We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our (...) investigation. We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit. (shrink)

The implicational fragment of the logic of relevant implication, $R_{\to}$ is one of the oldest relevance logics and in 1959 was shown by Kripke to be decidable. The proof is based on $LR_{\to}$ , a Gentzen-style calculus. In this paper, we add the truth constant $\mathbf{t}$ to $LR_{\to}$ , but more importantly we show how to reshape the sequent calculus as a consecution calculus containing a binary structural connective, in which permutation is replaced by two structural rules that involve (...) $\mathbf{t}$ . This calculus, $LT_\to^{\text{\textcircled{$\mathbf{t}$}}}$ , extends the consecution calculus $LT_{\to}^{\mathbf{t}}$ formalizing the implicational fragment of ticket entailment . We introduce two other new calculi as alternative formulations of $R_{\to}^{\mathbf{t}}$ . For each new calculus, we prove the cut theorem as well as the equivalence to the original Hilbert-style axiomatization of $R_{\to}^{\mathbf{t}}$ . These results serve as a basis for our positive solution to the long open problem of the decidability of $T_{\to}$ , which we present in another paper. (shrink)

Restall set forth a "consecution" calculus in his "An Introduction to Substructural Logics." This is a natural deduction type sequent calculus where the structural rules play an important role. This paper looks at different ways of extending Restall's calculus. It is shown that Restall's weak soundness and completeness result with regards to a Hilbert calculus can be extended to a strong one so as to encompass what Restall calls proofs from assumptions. It is also shown how to extend the (...) calculus so as to validate the metainferential rule of reasoning by cases, as well as certain theory-dependent rules. (shrink)

We show that from a supercompact cardinal $\kappa$, there is a forcing extension $V[G]$ that has a symmetric inner model $N$ in which $\mathrm {ZF}+\lnot\mathrm {AC}$ holds, $\kappa$ and $\kappa^{+}$ are both singular, and the continuum function at $\kappa$ can be precisely controlled, in the sense that the final model contains a sequence of distinct subsets of $\kappa$ of length equal to any predetermined ordinal. We also show that the above situation can be collapsed to obtain a model of $\mathrm (...) {ZF}+\lnot\mathrm {AC}_{\omega}$ in which either $\aleph_{1}$ and $\aleph_{2}$ are both singular and the continuum function at $\aleph_{1}$ can be precisely controlled, or $\aleph_{\omega}$ and $\aleph_{\omega+1}$ are both singular and the continuum function at $\aleph_{\omega}$ can be precisely controlled. Additionally, we discuss a result in which we separate the lengths of sequences of distinct subsets of consecutive singular cardinals $\kappa$ and $\kappa^{+}$ in a model of $\mathrm {ZF}$. Some open questions concerning the continuum function in models of $\mathrm {ZF}$ with consecutive singular cardinals are posed. (shrink)

We obtain 2 models in which AC is false and in which there are long sequences of consecutive large cardinals.

Consecutive constructivism is a moral and political theory which mitigates structural injustice by securing individuals' perception of private morality--that is, inventing procedural devices to make people enhance their moral consciousness--and, at the same time, encourages people to voluntarily concern themselves with procedural justice and public morality. The crucial reason for this position is that a detouring method of not directly dealing with the problem of justice but rather discussing the problem of morals is required to avoid the lucid criticisms of (...) statists that the sovereign ruling states with authority or the world government does not exist. This book suggests a new approach to the problem of global justice, termed here consecutive constructivism. It provides a way of coping with procedural justice at the global level, while also alleviating the problem of structural injustice insofar as it exacerbates procedural injustice. Acknowledging the fact that the discussion of global justice is difficult in a world constituted of lots of sovereign states, it sketches out a political theory which begins with the problem of morals and then consecutively moves on to the matter of justice. The result is a novel normative theory narrowing the gap between Neo-Westphalian and Post-Westphalian traditions. (shrink)

This article examines the pronunciation of identical consecutive letters in the Yemenite Jewish tradition, with a basic comparison with the pronunciation of identical letters in other present-day traditions. It is notable that in the Yemenite tradition also there are differences of opinion as to the pronunciation of these letters as a result of the effect of their pronunciation in other present-day traditions. In this article, we present the fundamental views with regard to the pronunciation of identical consecutive letters as well (...) as their possible pronunciations in light of the grammar rules evident from the grammarians. The article does not purport to provide a historical, developmental or chronological investigation of the grammar rules; rather, it focuses on one specific topic involving the pronunciation of identical consecutive letters in the Yemenite tradition. (shrink)

