皆様
東北大の横山です． 直前のご案内になりまして恐縮ですが，以下の通りセミナーを開催いたしますのでご案内いたします．
https://sites.google.com/view/sendai-logic/
日時：8月29日(火) 15:00- 場所：東北大学理学研究科合同A棟803号室 (当日はzoom配信を実施予定です． zoomにて参加を希望される方は，五十里さん([email protected])までご連絡ください)
講演者：仁木哲 (ルール大学ボーフム)
題目： How can an intuitionistic logician understand connexive constructible falsity?
概要： Constructivists have usually understood negation as an implication to absurdity. Nonetheless, there have also been dissenting voices to this conception, one of the most notable among which are ones who advocate an alternative notion called constructible falsity. Nels David Nelson (1918-2003) introduced this notion as a `strong’ form of negation, which provides a direct counter-example to its negand. This `strongness’ is however often eschewed in favour of paraconsistency, making the resulting negation, severed of its relationship with intuitionistic negation, harder for intuitionistic logicians to comprehend. The issue is more serious in a variant of constructible falsity introduced by Heinrich Wansing, which validates so-called `connexive’ principles. This is due to the provability of a contradictory pair of formulas, which prohibits an interpretation of it as a `strong’ negation without bringing triviality. As a result, Wansingian negation should appear even more mysterious to the eyes of intuitionistic logicians. Another way to relate intuitionistic and Wansingian negations is to accept the law of excluded middle for the latter, as studied by Wansing and Hitoshi Omori. This move, however, compromises constructivity, and therefore is perhaps not so preferable either. In this talk, I will try to shed some lights on this issue, by discussing other ways to introduce an interaction between intuitionistic and Wansing negations. I will compare relative advantages of the interactions, which may enable intuitionistic logicians to better understand Wansingian negation and its connexivity.
どうぞよろしくお願いいたします．
横山啓太