Visual experience is often characterised as being essentially spatial, and auditory experience essentially temporal. But this contrast, which is based upon the temporal structure of the objects of sensory experience rather than the experiences to which they give rise, is somewhat superficial. By carefully examining the various sources of temporal variation in the chemical senses we can more clearly identify the temporal profile of the resulting smell and taste (aka flavour) experiences. This in turn suggests (...) that at least some of the objects of olfactory experience have significant temporal structure, including interactions between odorants and the body’s own sensory systems. This can help to inform our understanding not only of the metaphysics of olfaction, but the temporal structure of sensory processing and experience in other sense-modalities, including vision and audition. (shrink)

Temporal logic arose at the border of philosophy and linguistics. From the seventies onward, it because a major tool also in computer science and artificial intelligence, which have turned into the most powerful source of new logical developments since. We discuss some recent themes demonstrating new connections with modal logic. In the course of this, we also point out some new types of open research questions.

In the 4th century BC, the Greek philosopher Diodoros Chronos gave a temporal definition of necessity. Because it connects modality and temporality, this definition is of interest to philosophers working within branching time or branching space-time models. This definition of necessity can be formalized and treated within a logical framework. We give a survey of the several known modal and temporal logics of abstract space-time structures based on the real numbers and the integers, considering three different accessibility (...) relations between spatio-temporal points. (shrink)

In this paper the structure of pretemporal algebra is used to study some aspects of temporal algebras and modal algebras. The paper contains a computational approach to finite temporal algebras and a general splitting theorem for finite temporal algebras.

van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic ( ETL : Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic ( DEL : Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged semantic framework, and its (...) extension with the labeled past-operator “ P ϵ ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc. (shrink)

Face recognition is impaired in patients with prosopagnosia, which may occur as a side effect of neurosurgical procedures. Face selective regions on the ventral temporal cortex have been localized with electrical cortical stimulation, electrocorticography, and functional magnetic resonance imagining. This is the first group study using within-patient comparisons to validate face selective regions mapping, utilizing the aforementioned modalities. Five patients underwent surgical treatment of intractable epilepsy and joined the study. Subdural grid electrodes were implanted on their ventral temporal (...) cortices to localize seizure foci and face selective regions as part of the functional mapping protocol. Face selective regions were identified in all patients with fMRI, four patients with ECoG, and two patients with ECS. From 177 tested electrode locations in the region of interest, which is defined by the fusiform gyrus and the inferior temporal gyrus, 54 face locations were identified by at least one modality in all patients. fMRI mapping showed the highest detection rate, revealing 70.4% for face selective locations, whereas ECoG and ECS identified 64.8 and 31.5%, respectively. Thus, 28 face locations were co-localized by at least two modalities, with detection rates of 89.3% for fMRI, 85.7% for ECoG and 53.6 % for ECS. All five patients had no face recognition deficits after surgery, even though five of the face selective locations, one obtained by ECoG and the other four by fMRI, were within 10 mm to the resected volumes. Moreover, fMRI included a quite large volume artifact on the ventral temporal cortex in the ROI from the anatomical structures of the temporal base. In conclusion, ECS was not sensitive in several patients, whereas ECoG and fMRI even showed activation within 10 mm to the resected volumes. Considering the potential signal drop-out in fMRI makes ECoG the most reliable tool to identify face selective locations in this study. A multimodal approach can improve the specificity of ECoG and fMRI, while simultaneously minimizing the number of required ECS sessions. Hence, all modalities should be considered in a clinical mapping protocol entailing combined results of co-localized face selective locations. (shrink)

In this paper an algebraic version for temporal algebras of the logical filtrations for modal and temporal logics is analysed. A structure theorem for free temporal algebras and also some results with regard to the variety of temporal algebras are obtained.

This thesis develops a theory about the structure of modal judgment and knowledge. Arguing in favour of pluralism about the source of modal knowledge, it focuses on the questions of the varieties of modal judgment and their relations, the function of modal judgment and the scope of modal knowledge. It offers a hypothesis about the development of the framework of modal knowledge, grounding it on the capacity to evaluate temporal judgments, from which (...) the capacity to evaluate alternatives comes from, and it suggests that the most basic framework of modal judgments consists in that of agentive modality, and in particular, about what one can do, and how. Then, it is argued that the rest of the framework of modal judgment can be developed on this basis, although this imposes certain restrictions about the scope of modal knowledge. Additionally, the thesis provides analyses of various agentive modal notions, such as imaginability, what is a way to do something, and discusses how to understand counterfactuals with impossible antecedents. (shrink)

