In some presentations of classical and intuitionistic logics, the objectlanguage is assumed to contain (two) truth-value constants: ⊤ (verum) and ⊥ (falsum), that are, respectively, true and false under every bivalent valuation. We are interested to define and study analogical constants ‡, 1 ≤ i ≤ n, that in an arbitrary multi-valued logic over truth-values V = {v1,..., vn} have the truth-value vi under every (multi-valued) valuation. As is well known, the absence or presence of such constants has a significant (...) deductive impact on the logics studied. We define such constants proof-theoretically via their associated I/E-rules in a natural-deduction proof system. In particular, we propose a generalization of the notions of contradiction and explosiveness of a logic to the context of multi-valued logics. (shrink)

It is shown that the expressive power of second-order propositional modal logic whose modalities are S4.2 or weaker is the same as that of second-order predicate logic.

We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.

We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.

This paper contributes to the principled construction of tableau-based decision procedures for hybrid logic with global, difference, and converse modalities. We also consider reflexive and transitive relations. For converse-free formulas we present a terminating control that does not rely on the usual chain-based blocking scheme. Our tableau systems are based on a new model existence theorem.

The paper presents a generalization of pregroup, by which a freely-generated pregroup is augmented with a finite set of commuting inequations, allowing limited commutativity and cancelability. It is shown that grammars based on the commutation-augmented pregroups generate mildly context-sensitive languages. A version of Lambek’s switching lemma is established for these pregroups. Polynomial parsability and semilinearity are shown for languages generated by these grammars.

We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. We (...) prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive “flavor.” The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper. (shrink)

Next SectionObjectives A statute enacted in 2005 modified the legislative framework of the rights of terminally ill persons in France. Ten years after the EURONIC study, which described the self-reported practices of neonatal caregivers towards ethical decision-making, a new study was conducted to assess the impact of the new law in neonatal intensive care units (NICU) and compare the results reported by EURONIC with current practices. Setting and design The study was carried out in the same two NICU as in (...) the EURONIC qualitative study. A third centre was added to increase the sample size. From February to October 2007, 19 physicians and 17 nurses participated in semistructured interviews very similar to those for EURONIC. Content analysis identified the recurring themes emerging from the interviews. Results Compared with the EURONIC results, the caregivers reported that they pay greater attention to the views of parents and provided respectful support to the neonates when life-sustaining treatment is withdrawn. Active termination of life has become exceptional. The possibility of withdrawal of treatment, the administration of sedatives to control pain even at the risk of hastening death, the emphasis on sparing parents the burden of decision, and the relative ignorance of the law were very similar to the EURONIC findings. Conclusion Both the medical and the legal regulation of practices has allowed more dialogue with the parents and more humane care for dying newborns. A new European study is necessary to investigate the possible changes in practices and attitudes also in other countries. (shrink)

We present sound and complete semantics and a sequent calculus for the Lambek calculus extended with intuitionistic propositional logic.

It is shown that de re formulas are eliminable in the modal logic S5 extended with the axiom scheme □∃xφ ⊃ ∃x□φ.

In this paper, we propose an extension of free pregroups with lower bounds on sets of pregroup elements. Pregroup grammars based on such pregroups provide a kind of an algebraic counterpart to universal quantification over type-variables. In particular, we show how our pregroup extensions can be used for pregroup grammars expressing natural-language coordination and extraction.

The paper provides a proof-theory for a negative presentation of classical logic based on a single primitive of exclusion, generalizing the known presentation via the binary ‘nand. The completeness is established via deductive equivalence to Gentzens NK/LK systems.

We study structural rules in the context of multi-valued logics with finitely-many truth-values. We first extend Gentzen’s traditional structural rules to a multi-valued logic context; in addition, we propos some novel structural rules, fitting only multi-valued logics. Then, we propose a novel definition, namely, structural rules completeness of a collection of structural rules, requiring derivability of the restriction of consequence to atomic formulas by structural rules only. The restriction to atomic formulas relieves the need to concern logical rules in the (...) derivation. (shrink)

We present an embedding of the Lambek–Grishin calculus into an extension of the nonassociative Lambek calculus with negation. The embedding is based on the De Morgan interpretation of the dual Grishin connectives.

This book presents the proceedings of the 2nd Karl Schwarzschild Meeting on Gravitational Physics, focused on the general theme of black holes, gravity and information. Specialists in the field of black hole physics and rising young researchers present the latest findings on the broad topic of black holes, gravity, and information, highlighting its applications to astrophysics, cosmology, particle physics, and strongly correlated systems.