While specifications and verifications of concurrent systems employ Linear Temporal Logic , it is increasingly likely that logical consequence in image will be used in the description of computations and parallel reasoning. Our paper considers logical consequence in the standard image with temporal operations image and image . The prime result is an algorithm recognizing consecutions admissible in image, so we prove that image is decidable w.r.t. admissible inference rules. As a consequence we obtain algorithms verifying the validity of consecutions (...) in image and solving the satisfiability problem. We start by a simple reduction of logical consecutions of image to equivalent ones in the reduced normal form . Then we apply a semantic technique based on image-Kripke structures with formula definable subsets. This yields necessary and sufficient conditions for a consecution to be not admissible in image. These conditions lead to an algorithm which recognizes consecutions admissible in image by verifying the validity of consecutions in special finite Kripke structures of size square polynomial in reduced normal forms of the consecutions. As a consequence, this also solves the satisfiability problem for image. (shrink)

In this paper1 we study admissible consecutions in multi-modal logics with the universal modality. We consider extensions of multi-modal logic S4n augmented with the universal modality. Admissible consecutions form the largest class of rules, under which a logic is closed. We propose an approach based on the context effective finite model property. Theorem 7, the main result of the paper, gives sufficient conditions for decidability of admissible consecutions in our logics. This theorem also provides an explicit algorithm for recognizing such (...) consecutions. Some applications to particular logics with the universal modality are given. (shrink)

Remote interpreting via video-link is increasingly being employed in investigative interviews chiefly due to its apparent increased accessibility and efficiency. However, risks of miscommunication have been shown to be magnified in remote interpreting and empirical research specifically on video-link remote interpreting is in its infancy which greatly limits the evidence base available to inform and direct evidence-based policy and best practice, particularly in the identification of the optimal mode of interpreting to be used, namely consecutive and simultaneous. Consecutive interpreting refers (...) to a process in which the interpreter transfers short segments of speech from one language into the other as each person speaks in managed turn-taking, while simultaneous interpreting refers to the transfer of natural speech from one language into another in a concurrent manner without the need for speakers to segment their speech. This study provides novel empirical evidence by using eye tracking to compare the overt visual attention of interpreters working in a remote setting in which an English-speaking Interviewer interacts with a non-English-speaking Suspect in person, for whom interpretation is provided via video-link in real time. Using a within-subject design, we analyze eye-movement data from 28 professionally accredited interpreters who interpreted via video-link an investigative interview in which consecutive and simultaneous interpreting modes were counterbalanced. Taking interpreting performance into account, our results showed that, the consecutive mode yielded significantly less gaze time and therefore significantly less on-screen overt visual attention due to off-screen notetaking, an essential component of the consecutive interpreting mode. Relative to gaze time, the consecutive mode also resulted in significantly more and longer fixations and shifts of attention. Participants also allocated significantly more overt visual attention to the Interviewer than the Suspect, particularly in the consecutive mode. Furthermore, we found informative significant correlations between eye tracking measures and interpreting performance: accuracy, verbal rapport, and management. Finally, we found no significant differences between the three language pairs tested. We conclude with a discussion of limitations and the contributions of the study and an outline for future work on this topic of growing importance. (shrink)

Two results of elementary number theory, going back to Kürschák and Nagell, stating that the sums $\sum_{i=1}^k \frac{m_i}{n+i}$ (with $k\geq 1$, $(m_i, n+i)=1$, $m_i\lessthan n+i$) and $\sum_{i=0}^k \frac{1}{m+in}$ (with $n, m, k$ positive integers) are never integers, are shown to hold in $\mathrm{PA}^{-}$, a very weak arithmetic, whose axiom system has no induction axiom.

In 2019–2020, Israel went through three consecutive elections in less than a year on grounds of alleged corruption by Prime Minister Netanyahu, and his lack of ability to form a coalition. This study aims to contribute to analyses of the media mobilization/malaise effect by examining the impact of such a prolonged period of campaigning on citizens’ political behavior. Thus, we conducted six online surveys using a longitudinal sample of Israeli society before and after each election. The analysis found that, despite (...) participants’ testimonies that they were increasingly “tired of dealing with elections,” there was a significant increase in participants’ reported certainty in their vote, news consumption, participation in online political discussions, and level of political efficacy between the elections. Next, a multivariate analysis aiming to explain variations in voters’ political efficacy found that political trust, participants’ reported certainty about their vote, and political interest all explained high levels of political efficacy. The analysis provides one of the strongest reinforcements to date regarding the validity of political mobilization theory, demonstrating its relevance under challenging conditions. We discuss further implications and generalizability of our findings. (shrink)