The traditional Dung networks depict arguments as atomic and study the relationships of attack between them. This can be generalised in two ways. One is to consider various forms of attack, support, feedback, etc. Another is to add content to nodes and put there not just atomic arguments but more structure, e.g. proofs in some logic or simply just formulas from a richer language. This paper offers to use temporal and modal language formulas to represent arguments in (...) the nodes of a network. The suitable semantics for such networks is Kripke semantics. We also introduce a new key concept of usability of an argument. This is the beginning of a continuing research for adding contents to the nodes of an argumentation network. This research will allow us to address notions like ?what does it exactly mean for a node to attack another? or ?what does it mean for a network to be consistent? or ?can we give proper proof rules to manipulate networks?, and more. (shrink)

In previous works, we presented a modification of the usual possible world semantics by introducing an independent temporal structure in each world and using accessibility functions to represent the relation among them. Different properties ofthe accessibility functions have been considered and axiomatic systems which define these properties have been given. Only a few ofthese systems have been proved tobe complete. The aim ofthis paper is to make a progress in the study ofcompleteness for functional systems. For this end, (...) we use indexes as names for temporal flows and give new proofs of completeness. Specifically, we focus our attention on the system which defines injectivity, because the system which defines this property without using indexes was proved to be incomplete in previous works. The only system considered which remains incomplete is the one which defines surjectivity, even ifwe consider a sequence ofnatural extensions ofthe previous one. (shrink)

The temporal structure of behavior contains a rich source of information about its dynamic organization, origins, and development. Today, advances in sensing and data storage allow researchers to collect multiple dimensions of behavioral data at a fine temporal scale both in and out of the laboratory, leading to the curation of massive multimodal corpora of behavior. However, along with these new opportunities come new challenges. Theories are often underspecified as to the exact nature of these unfolding interactions, (...) and psychologists have limited ready-to-use methods and training for quantifying structures and patterns in behavioral time series. In this paper, we will introduce four techniques to interpret and analyze high-density multi-modal behavior data, namely, to: (1) visualize the raw time series, (2) describe the overall distributional structure of temporal events (Burstiness calculation), (3) characterize the nonlinear dynamics over multiple timescales with Chromatic and Anisotropic Cross-Recurrence Quantification Analysis (CRQA), (4) and quantify the directional relations among a set of interdependent multimodal behavioral variables with Granger Causality. Each technique is introduced in a module with conceptual background, sample data drawn from empirical studies and ready-to-use Matlab scripts. The code modules showcase each technique’s application with detailed documentation to allow more advanced users to adapt them to their own datasets. Additionally, to make our modules more accessible to beginner programmers, we provide a “Programming Basics” module that introduces common functions for working with behavioral timeseries data in Matlab. Together, the materials provide a practical introduction to a range of analyses that psychologists can use to discover temporal structure in high-density behavioral data. (shrink)

Natural language involves both speaking and listening. Recent models claim that production and comprehension share aspects of processing and are linked within individuals (Dell & Chang, 2014; MacDonald, 2013; Pickering & Garrod, 2004; 2013a). Evidence for this claim has come from studies of cross-modality structural priming, mainly examining processing in the direction of comprehension to production. The current study replicated these comprehension to production findings and developed a novel cross-modal structural priming paradigm from production to comprehension using a temporally-sensitive (...) online measure of comprehension, Event-Related Potentials. For Comprehension-to-Production priming, participants first listened to active or passive sentences and then described target pictures using either structure. In Production-to-Comprehension priming, participants first described a picture using either structure and then listened to target passive sentences while EEG was recorded. Comprehension-to-Production priming showed the expected passive sentence priming for syntactic choice, but not response time or average syllable duration. In Production-to-Comprehension priming, primed, versus unprimed, passive sentences elicited a reduced N400. These effects support the notion that production and comprehension share aspects of processing and are linked within the individual. Moreover, this paradigm can be used for the exploration priming at different linguistic levels as well as the influence of extra-linguistic factors on natural language use. (shrink)

For humans, the ability to communicate and use language is instantiated not only in the vocal modality but also in the visual modality. The main examples of this are sign languages and gestures. Sign languages, the natural languages of Deaf communities, use systematic and conventionalized movements of the hands, face, and body for linguistic expression. Co-speech gestures, though non-linguistic, are produced in tight semantic and temporal integration with speech and constitute an integral part of language together with speech. The (...) articles in this issue explore and document how gestures and sign languages are similar or different and how communicative expression in the visual modality can change from being gestural to grammatical in nature through processes of conventionalization. As such, this issue contributes to our understanding of how the visual modality shapes language and the emergence of linguistic structure in newly developing systems. Studying the relationship between signs and gestures provides a new window onto the human ability to recruit multiple levels of representation in the service of using or creating conventionalized communicative systems. (shrink)

