics and the tableaux systems for some alethic-tense logics. I review one in which worlds differ on their time orders, another in which they agree on the time order, a pair of conditional tense logics ), and the first-order version of MT. A brief philosophical discussion arises from every system. (shrink)

We propose a new intensional semantics for modal-tense second-order languages with sortal predicates. The semantics provides a variable-domain interpretation of the second-order quantifiers. A formal logical system is characterized and proved to be sound and complete with respect to the semantics. A contemporary variant of conceptualism as a theory of universals is the philosophical background of the semantics. Justification for the variable-domain interpretation of the second-order quantifiers presupposes such a conceptualist framework.

This is not your typical book about the A-theory/B-theory controversy in metaphysics. Peter Ludlow attempts something that few philosophers have tried in the last thirty years: he actually argues from linguistic premises for metaphysical conclusions. The relevant linguistic premises have to do with the nature of language, a general theory of semantics, the proper analysis of tense, and various technical theses involving the treatment of temporal indexicals and temporal anaphora. The metaphysical conclusions that Ludlow argues for from these (...) linguistic premises are some of the main claims normally associated with the A-theory in the philosophy of time, namely, that tense is a genuine feature of the world – and that the instantiation of these properties does not somehow reduce to the instantiation of two-place, temporal relations like earlier than, simultaneous with, later than, etc.), that temporal becoming is intrinsic to all events, and that only the present is real. The overall plan of the book is as follows. First Ludlow spends four chapters defending a cluster of related claims about language and semantics in general and, in particular, the semantics for temporal indexicals and temporal anaphora. (Ludlow says that none of this material is original – he attributes most of it to Davidson, Chomsky, Evans, and Higginbotham – but it seems to me that a fair portion of what goes into this part of the book (including, especially. (shrink)

An introductory text in linguistic semantics, uniquely balancing empirical coverage and formalism with development of intuition and methodology. -/- This introductory textbook in linguistic semantics for undergraduates features a unique balance between empirical coverage and formalism on the one hand and development of intuition and methodology on the other. It will equip students to form intuitions about a set of data, explain how well an analysis of the data accords with their intuitions, and extend the analysis or seek (...) an alternative. No prior knowledge of linguistics is required. After mastering the material, students will be able to tackle some of the most difficult questions in the field even if they have never taken a linguistics course before. -/- After introducing such concepts as truth conditions and compositionality, the book presents a basic symbolic logic with negation, conjunction, and generalized quantifiers, to serve as the basis for translation throughout the book. It then develops a detailed compositional semantics, covering quantification (scope and binding), adverbial modification, relative clauses, event semantics, tense and aspect, as well as pragmatic phenomena, notably deictic pronouns and narrative progression. -/- A Course in Semantics offers a large and diverse set of exercises, interspersed throughout the text; those labeled “Important practice and looking ahead” prepare students for material to come; those labeled “Thinking about ” invite students to think beyond the content of the book. (shrink)

The article discusses Nicholas Wolterstorff’s explanations for the flourishing of philosophical theology in analytic philosophy by taking Arthur Norman Prior’s (1914–1969) development of tense-logic into account. Prior’s work challenged the prevailing anti-metaphysical norms in analytic philosophy and introduced an alternative understanding of the relationship between logic and metaphysics. Prior’s application of tense-logic to an analysis of the concept of existence in quantified tense-logic and his exploration of future contingency in branching time semantics provide a strong reason (...) for why analytic philosophy naturally incorporates philosophical theology. These considerations lead us to modify Wolterstorff’s emphasis on the importance of meta-epistemology for the resurgence of philosophical theology. A development in logic was necessary. Furthermore, Prior’s importance questions the assumption that philosophical theology was a consequence of theistic philosophers seeking ways to defend theistic beliefs in analytic philosophy. This is not true for Prior. His invention of tense-logic and discussion of omniscience was driven by an existential interest in finding answers to philosophical problems concerning divine foreknowledge and human freedom which ultimately led him to reject his Christian beliefs. (shrink)

Based on the results of [11] this paper delivers uniform algorithms for deciding whether a finitely axiomatizable tense logic has the finite model property, is complete with respect to Kripke semantics, is strongly complete with respect to Kripke semantics, is d-persistent, is r-persistent.It is also proved that a tense logic is strongly complete iff the corresponding variety of bimodal algebras is complex, and that a tense logic is d-persistent iff it is complete and its Kripke (...) frames form a first order definable class. From this we obtain many natural non-d-persistent tense logics whose corresponding varieties of bimodal algebras are complex. (shrink)