Hobbes établit une distinction entre signes certains et signes incertains, qui correspond à la distinction entre science et prudence. Mais il précise toutefois que les signes de la science ne sont pas tous certains, ni infaillibles. Cette recommandation n’est pas tant une critique de la science, qu’une mise en garde adressée à ceux qui renoncent à leur jugement naturel et s’en remettent aveuglément à l’autorité des livres. La certitude dépend donc d’un bon usage des signes de la part du sujet (...) qui connaît ou interprète. Hobbes affirme ainsi le primat du sujet ou de l’esprit dans la constitution du signe et sa manipulation. La différence entre signes certains et signes incertains ne dépend pas seulement du type de signes, mais également des conditions de l’interprétation. Cette solution s’impose si l’on comprend la définition de Hobbes selon laquelle il n’y a de signe que pour et par un sujet, comme une définition générale s’appliquant à tout type de signe. On pourra alors rendre compte de la certitude ou de l’incertitude des signes à partir de la manière dont le sujet fait usage des signes dans le calcul des conséquences. À cet égard, la distinction entre consécutions de l’imagination et consécutions de la raison joue un rôle au moins aussi essentiel que la distinction entre signes naturels et signes d’institution : s’il est vrai que l’imagination dépend de l’ordre aléatoire des perceptions, alors que les calculs de la raison se fondent sur des signes arbitraires, la notion de consécution apparaît comme le fondement de toute activité portant sur les signes, puisque tout signe, qu’il soit naturel ou conventionnel, suppose un rapport posé ou effectué par l’esprit. L’originalité de Hobbes consiste notamment à envisager le signe comme un rapport entre deux événements, entre un conséquent et un antécédent : plutôt que le rapport entre une présence et une absence, c’est la notion d’ordre qui est au cœur de la pensée hobbesienne du signe. (shrink)

Hobbes établit une distinction entre signes certains et signes incertains, qui correspond à la distinction entre science et prudence. Mais il précise toutefois que les signes de la science ne sont pas tous certains, ni infaillibles. Cette recommandation n’est pas tant une critique de la science, qu’une mise en garde adressée à ceux qui renoncent à leur jugement naturel et s’en remettent aveuglément à l’autorité des livres. La certitude dépend donc d’un bon usage des signes de la part du sujet (...) qui connaît ou interprète. Hobbes affirme ainsi le primat du sujet ou de l’esprit dans la constitution du signe et sa manipulation. La différence entre signes certains et signes incertains ne dépend pas seulement du type de signes, mais également des conditions de l’interprétation. Cette solution s’impose si l’on comprend la définition de Hobbes selon laquelle il n’y a de signe que pour et par un sujet, comme une définition générale s’appliquant à tout type de signe. On pourra alors rendre compte de la certitude ou de l’incertitude des signes à partir de la manière dont le sujet fait usage des signes dans le calcul des conséquences. À cet égard, la distinction entre consécutions de l’imagination et consécutions de la raison joue un rôle au moins aussi essentiel que la distinction entre signes naturels et signes d’institution : s’il est vrai que l’imagination dépend de l’ordre aléatoire des perceptions, alors que les calculs de la raison se fondent sur des signes arbitraires, la notion de consécution apparaît comme le fondement de toute activité portant sur les signes, puisque tout signe, qu’il soit naturel ou conventionnel, suppose un rapport posé ou effectué par l’esprit. L’originalité de Hobbes consiste notamment à envisager le signe comme un rapport entre deux événements, entre un conséquent et un antécédent : plutôt que le rapport entre une présence et une absence, c’est la notion d’ordre qui est au cœur de la pensée hobbesienne du signe. (shrink)

Consecutive measurements performed on the same quantum system can reveal fundamental insights into quantum theory’s causal structure, and probe different aspects of the quantum measurement problem. According to the Copenhagen interpretation, measurements affect the quantum system in such a way that the quantum superposition collapses after each measurement, erasing any memory of the prior state. We show here that counter to this view, un-amplified measurements have coherent ancilla density matrices that encode the memory of the entire set of quantum measurements (...) that came before, and that the chain of this entire set is therefore non-Markovian. In contrast, sequences of amplified measurements are equivalent to a quantum Markov chain. We argue that the non-Markovian nature of quantum measurement has empirical consequences that are incompatible with the assumption of wave function collapse, thus elevating the collapse assumption into a testable hypothesis. Finally, we find that all of the information necessary to reconstruct an arbitrary non-Markovian quantum chain of measurements is encoded on the boundary of that chain, reminiscent of the holographic principle. (shrink)