Temporal logic of causal knowledge over general partially ordered structures of local states is defined. The definition of knowledge captures the change of state due to action executions. The structures are a variant of flow event structures including prime event structures and branching processes of Petri Nets. Modalities corresponding to the causality, concurrency, and indistinguishability relations are used. Formulas are interpreted over local state occurrences. The logic is proved to be decidable and a complete axiomatization is provided.

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)

In this paper, we study temporal logic for finite linear structures and surjective bounded morphisms between them. We give a characterisation of such structures by modal formulas and show that every pair of linear structures with a bounded morphism between them can be uniquely characterised by a temporal formula up to an isomorphism. As the main result, we prove Kripke completeness of the logic with respect to the class of finite linear structures with bounded morphisms between them.

Previous research on linguistic relativity and economic decisions hypothesized that speakers of languages with obligatory tense marking of future time reference (FTR) should value future rewards less than speakers of languages which permit present tense FTR. This was hypothesized on the basis of obligatory linguistic marking (e.g., will) causing speakers to construe future events as more temporally distal and thereby to exhibit increased “temporal discounting”: the subjective devaluation of outcomes as the delay until they will occur increases. However, several (...) aspects of this hypothesis are incomplete. First, it overlooks the role of “modal” FTR structures which encode notions about the likelihood of future outcomes (e.g., might). This may influence “probability discounting”: the subjective devaluation of outcomes as the probability of their occurrence decreases. Second, the extent to which linguistic structures are subjectively related to temporal or probability discounting differences is currently unknown. To address these, we elicited FTR language and subjective ratings of temporal distance and probability from speakers of English, which exhibits strongly grammaticized FTR, and Dutch, which does not. Several findings went against the predictions of the previous hypothesis: Framing an FTR statement in the present (“Ellie arrives later on”) versus the future tense (“…will arrive…”) did not affect ratings of temporal distance; English speakers rated future statements as relatively more temporally proximal than Dutch speakers; and English and Dutch speakers rated future tenses as encoding high certainty, which suggests that obligatory future tense marking might result in less discounting. Additionally, compared with Dutch speakers, English speakers used more low-certainty terms in general (e.g., may) and as a function of various experimental factors. We conclude that the prior cross-linguistic observations of the link between FTR and psychological discounting may be caused by the connection between low-certainty modal structures and probability discounting, rather than future tense and temporality. (shrink)

This paper adds temporal logic to public announcement logic (PAL) and dynamic epistemic logic (DEL). By adding a previous-time operator to PAL, we express in the language statements concerning the muddy children puzzle and sum and product. We also express a true statement that an agent’s beliefs about another agent’s knowledge flipped twice, and use a sound proof system to prove this statement. Adding a next-time operator to PAL, we provide formulas that express that belief revision does not take (...) place in PAL. We also discuss relationships between announcements and the new knowledge agents thus acquire; such relationships are related to learning and to Fitch’s paradox. We also show how inverse programs and hybrid logic each can be used to help determine whether or not an arbitrary structure represents the play of a game. We then add a past-time operator to DEL, and discuss the importance of adding yet another component to the language in order to prove completeness. (shrink)

Various four- and three-valued modal propositional logics are studied. The basic systems are modal extensions BK and BS4 of Belnap and Dunn's four-valued logic of firstdegree entailment. Three-valued extensions of BK and BS4 are considered as well. These logics are introduced semantically by means of relational models with two distinct evaluation relations, one for verification and the other for falsification. Axiom systems are defined and shown to be sound and complete with respect to the relational semantics and with (...) respect to twist structures over modal algebras. Sound and complete tableau calculi are presented as well. Moreover, a number of constructive non-modal logics with strong negation are faithfully embedded into BS4, into its three-valued extension B3S4, or into temporal BS4, BtS4. These logics include David Nelson's three-valued logic N3, the four-valued logic N4 bottom, the connexive logic C, and several extensions of bi-intuitionistic logic by strong negation. (shrink)

