This will be a joint session together with the NihiL seminar.
Speakers: Yanjing Wang and Zilu Wang (Peking University)
Date and Time: Tuesday, September 26th 2023, 14:00-15:30 (NOTE the unusual day and time)
Venue: hybrid! KdVI seminar room F3.20 in Science Park 107 and the zoom link of the NihiL seminar: https://uva-live.zoom.us/j/87618965843
Title: A Bundled Approach to Deontic Logic
Abstract. In this talk, we will introduce a new semantic approach to deontic logic based on the so-called bundled modalities, which essentially pack a quantifier and a modality together. Our starting point is the observation that many “strange” logical behaviors of modalities and logical connectives in natural language are due to the fact that they have more complicated inner logical structures in the semantics. Many examples can be found in epistemic logics of know-wh, where the know-wh modalities often have the implicit ∃x structure based on the mention-some interpretation. As the logical puzzles are abundant in deontic logic, a natural question arises for us: are there also some bundles hidden in the deontic modalities? In fact, the possibilities of viewing permissions and obligations as bundles were informally discussed by Hintikka in the early days of deontic logic. For example, Hintikka proposed to understand permission as a bundle of ∀x◇, i.e., an action type α is permitted iff every token of α is executable on some deontically ideal world. Given the techniques of the bundled modalities, we can flesh out this proposal formally, which results in a desirable logic of free-choice permission satisfying most of the intuitive properties. Moreover, this semantics also predicts new logical behaviors not yet discussed in the literature. For example, according to our semantics, one of the four distributive laws of conjunction and disjunction is invalid, which aligns with our linguistic intuition. Besides the bundled modalities, our approach also features the Brouwer-Heyting-Kolmogorov (BHK) style treatment of propositions as action types inspired by intuitionistic logic. This opens the possibility of fine-grained control of the composition of action types in terms of non-classical connectives. It also reveals the subtleties behind the negation, conjunction, and implication in deontic logic. We will end with a discussion on higher-order permissions that can be treated in our approach by allowing nested permission modalities in the language.