The chapter considers two semantic issues concerning will-sentences: Stalnaker’s Asymmetry and modal subordination in Karttunen-type discourses. The former points to a distinction between will and modal verbs, seeming to show that will does not license non-specific indefinites. The latter, conversely, suggests that will-sentences involve some kind of modality. To account for the data, the chapter proposes that will is semantically a tense, hence it doesn’t contribute a quantifier over modal alternatives; a modal feature, however, is introduced in the interpretation (...) of a will-sentence through a supervaluational strategy universally quantifying over possible futures. That this is not part of will’s lexical semantics is shown to have consequences that ultimately contribute to explain Stalnaker’s Asymmetry. Furthermore, that a modal quantification is present in the interpretation of a will-sentence is shown to imply the availability of modal subordination in Karttunen-type discourses. (shrink)

Natural languages exhibit a great variety of grammatical paradigms. For instance, in English verbs are grammatically marked for tense, whereas in the tenseless Eskimo-Aleut language Kalaallisut they are marked for illocutionary mood. Although time is a universal dimension of the human experience and speaking is part of that experience, some languages encode reference to time without any grammatical tense morphology, or reference to speech acts without any illocutionary mood morphology. Nevertheless, different grammatical systems are semantically parallel in certain (...) respects. Specifically, I propose that English tenses form a temporal centering system, which monitors and updates topic times, whereas Kalaallisut moods form a modal centering system, which monitors and updates modal discourse referents. To formalize these centering parallels I define a dynamic logic that represents not only changing information but also changing focus of attention in discourse (Update with Centering, formalizing Grosz et al 1995). Different languages can be translated into this typed logic by directly compositional universal rules of Combinatory Categorial Grammar (CCG) The resulting centering theory of tense and illocutionary mood draws semantic parallels across different grammatical systems. The centering generalizations span the extremes of the typological spectrum, so they are likely to be universal. In addition, the theory accounts for the translation equivalence of tense and illocutionary mood in a given utterance context. Following Stalnaker (1978) I assume that the very act of speaking up has a ‘commonplace effect’ on the context. It focuses attention on the speech act and thereby introduces default modal and temporal topics. These universal defaults complement language-specific grammars, e.g. English tenses and Kalaallisut moods. In a given utterance context the universal discourse-initial defaults plus language-specific grammatical marking may add up to the same truth conditions.. (shrink)

One of the difficult areas for persons learning a foreign language is to grasp the range of usages of syntactic patterns that exist in the foreign language. It is not sufficient to learn how passive formation works, or how pre- or postpositional phrases are constructed, or how perfect tenses are expressed. One also has to learn which verbs can passivize at all, which verbs go with which pre- or postpositions, and, in case perfect tenses are expressed, as in a number (...) of European languages, with different auxiliaries like ‘have’ and ‘be’, which verb needs which auxiliary. For English, Levin (1993) distinguishes no less than 57 verb classes, most of them with a number of subclasses, that show distinct syntactic behavior. (shrink)

This paper is concerned with uses of certain morphemes, most notably the past, to represent meanings of distance from reality in modal expressions. This class of morphology has been identified with the names subjunctive, fake tense, fake past, modal past and is referred to here as X-marking, after von Fintel and Iatridou (Linguist Philos, 2020). X-marking has been most studied in the context of English conditionals however, it is well-known that the morphology is observed in many non-English languages and (...) can appear in various other types of constructions, including counterfactual desire expressions. I motivate two desiderata for theories of X-marking in pursuit of an analysis that unifies the phenomenon across expression types and languages. I then develop a novel, formally explicit analysis of X-marking which I show to satisfy these desiderata while providing greater empirical coverage of well-known cases compared to existing accounts. The proposed analysis makes use of modal presupposition projection together with pragmatic inference via Maximize Presupposition to provide a unified treatment of X-marking in English conditionals and counterfactual desires expressions of English featuring wish. I show how previous proposals for X-marking cannot satisfy these desiderata, making them insufficient for a unified account. Lastly, I introduce a hypothesis that all varieties of morphology that can be used as X-marking cross-linguistically-including past, imperfective, plural and habitual-are vacuous in both their X-marked and ordinary uses. (shrink)