This paper provides a semantic analysis of the particles afinal (European Portuguese) and alla fine (Italian) in terms of the notion of truth unpersistence, which can be situated at the intersection of epistemic modality and discourse structure. In the analysis proposed, the particles are propositional operators and require that the truth of a proposition p* fail to persist through a temporal succession of epistemic states, this proposition being incompatible with the prejacent, and that the interlocutors share knowledge of (...) a previous epistemic attitude toward p*. We analyze two main cases (plan-related and non plan-related propositions) and also show that these particles are indexical to one (or more) epistemic agent(s) and allow for shifts in perspective. (shrink)

ABSTRACT We critically review two extant paradigms for understanding the systematic interaction between modality and tense, as well as their respective modifications designed to do justice to the contingency of time’s structure and composition. We show that on either type of theory, as well as their respective modifications, some principles prove logically valid whose truth might sensibly be questioned on metaphysical grounds. These considerations lead us to devise a more general logical framework that allows accommodation of those metaphysical views (...) that its predecessors rule out by fiat. (shrink)

The theory of relativity is often regarded as inhospitable to the idea that there is an objective passage of time in the world. In light of this, many philosophers and physicists embrace a “block universe” view, according to which change and temporal passage are merely a subjective appearance or illusion. My aim in this paper is to argue against such a view, and show that we can make sense of an objective passage of time in the setting of relativity (...) theory by abandoning the assumption that the now must be global, and re-conceiving temporal passage as a purely local phenomenon. Various versions of local becoming have been proposed in the literature. Here I focus on the causal diamond theory proposed by Steven F. Savitt and Richard Arthur, which models the now in terms of a local structure called a causal diamond. After defending the reality of temporal passage and exploring its compatibility with relativity theory, I show how the causal diamond approach can be used to counter the argument for the ideality of time due to Kurt Gödel, based on his “rotating universe” solution to the Einstein field equations. I defend the second component of his argument, the modal step, against the consensus view that finds it wanting, and reject the first step, showing that the Gödel universe is compatible with an objective passage of time as long as the latter is construed locally, along the lines of the causal diamond approach. (shrink)

We argue that the temporal asymmetry of influence is not merely the result of thermodynamics: it is a consequence of the fact that modal structure of the universe must admit only processes which cannot give rise to contradictions. We appeal to the process matrix formalism developed in the field of quantum foundations to characterise processes which are compatible with local free will whilst ruling out contradictions, and argue that this gives rise to ‘consistent chaining’ requirements that explain (...) the temporal asymmetry of influence. We compare this view to the perspectival account of causation advocated by Price and Ramsey. (shrink)

Is what could have happened but never did as real as what did happen? What did happen, but isn't happening now, happened at another time. Analogously, one can say that what could have happened happens in another possible world. Whatever their views about the reality of such things as possible worlds, philosophers need to take this analogy seriously. Adriane Rini and Max Cresswell exhibit, in an easy step-by-step manner, the logical structure of temporal and modal discourse, and (...) show that every temporal construction has an exact parallel that requires a language that can refer to worlds, and vice versa. They make precise, in a way which can be articulated and tested, the claim that the parallel is at work behind even ordinary talk about time and modality. The book gives metaphysicians a sturdy framework for the investigation of time and modality - one that does not presuppose any particular metaphysical view. (shrink)

Each of our sensory modalities—vision, touch, taste, etc.—works on a slightly different timescale, with differing temporal resolutions and processing lag. This raises the question of how, or indeed whether, these sensory streams are co-ordinated or ‘bound’ into a coherent multisensory experience of the perceptual ‘now’. In this paper I evaluate one account of how temporal binding is achieved: the temporal windows hypothesis, concluding that, in its simplest form, this hypothesis is inadequate to capture a variety of multisensory (...) phenomena. Rather, the evidence suggests the existence of a more complex temporal structure in which multiple overlapping windows support distinct functional mechanisms. To aid in the precise formulation of such views, I propose a taxonomy of temporal window types and their characteristics that in turn suggests promising avenues for future empirical and philosophical research. I conclude by examining some philosophical implications of multi-window models for the metaphysics of perception and perceptual experience more generally. (shrink)

The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules in special (...) reduced normal form, and, then, on checking validity of such rules in models of singleexponential size in the rules. Also we consider the admissibility problem for TL(NBox+-wC) and show how to reduce the problem for admissibility to the decidability of TL(NBox+-wC) itself using definable universal modalities. (shrink)

ABSTRACT Many temporal and modal logic languages can be regarded as subsets of first order logic, i.e. the semantics of a temporal logic formula is given as a first order condition on points of the underlying models (Kripke structures). Often the set of possible models is restricted to models which are trees. A temporal logic language is (first order) expressively complete, if for every first order condition for a node of a tree there exists an equivalent (...) temporal formula which expresses the same condition. In this paper expressive completeness of the temporal logic language with the set of operators U (until), S (since), and X k (k-next) is proved, and the result is extended to various other tree-like structures. (shrink)