Consecutive waves of paleolithic migrants crossing the Bering land bridge from Siberia to North America between 80,000 and 7,000 b.c. brought with them the shamanic way of harnessing supernatural powers. This way prevailed until the White intrusion 400 years ago, into the living space of the aboriginal peoples of North America. Wherever European political, religious, and economic dominance was established, shamanic institutions became the focus of negative attention. The shamanic practitioner was variously depicted by governmental and ecclesiastic authorities as a (...) charlatan and imposter or a purveyor of evil influence. Some well-known ethnological and medico-psychological experts have until very recently portrayed the shaman as a mentally deranged person whose “primitive” culture permits the acting-out of psychopathology in a prestigious role, a eurocentric and positivistic fallacy rooted in Western misinterpretations of learned behavior manifested during shamanic rituals involving altered states of consciousness. Legal measures to suppress shamanic ceremonials were taken in the United States, especially in the aftermath of the Ghost Dance. This shaman-inspired movement, originating in the Prophet Dance of the Pacific Northwest (Spier 1935), sent waves of hectic sacro-nativistic ceremonial activity through many Amerindian tribes, and finally culminated in the Sioux uprising of 1890 which ended in the tragedy of Wounded Knee (cf. Mooney 1896). (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with (...) additional inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix. (shrink)

Two consecution calculi are introduced: one for the implicational fragment of the logic of entailment with truth and another one for the disjunction free logic of nondistributive relevant implication. The proof technique—attributable to Gentzen—that uses a double induction on the degree and on the rank of the cut formula is shown to be insufficient to prove admissible various forms of cut and mix in these calculi. The elimination theorem is proven, however, by augmenting the earlier double inductive proof with (...) additional inductions. We also give a new purely inductive proof of the cut theorem for the original single cut rule in Gentzen’s sequent calculus $ LK $ without any use of mix. (shrink)

El objetivo del presente trabajo es ofrecer una serie de directrices didácticas para la formación de intérpretes, haciendo especial hincapié en el desarrollo de la capacidad de análisis, comprensión y dominio de la comunicación no verbal. En concreto, se centra en el paralenguaje, esto es, la voz y todas sus características, para poder interpretar adecuadamente su influencia en el mensaje verbal y poder realizar una traducción fiel al mensaje original, manteniendo su intención y sentido intactos. Asimismo, el trabajo propone una (...) serie de ejercicios básicos para el desarrollo de la capacidad interpretativa en su totalidad. (shrink)

I argue that Descartes' Second Causal Proof of God in the Third Meditation evidences, and commits him to, the belief that time is "strongly discontinuous" -- that is, that there is actually a gap between each consecutive moment of time. Much of my article attempts to reconcile this interpretation, the "received view," with Descartes' statements about time, space, and matter in his other writings, including his correspondence with various philosophers.

Sequent calculi constitute an interesting and important category of proof systems. They are much less known than axiomatic systems or natural deduction systems are, and they are much less known than they should be. Sequent calculi were designed as a theoretical framework for investigations of logical consequence, and they live up to the expectations completely as an abundant source of meta-logical results. The goal of this book is to provide a fairly comprehensive view of sequent calculi -- including a wide (...) range of variations. The focus is on sequent calculi for various non-classical logics, from intuitionistic logic to relevance logic, through linear and modal logics. A particular version of sequent calculi, the so-called consecution calculi, have seen important new developments in the last decade or so. The invention of new consecution calculi for various relevance logics allowed the last major open problem in the area of relevance logic to be solved positively: pure ticket entailment is decidable. An exposition of this result is included in chapter 9 together with further new decidability results (for less famous systems). A series of other results that were obtained by J. M. Dunn and me, or by me in the last decade or so, are also presented in various places in the book. Some of these results are slightly improved in their current presentation. Obviously, many calculi and several important theorems are not new. They are included here to ensure the completeness of the picture; their original formulations may be found in the referenced publications. This book contains very little about semantics, in general, and about the semantics of non-classical logic in particular. (shrink)

There are 1,000 of us and one victim. We each increase the level at which a "discomfort machine" operates on the victim---leading to great discomfort. Suppose that consecutive levels of the machine are so similar that the victim cannot distinguish them. Have we acted permissibly? According to the "no-difference argument" the answer is "yes" because each of our actions was guaranteed to make the victim no worse off. This argument is of interest because if it is sound, similar arguments threaten (...) intuitive moral verdicts about many cases in which a large number of individual choices cumulatively make a great difference, while each choice seems to make no difference on its own. But the argument is not sound, as is shown by a simple objection based on a plausible dominance principle---an objection that avoids challenges that have been brought against previous criticisms of the no difference argument. (shrink)