It is argued that the assignment of truth values to future contingents is threatened not by a tensed metaphysics but by a temporally “local” notion of truth, i.e., by the assumption that whatever is true at a given time needs to be grounded in what exists at that time. If this assumption is accepted, tensed and tenseless metaphysics are equally vulnerable; if it is rejected, both can accommodate true future contingents. This means that semantic decisions are largely independent of metaphysical (...) considerations. The work of Correia and Rosenkranz (2018) is a clear example of how the tensed metaphysics of the growing block can incorporate true future contingents. Two potential worries are discussed in the context of their work: (a) that their grounding strategy overgeneralizes and admits true counterfactual contingents; and (b) that the growing block theory lacks sufficient resources to distinguish the unique possible future course of events that is relevant for the grounding of future contingents. (shrink)

An essential part of natural language understanding, and hence of formal semantics, is the interpretation of temporal expressions. But the very variety of temporal phenomena---such as tense, aspect, aktionsart, temporal adverbials, and the temporal structure of extended text---has tended to result in formal semantic analyses using a wide variety of formal tools, often of a complex nature. It seems important to try and find unifying perspectives on this work, and above all, to try and gain some insight into (...) the logical resources needed to deal with natural language temporal phenomena. (shrink)

This book is an examination of the foundations and applications of the program of truth-theoretic semantics for natural languages introduced in 1967 by Donald Davidson in his classic paper “Truth and Meaning.” This is the second of two books on Donald Davidson’s central philosophical project. The first, Donald Davidson: Meaning, Truth, Language and Reality (Oxford: Oxford University Press, 2005), dealt with the basic framework of Davidson’s truth-theoretic approach to providing a meaning theory for a natural language, and then with (...) his development of his general project in the philosophy of language and theory of meaning by way of the analysis of the empirical confirmation of a meaning theory for a speaker, from the stance of the radial interpreter, that is, the interpreter who starts out without any detailed knowledge of the speakers’ meanings or attitudes. This book turns to the development of details of Davidson’s semantic program, specifically, the pursuit of the project of providing a compositional semantic theory for natural languages by making strategic use of an appropriately adapted Tarski-style axiomatic truth theory. Such a theory aims to provide a specification of the truth conditions of any felicitous utterance of a natural language sentence which serves to interpret it, and exhibits in the proof of the theorem that gives the truth conditions the compositional structure of the sentence and how its truth depends on its context of utterance. The book develops the basic framework, applies it to quantifiers, proper names, indexicals, simple and complex demonstratives, quotation, adjectives and adverbs, simple tenses of state and event verbs, temporal adverbs and quantifiers, tense in sentential complements and perfect tenses, opaque contexts, especially indirect discourse and attitude sentences, non-declarative sentences, semantic structure and logical form, and discusses the relation of the framework the metaphysics of truth. (shrink)

Paraguayan Guarani does not overtly mark tense in its inflectional system. Prior accounts of languages without obligatory morphological tense have posited a phonologically covert lexical tense, or have introduced tense semantics via a rule, in the post-syntactic interpretative component. We offer a more radical approach: Paraguayan Guarani does not have tense at the level of lexical or logical semantics. We propose that evaluation time shift, a mechanism independently attested in the narrative present in (...) languages with tense, is more widely used in Paraguayan Guarani for encoding temporal meaning. The broader consequence of our proposal is that tense is not a linguistic universal. (shrink)

We consider a formal language whose logical syntax involves both modal and tense propositional operators, as well as sortal quantifiers, sortal identities and (second order) quantifiers over sortals. We construct an intensional semantics for the language and characterize a formal logical system which we prove to be sound and complete with respect to the semantics. Conceptualism is the philosophical background of the semantic system.

This book argues that the verbal aspect of the Greek Perfect is complex, involving not one but two aspects, where the perfective applies to events and the imperfective applies to states. These two aspects are connected to specific morphemes in the Perfect tense-form. This study analyses Perfect tense-forms in discursive text by focusing on the Pauline Corpus. The method is grounded in grammaticalisation studies and informed by morphology, comparative linguistics, and historical linguistics. The argument is further supported by (...) a corpus-based study showing both the Greek Perfect tense-form use in letters over an 800-year period and adverb collocations of the Perfect tense-form. The adverb collocations establish when a Perfect is used for an event or for a state. This study challenges other verbal aspect studies that find only one verbal aspect to explain the Greek Perfect. This study situates the Pauline Perfect tense-form usage within a spectrum of other letter writers, and finds that within the Pauline Corpus the Perfects within supplemental clauses are more likely to use active lexemes than other letter writers. This study also finds that most of the Perfects used in letters are supplemental to the mainline and are often backgrounded rather than foregrounded. (shrink)

