We introduce an effective translation from proofs in the display calculus to proofs in the labelled calculus in the context of tense logics. We identify the labelled calculus proofs in the image of this translation as those built from labelled sequents whose underlying directed graph possesses certain properties. For the basic normal tense logic Kt, the image is shown to be the set of all proofs in the labelled calculus G3Kt.

We introduce translations between display calculus proofs and labeled calculus proofs in the context of tense logics. First, we show that every derivation in the display calculus for the minimal tense logic Kt extended with general path axioms can be effectively transformed into a derivation in the corresponding labeled calculus. Concerning the converse translation, we show that for Kt extended with path axioms, every derivation in the corresponding labeled calculus can be put into a special form that is translatable to (...) a derivation in the associated display calculus. A key insight in this converse translation is a canonical representation of display sequents as labeled polytrees. Labeled polytrees, which represent equivalence classes of display sequents modulo display postulates, also shed light on related correspondence results for tense logics. (shrink)

It is shown that Gqp↑, the quantified propositional Gödel logic based on the truth-value set V↑ = {1 - 1/n : n≥1}∪{1}, is decidable. This result is obtained by reduction to Büchi's theory S1S. An alternative proof based on elimination of quantifiers is also given, which yields both an axiomatization and a characterization of Gqp↑ as the intersection of all finite-valued quantified propositional Gödel logics.

My essay will take as its point of departure the paragraph from Gershom Scholem’s “Reflections on Jewish Theology,” in which he depicts the modern religious experience as the one of the "void of God" or as "pious atheism". I will first argue that the "void of God" cannot be reduced to atheistic non-belief in the presence of God. Then, I will demonstrate the further development of the Scholemian notion of the ‘pious atheism’ in Derrida, especially in his Lurianic treatment of (...) Angelus Silesius, whose modern mysticism emerges in Derrida’s reading as the ‘almost-atheism’. The interesting feature of this development is that, while for Scholem, the ‘void of God’ is a predominantly negative experience, for Derrida, it becomes an affirmative model of modern – not just Jewish, but more generally, Abrahamic – religiosity which, on the one hand, touches upon atheistic non-belief in the divine presence here and now, yet, on the other, still insists on commemorating the ‘withdrawn God’ through his ‘traces.’ What, therefore, for Scholem, constitutes the ultimate cry of despair, best embodied in Kafka’s work – for Derrida, reveals the more positive face of the modern predicament in which God has absented himself in order to make room for the creaturely reality. And while Scholem envisages redemption as the full restoration of the divine presence – Derrida redefines redemption as the ‘pious’ work of deconstruction to be undertaken in the ‘almost-atheistic’ condition of irreversible separation between God and the world. (shrink)

Obóz Kultury 2.0 Mirosław Filiciak, Alek Tarkowski, Agata Jałosińska, Andrzej Klimczuk, Maciej Rynarzewski, Jacek Seweryn, Stunża M., D. Grzegorz, Marcin Wilkowski & Anna Orlik .

All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.