The uniqueness of Poland’s experience with the 2020 coronavirus lays in the interplay of two factors: the decisive governmental response to the pandemic, and the overlap of the pandemic with the country’s presidential election scheduled on May 10, 2020. The government’s fast reaction, combined with the citizens’ discipline, resulted in the suppression of the virus’s spread. The ratings of the current President Duda skyrocketed well above 50% needed for re-election in the first round. However, the expectation was that they would (...) be going down with the pandemic and lockdown fatigue. For almost two months, the government tried to organize the elections under the normal schedule while the opposition tried to block them. Finally, the opposition won, and the elections were rescheduled on June 28, with the President Duda’s ratings substantially lower. Nevertheless, in the runoff on July 11, Duda won. Our conclusion goes against the common opinion that electoral engineering is always one-sided. The reconstruction of the pre-electoral political maneuvers shows that many independent players were simultaneously involved in complex engineering, and that the final outcome was hard to predict until almost the very end. (shrink)

Backward induction was one of the earliest methods developed for solving finite sequential games with perfect information. It proved to be especially useful in the context of Tom Schelling’s ideas of credible versus incredible threats. BI can be also extended to solve complex games that include an infinite number of actions or an infinite number of periods. However, some more complex empirical or experimental predictions remain dramatically at odds with theoretical predictions obtained by BI. The primary example of such a (...) troublesome game is Centipede. The problems appear in other long games with sufficiently complex structure. BI also shares the problems of subgame perfect equilibrium and fails to eliminate certain unreasonable Nash equilibria. (shrink)

We present an axiomatization of the non-associative Lambek calculus extended with classical negation for which the frame semantics with the classical interpretation of negation is sound and complete.

In lieu of an abstract, here is a brief excerpt of the content:684 Feminist Studies 43, no. 3. © 2017 by Feminist Studies, Inc. Megan Kaminski This Century This century is full-on burning the past past carrying back lost to re-memory the year brings millennial want: a bright new coat red shoes an end to oil pipelines and student loans encase us all in warmth not waged labor drab curtains pulled aside reveal window onto window echo us many permutations bring (...) responses wrought and metaled down empty that treasury steal back from church coffers there is something that binds more than moth-eaten sweaters more than stripped-soled shoes we wanting we to mean banks burning profits redistributed we holding the soft hands of we Megan Kaminski 685 This Century This century is not so good filled with tsunamis and snowstorms people displaced by capital and rising waters threaten to make even Kansas beach-front I’d like to stick a fork in the eye of the governor and the Koch brothers too help liberate people from bad shit minimum wage jobs and medical bills give all of us something real to be happy about like city parks clean water and a few fewer grams of rocket fuel in the arugula cats sunning themselves on warm days no old dudes wanting to mess with my uterus and a new sundress trimmed with ribbon This Century This century makes me say things about burning and baddies and whether poetry can really do much of anything unacknowledged legislator or just a lady ass atrophying perched in front of a laptop this century makes me write about changing and loving all of you and getting closer with warm-nosed nudges under your chin embraces while wearing my softest of sweaters these poems want to get out of my chair out of the house and the neighborhood out of capital and with people in favor of all of us animals and plants 686 Megan Kaminski This Century This century takes place in the streets in living rooms of friends in shared words exchanged across borders bridging the distance between you and me and we and ours and taking from board rooms and markets this century is full of things eroding making way for bodies for gardens for libraries for a commoning a burning of gates and fences and debts we spring forth in multitudes occupy more than street corners cordoned off we singing we and the streets the open fields... (shrink)

We deal with the modal logic of cluster-decomposable Kripke interpretations, present an axiomatization, and prove some additional results regarding this logic.

These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the 140th anniversary of Schwarzschild's birth. They are grouped into 4 main themes: I. The Life and Work of Karl Schwarzschild; II. Black Holes in Classical General Relativity, Numerical Relativity, Astrophysics, Cosmology, and Alternative Theories of Gravity; III. Black Holes in Quantum Gravity and String Theory; IV. Other Topics in Contemporary Gravitation. Inspired by the foundational principle ``By (...) acknowledging the past, we open a route to the future", the week-long meeting, envisioned as a forum for exchange between scientists from all locations and levels of education, drew participants from 15 countries across 4 continents. In addition to plenary talks from leading researchers, a special focus on young talent was provided, a feature underlined by the Springer Prize for the best student and junior presentations. (shrink)