We provide tools for a concise axiomatization of a broad class of quantifiers in many-valued logic, so-called distribution quantifiers. Although sound and complete axiomatizations for such quantifiers exist, their size renders them virtually useless for practical purposes. We show that for quantifiers based on finite distributive lattices compact axiomatizations can be obtained schematically. This is achieved by providing a link between skolemized signed formulas and filters/ideals in Boolean set lattices. Then lattice theoretic tools such as Birkhoff's representation theorem for finite (...) distributive lattices are used to derive tableau-style axiomatizations of distribution quantifiers. (shrink)

Recent years have been blessed with an abundance of logical systems, arising from a multitude of applications. A logic can be characterised in many different ways. Traditionally, a logic is presented via the following three components: 1. an intuitive non-formal motivation, perhaps tie it in to some application area 2. a semantical interpretation 3. a proof theoretical formulation. There are several types of proof theoretical methodologies, Hilbert style, Gentzen style, goal directed style, labelled deductive system style, and so on. The (...) tableau methodology, invented in the 1950s by Beth and Hintikka and later per fected by Smullyan and Fitting, is today one of the most popular, since it appears to bring together the proof-theoretical and the semantical approaches to the pre of a logical system and is also very intuitive. In many universities it is sentation the style first taught to students. Recently interest in tableaux has become more widespread and a community crystallised around the subject. An annual tableaux conference is being held and proceedings are published. The present volume is a Handbook a/Tableaux pre senting to the community a wide coverage of tableaux systems for a variety of logics. It is written by active members of the community and brings the reader up to frontline research. It will be of interest to any formal logician from any area. (shrink)

Approaching the Ovidian story of Pygmalion, scholars mainly focus on the moment in which the artist carves his ideal woman out of ivory. But the reasons that led him to sculpt the statue tend to remain in the background. Ovid informs us that, before giving toeburthe shape of auirgo, the ‘Paphian hero’ (Met. 10.290), shocked by the lascivious conduct of the Propoetides, had declared war on the whole of womankind (Met. 10.238–46):sunt tamen obscenae Venerem Propoetides ausaeesse negare deam; pro quo (...) sua numinis iracorpora cum forma primae uulgasse feruntur;utque pudor cessit, sanguisque induruit oris,in rigidum paruo silicem discrimine uersae.quas quia Pygmalion aeuum per crimen agentesuiderat, offensus uitiis, quae plurima mentifemineae natura dedit, sine coniuge caelebsuiuebat thalamique diu consorte carebat. (shrink)

This essay critically analyzes two dominant narratives that explain and lament the rise of Donald Trump in the United States. First, I extend Jill Locke’s (2016) concept of “The Lament that Shame is Dead" to show the limitations of criticizing Trump in terms of the “death of shame.” I then turn my attention to the problems inerent in recent characterizations of Trump as a petulant child. Drawing from Locke (2016) on shame and Freud (1914) and Lee Edelman (2004) on the (...) politics of “the child,” I argue that characterizing Trump as shameless, childish, or as a shameless child only affirms, rather than deposes, Trump’s right-wing populist strategy and keeps the focus on him as a personality rather than on the broader social and political context in which he emerged. I argue this has implications for the rise of right-wing populism in the West, more broadly. (shrink)

…vel quod res omnes timide gelideque ministrat, dilator, † spe longus, iners avidusque futuri, diffcilis, querulus… I agree with Brink, and other editors referred to by him ad loe, that spe longus in Horace's description of the typical old man's character cannot be made to give sense. For earlier attempts at emendation, see Brink's note . Most of those who have tried to emend the passage concentrate on longus, and are reluctant to relinquish spe: this is largely due to the (...) parallel with Aristotle's account of the character of old men in Rhetoric 2. 13. 1389b 13ff., in which they are said to be, among other things it seems to me that this parallel should not be pressed too far. There is much in Aristotle that is not in Horace, and nothing to suggest close and detailed dependence. The parallel can only be relevant if spe longus can be turned into a reasonable Latin equivalent for Otherwise there is no good reason to suppose that spe is any less likely to be corrupt than longus. (shrink)

…vel quod res omnes timide gelideque ministrat,dilator, † spe longus, iners avidusque futuri,diffcilis, querulus…I agree with Brink, and other editors referred to by him ad loe, that spe longus in Horace's description of the typical old man's character cannot be made to give sense. For earlier attempts at emendation, see Brink's note. Most of those who have tried to emend the passage concentrate on longus, and are reluctant to relinquish spe: this is largely due to the parallel with Aristotle's account (...) of the character of old men in Rhetoric 2. 13. 1389b 13ff., in which they are said to be, among other things it seems to me that this parallel should not be pressed too far. There is much in Aristotle that is not in Horace, and nothing to suggest close and detailed dependence. The parallel can only be relevant if spe longus can be turned into a reasonable Latin equivalent for Otherwise there is no good reason to suppose that spe is any less likely to be corrupt than longus. (shrink)