We interpret the modal µ-calculus over a new model [10], to give a temporal logic suitable for systems exhibiting both probabilistic and demonic nondeterminism. The logical formulae are real-valued, and the statements are not limited to properties that hold with probability 1. In achieving that conceptual step, our technical contribution is to determine the correct quantitative generalisation of the Boolean operators: one that allows many of the standard Boolean-based temporal laws to carry over the reals with little (...) or no structural alteration, even for properties that hold with probability strictly between 0 and 1. The generalisation is not obvious, but is dictated by our discovery elsewhere of the algebraic property that characterises the next-time operator over the new model: it is arithmetic 'sublinearity' [20, Fig. 4 p. 342], which replaces the Boolean conjunctivity that characterises next-time in a modal algebra.We confirm by example that the new modal laws can be used for quantitative reasoning about probabilistic/demonic behavior. The random walk is treated using only those laws and real-number arithmetic: arguing from precise numeric premises, more specific than simply 'with some non-zero probability', we reach numeric conclusions that are not simply 'with probability 1'. (shrink)

Asymmetric distribution of function between the cerebral hemispheres has been widely investigated in the auditory modality. The current approach borrows heavily from visual local–global research in an attempt to determine whether, as in vision, local–global auditory processing is lateralised. In vision, lateralised local–global processing likely relies on spatial frequency information. Drawing analogies between visual spatial frequency and auditory dimensions, two sets of auditory stimuli were developed. In the high–low stimulus set we manipulate frequency information, and in the fast–slow stimulus set (...) we manipulate temporal information. The fast–slow stimuli additionally mimic visual hierarchical stimulus structure, in which the arrangement of local patterns determines the global pattern. Unlike previous auditory stimuli, the current stimulus sets contain the experimental flexibility of visual local–global hierarchical stimuli allowing independent manipulation of structural levels. Previous findings of frequency and temporal range priming were replicated. Additionally, by presenting stimuli monaurally, we found that priming of frequency ranges (but not temporal ranges) was found to vary by ear, supporting the contention that the hemispheres asymmetrically retain traces of prior frequency processing. These results contribute to the extensive literature revealing cerebral asymmetries for the processing of frequency information, and extend those results to the realm of priming. (shrink)

In this essay I will explore the syntactic expression of the notion ‘clause’ by focusing on some syntactic and semantic properties of bare infinitive (BI) complements to perception verbs in English. I shall argue briefly that perception BI complements must be clausal, and then turn in more detail to the issue of what sort of clause the BI complement must be. It will be established that the categorical nature of the perception BI complement as IP or VP is contingent on (...) selectional properties of the perception verb, properties which may be contextually influenced by modality and negation. More specifically, an interpretative distinction between ‘vision’ and ‘non-vision’see first suggested by Napoli (1988) will be shown, contrary to her proposal, to provide the key to the contrast in the selection of clausal types. The IP/VP distinction will be shown to correlate with the viability of interpretations for the BI clause that are ‘temporally independent’ of the matrix clause. Given the IP/VP distinction, it will be demonstrated further that the peculiarly limited distribution of the expletive formativethere in BI complements may be predicted from independently motivated syntactic principles that determine clausal structure. (shrink)

In this article I argue that phenomenal intentionality fundamentally consists in a horizonality structure, rather than in a relation to a representational content or the determination of accuracy conditions. I provide a distinctive modal model of intentionality that conceives of phenomenal intentionality as the enjoyment of a plus ultra that points beyond what is actual. The directedness of intentionality on the world, thus, consists in “pointing ahead” to possibilities. The principal difficulty for the modal model is logical: (...) the most obvious way of implementing such a structure results in an analogue of Russell’s paradox. However, this paradox can be avoided by fine-tuning the modal logic deployed in this setting. This way of fine-tuning the logic ultimately amounts to intuitive benefits. For, it captures the intensional character of intentionality, since the way that our mental states refer to things is conception-dependent. Moreover, the way I interpret the modal model leads to a conception of intentionality as a feature of dynamic, diachronic patterns in the way that mental acts subjectively appear, rather than as a synchronic property. We ought to think of intentionality as fundamentally a temporal, subjective determination. In a generalization on Sellars’ approach to concepts, I hold that phenomenally intentional mental presentations involve modal laws and are inconceivable without them. (shrink)