According to the actualist view, what is essential to the truth conditions of a future-tensed sentence ‘it will be the case that ϕ’ is reference to the unique course of events that will become actual. On the other hand, the modal view has it that the truth conditions of such a sentence require that the truth of ϕ be already “settled” at the time of utterance, where “being settled at time t” is defined by universal quantification over a domain of (...) courses of events, the futures compatible with what has happened up to time t. On the proposal we discuss in this paper, the actualist view and the modal view are seen as two related attitudes that speakers can have when they evaluate future-tensed sentences, and the corresponding interpretations undergo a unified semantic treatment based on a contextual notion of settledness. A central feature of our approach is a dynamic view of contexts of utterance, whereby the world of the utterance is not fixed once and for all, as different worlds, by the passing of time, can play this role in turn. Finally, one major goal of the paper is to show how the unified analysis we propose accounts for a particularly interesting interpretation of future-tensed sentences, often referred to as ‘epistemic reading’. (shrink)

In this chapter I argue that there can be no mental representation of objective ‘tensed’ features of reality of the kind that might be thought to occur when we experience time passing or think of times as past, present or future, whether or not such features are part of mind-independent reality. This, I hold, has important consequences for metaphysics; but (as will be most relevant to this volume) it is also likely to have important consequences for a correct semantics (...) for tense. In a nutshell, no correct semantics for tense can treat what philosophers call ‘A-properties’ (such as real pastness, presentness or futurity) as semantic values. (shrink)

This paper contributes to the debate about ‘tenseless languages’ by defending a tensed analysis of a superficially tenseless language. The language investigated is St’át’imcets (Lillooet Salish). I argue that although St’át’imcets lacks overt tense morphology, every finite clause in the language possesses a phonologically covert tense morpheme; this tense morpheme restricts the reference time to being non-future. Future interpretations, as well as ‘past future’ would-readings, are obtained by the combination of covert tense with an operator analogous (...) to Abusch’s (1985) WOLL. I offer St’át’imcets-internal evidence (of a kind not previously adduced) that the WOLL-like operator is modal in nature. It follows from the analysis presented here that there are only two (probably related) differences between St’át’imcets and English in the area of tense. The first is that St’át’imcets lacks tense morphemes which are pronounced. The second is that the St’át’imcets tense morpheme is semantically underspecified compared to English ones. In each of these respects, the St’át’imcets tense morpheme displays similar properties to pronouns, which may be covert and which may fail to distinguish person, number or gender. Along the way, I point out several striking and subtle similarities in the interpretive possibilities of St’át’imcets and English. I suggest that these similarities may reveal non-accidental properties of tense systems in natural language. I conclude with discussion of the implications of the analysis for cross-linguistic variation, learnability and the possible existence of tenseless languages. (shrink)

At the centre of Arthur Prior’s ‘Thank goodness’ argument for the A-theory of time is a particular form of relief. Time must objectively pass, Prior argues, or else the relief felt when a painful experience has ended is not intelligible. In this paper, I offer a detailed analysis of the type of relief at issue in this argument, which I call temporal relief, and distinguish it from another form of relief, which I refer to as counterfactual relief. I also argue (...) that existing discussions of the ‘Thank goodness’ argument—including Prior’s own—fail to give a satisfactory account of temporal relief, and that it needs to be seen as an emotion linked to the ability to engage in fairly sophisticated forms of planning. I also suggest that this has an impact on Prior’s claim that the idea of points in time plays no fundamental role in the semantic analysis of tenses. (shrink)

The syntactic domain of tense is the clause: tense appears in some form in every clause of a tensed language. Semantic interpretation of tense requires information from context, however. This has been clear at least since Partee's 1984 demonstration of the anaphoric properties of tense. In this talk I will show that the facts about context are quite complex, perhaps more so than has been appreciated. There are three patterns of tense interpretation, depending on the (...) type of discourse context in which a clause appears. I will introduce the notion of discourse mode to account for the different types of context.1 I offer an interpretation of tense in Discourse Representation Theory, a framework which is organized to deal with information from the context. I also show that a syntactically based theory can handle contextually-based tense interpretation. In §1 I set out the basic analysis of tense and show how it applies to sentences in isolation. §2 discusses types of discourse context and patterns of tense interpretation; §3 considers the formal analysis of tense; §4 concludes with a summary and a prediction about temporal interpretation in tenseless languages. (shrink)