We propose a semantic analysis of the particles afinal (European Portuguese) and alla fine (Italian) in terms of the notion of truth unpersistence, which combines both epistemic modality and constraints on discourse structure. We argue that the felicitous use of these modal particles requires that the truth of a proposition p* fail to persist through a temporal succession of epistemic states, where p* is incompatible with the proposition modified by afinal/alla fine, and that the interlocutors share knowledge (...) of a previous epistemic attitude toward p*. We analyze two main cases, that of plan-related propositions and that of propositions without plans. We also discuss the connections between truth unpersistence and evidentiality. (shrink)

This paper establishes a connection between structure sensitive categorial inference and classical modal logic. The embedding theorems for non-associative Lambek Calculus and the whole class of its weak Sahlqvist extensions demonstrate that various resource sensitive regimes can be modelled within the framework of unimodal temporal logic. On the semantic side, this requires decomposition of the ternary accessibility relation to provide its correlation with standard binary Kripke frames and models.

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)

In this article we introduce a logical structure for normative reasoning, called Normative Detachment Structure with Ideal Conditions, that can be used to represent the content of certain legal texts in a normalized way. The structure exploits the deductive properties of a system of bimodal logic able to distinguish between ideal and actual normative statements, as well as a novel formalization of conditional normative statements able to capture interesting cases of contrary-to-duty reasoning and to avoid deontic paradoxes. (...) Furthermore, we illustrate how the theoretical framework proposed can be mechanized to get an automated procedure of query-answering on an example of legal text. (shrink)

This essay expands upon the suggestion that Lessing's infamous ‘ditch’ is actually three ditches: temporal, metaphysical, and existential gaps. It examines the complex problems these ditches raise, and then proposes that Kierkegaard's Fragments and Postscript exhibit a similar triadic organizational structure, which may signal a deliberate attempt to engage and respond to Lessing's three gaps. Viewing the Climacean project in this way offers an enhanced understanding of the intricacies of Lessing's rationalist approach to both religion and historical truth, (...) and illuminates Climacus's subjective response to Lessing. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Tracing a Traumatic Temporality: Levinas and Derrida on Trauma and ResponsibilityCathrine Bjørnholt Michaelsen (bio)For more than three decades, Jacques Derrida and Emmanuel Levinas develop their conceptions of trauma and responsibility in close, critical, and engaged readings of each other’s works.1 In a text first published in 1973, Levinas explicitly considers different aspects and implications of Derrida’s “new style of thought,” as well as his own relation to Derrida, describing (...) their recurring crossing of paths as “a contact at the heart of a chiasmus,” which is further said to constitute “the very modality of the philosophical encounter” (PN 56, 62).Since the publication of “Force of Law: The ‘Mystical Foundation of Authority’” in 1990, in which Derrida makes the somewhat surprising announcement that justice can be considered the undeconstructible condition of deconstruction (AR 243), as well as the subsequent publication of Specters of Marx in 1993, which is often designated as the work in which Derrida begins to consider ethico-political concerns more explicitly than hitherto, there has been much scholarly discussion about a so-called “ethical turn” of deconstruction.2 Throughout [End Page 43] the 1990s and up until this day a tendency prevails among certain scholars to strive for the establishment and legitimization of a more or less harmonic accordance between Levinas and Derrida with reference to concepts that preoccupy them both (e.g., “justice,” “hospitality,” “the other,” or “responsibility”). However, as Martin Hägglund has convincingly argued, a certain disjoining of Derrida and Levinas is required in order not to conflate what ultimately amount to two very different styles of writing and thinking. Such disjoining is particularly important when it comes to an issue such as responsibility, which is too often and too quickly categorized as an “ethical issue,” as if such a categorization were self-explanatory.3The aim of this article is not to carry out a comparative study focusing on the similarities and dissimilarities of the writings of Derrida and Levinas. Instead, the article is an attempt to let a “third” voice arise from the ongoing philosophical conversation between Derrida and Levinas, which is neither entirely accordant nor discordant, in order to emphasize a certain traumatic temporality of responsibility that finds a space in both their works while indicating the subtle nuances of disjuncture separating these spaces. In what follows, I therefore wish to explore some of the most significant displacements to which the notions of trauma and responsibility are subjected throughout the writings of Derrida and Levinas, as a result, to some extent at least, of their repeated chiasmic encounters.By way of introduction, it should be noted that both Derrida and Levinas transport the notion of trauma away from its most frequent psychopathological, psychoanalytic, or neurological areas of interpretation, just as they transport the notion of responsibility away from its usual autonomist or decisionist connotations toward a more extensive space of signification.4 Bearing this introductory note in mind, the question concerning what precisely enables this transport of trauma will direct the approach of the article. In other words, the article will question what it is about the structure of “trauma” or “traumatism” that allows the somewhat “fearsome” generalizations—to employ [End Page 44] Derrida’s own formulation from “Typewriter Ribbon”5 —to take place in the writings of both Derrida and Levinas.The suggestion in what follows will be that it is the peculiar temporality of trauma that allows for the generalizations, openings, and disseminations of trauma in Derrida and Levinas. More specifically, this traumatic temporality inscribes itself through an interruption of what might, with a reference to Heidegger, be called the vulgar understanding of time.6 Drawing attention to the temporality of trauma as a vehicle of transportation, the article advances in six main sections, each exploring different aspects of the relationship between temporality, trauma, and responsibility displayed in Derrida and Levinas.Traumatic TemporalityAs is well known, at least since Freud, trauma only becomes a trauma belatedly, or after its own fact, since a trauma only manifests itself by withdrawing itself in the traces it leaves behind, that is, by its aftermath and its effects of repetition and deferral. Trauma is somehow... (shrink)

We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a (...) class of non-wellfounded proofs with sequents of bounded size, called slim proofs, and a counter-model construction that shows slimness suffices to capture all validities. Slim proofs are further transformed into cyclic proofs by means of re-assigning ordinal annotations. (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)

"Accessibility" is a crucial concept of possible worlds semantics. The simplest approach to accessibility is the "magical theory" that construes this relation as analogous to spatial or temporal relations. In this paper I give a nonmagical structural account of the accessibility relation that can be used to give a necessitarian account of kinds and laws. Laws are characterized in a structural way as stable invariants of the world's gestalt. Finally, I point out how the structural approach can be embedded (...) in a general representational theory of modality. (shrink)

We investigate the major mathematical theories of space from a modal standpoint: topology, affine geometry, metric geometry, and vector algebra. This allows us to see new fine-structure in spatial patterns which suggests analogies across these mathematical theories in terms of modal, temporal, and conditional logics. Throughout the modal walk through space, expressive power is analyzed in terms of language design, bisimulations, and correspondence phenomena. The result is both unification across the areas visited, and the uncovering (...) of interesting new questions. (shrink)

Since 2007, Tomás Saraceno has been developing a project that aims to break out of the anthropocentric understanding of communication and coexistence with other animal organisms. In this article, I point out the importance of using modern visualization technologies to analyze and investigate the structure of communication frameworks and their modalities in the animal world, specifically using the example of spiders. The visualization of what is normally invisible to the eye and inaudible to the ear rearticulates the realm of (...) the visible and the audible, which Saraceno then uses for art-critical purposes, with the aim of forming a new type of posthuman attunement to the environment and other animal species. The condition for outlining and articulating Saraceno’s artistic vision is the use of the latest technologies of visualization, which operate on the principle of digital and algorithmic code. They synthesize different planes of affectivity and transform, modulate, and combine the different modes of signs into a single technical-organic complex: they offer new ways of seeing and feeling the world. Thus, hybrid ecology in Saraceno’s case does not imply a return to primordial ways of life, but on the contrary, it forms a semiosphere attuned to a specific plane of consistency that enfolds distinct modes of signs and develops them into an expression of hitherto unsuspected variants of life. (shrink)

In this commentary we raise three issues: (1) Is it motherese or song that sets the stage for very early mother-infant interaction? (2) Does the infant play a pivotal role in the complex temporal structure of social interaction? (3) Is the vocal channel primordial or do other modalities play an equally important role in social interaction?

This article explores the notion of pain in relation to its temporal experience. The assumption that pain is something experienced exclusively consciously in the present is challenged. To carry out this enterprise, we start from the notion of Husserlian sedimentation in order to be able to account for the relationship between the temporal structure of consciousness and pain. Exploration of sedimented, implicit experiences is first analyzed phenomenologically, drawing mainly on Husserlian _C Manuscripts_. It is then applied to (...) different medical cases, which highlights the paradoxical force of the past in the experience of pain. In another sense, it is argued that anticipation of the future can also be a painful experience. The appreciation of these aporetic situations in the experience of pain, analyzed along with two types of consciousness, explicit and implicit, raises the question of whether it is possible to experience “unnoticed pain”, purely implicit, in the present. The phenomenon is explained based on the distinction between original sedimentations and secondary sedimentations that Merleau-Ponty makes; these first ones, apparently contradictory, can nevertheless be interpreted as consciousness in its modality of inattention. As well as thematic or co-attended experiences, these also belong to the arc of intentionality. The idea of unnoticed pain makes the claim that pain is something experienced exclusively consciously in the present even more complex. (shrink)

Whatever the answer to Molyneux's question is, it is certainly not obvious that the answer is ‘yes’. In contrast, it seems clear that we should answer affirmatively a temporal variation on Molyneux's question, introduced by Gareth Evans. I offer a phenomenological explanation of this asymmetry in our responses to the two questions. This explanation appeals to the modality-specific spatial structure of perceptual experience and its amodal temporal structure. On this explanation, there are differences in the perception (...) of spatial properties in different modalities, but these differences do not stand in the way of the objectivity of perceptual experience. (shrink)

Merleau-Ponty suggests that to perceive is to be “geared into” the world. In perceiving, we are related to a temporally structured modal space of bodily possibilities that is co-constituted by the body and the world. When we perceive, we are “geared into” this structure and responsive to it; when we misperceive, we are not. In misperceiving, we are unaware of our failure to be geared into the world, and in this respect, we lack awareness of what we are (...) doing. In explaining misperception via this lack of self-awareness, Merleau-Ponty anticipates a key feature of M. G. F. Martin's epistemic disjunctivism: the idea that perceptions and misperceptions can be indiscriminable because of a self-awareness we lack, rather than a set of positive phenomenal features that two experiences share. However, because Merleau-Ponty's account of self-awareness imposes relatively few cognitive demands, he is able to explain how adults, infants, and dogs can be self-aware in the same sense, and how they can fail to discriminate between their experiences in the same way. This provides Merleau-Ponty with the resources to answer Susanna Siegel's objection to epistemic disjunctivism on the basis of “cognitively unsophisticated hallucinators.”. (shrink)

Normative concepts have a special taste, which many consider to be proof that they cannot be reductively analyzed into entirely nonnormative components. This paper demonstrates that at least some intuitively normative concepts can be reductively analyzed. I focus on so-called ‘hypothetical imperatives’ or ‘anankastic conditionals’, and show that the availability of normative readings of conditionals is determined by features of grammar, specifically features of tense. Properly interpreted, these grammatical features suggest that these deontic modals are analyzable in terms of conditional (...) necessity with a certain temporal structure. (shrink)

This paper assesses branching spacetime theories in light of metaphysical considerations concerning time. I present the A, B, and C series in terms of the temporal structure they impose on sets of events, and raise problems for two elements of extant branching spacetime theories—McCall’s ‘branch attrition’, and the ‘no backward branching’ feature of Belnap’s ‘branching space-time’—in terms of their respective A- and B-theoretic nature. I argue that McCall’s presentation of branch attrition can only be coherently formulated on a (...) model with at least two temporal dimensions, and that this results in severing the link between branch attrition and the flow of time. I argue that ‘no backward branching’ prohibits Belnap’s theory from capturing the modal content of indeterministic physical theories, and results in it ascribing to the world a time-asymmetric modal structure that lacks physical justification. (shrink)

The editors of the Applied Logic Series are happy to present to the reader the fifth volume in the series, a collection of papers on Logic, Language and Computation. One very striking feature of the application of logic to language and to computation is that it requires the combination, the integration and the use of many diverse systems and methodologies - all in the same single application. The papers in this volume will give the reader a glimpse into the problems (...) of this active frontier of logic. The Editors CONTENTS Preface IX 1. S. AKAMA Recent Issues in Logic, Language and Computation 1 2. M. J. CRESSWELL Restricted Quantification 27 3. B. H. SLATER The Epsilon Calculus' Problematic 39 4. K. VON HEUSINGER Definite Descriptions and Choice Functions 61 5. N. ASHER Spatio-Temporal Structure in Text 93 6. Y. NAKAYAMA DRT and Many-Valued Logics 131 7. S. AKAMA On Constructive Modality 143 8. H. W ANSING Displaying as Temporalizing: Sequent Systems for Subintuitionistic Logics 159 9. L. FARINAS DEL CERRO AND V. LUGARDON 179 Quantification and Dependence Logics 10. R. SYLVAN Relevant Conditionals, and Relevant Application Thereof 191 Index 245 Preface This is a collection of papers by distinguished researchers on Logic, Lin guistics, Philosophy and Computer Science. The aim of this book is to address a broad picture of the recent research on related areas. In particular, the contributions focus on natural language semantics and non-classical logics from different viewpoints. (shrink)