Proof-Theoretic Foundations of Intensional Semantics. Counterfactuals of belief and knowledge

当代的内涵语义学建立在模型论的基础上。该项目的总体科学目标是为内涵语义的证明理论基础的发展做出贡献，并探索该贡献的逻辑、语义和哲学成果。这个项目的更新旨在为形式为“如果是a的情况，那么它将是B的情况”的反事实发展一种证明理论语义，这是普通和科学反事实推理的核心。语义学要与可证明性真理的直觉主义概念一致。此外，它的基础将是自给自足的。具体来说，它不应该依赖于基于模型理论语义定义的证明系统。鉴于反事实的逻辑和语义目前几乎完全是根据扩展或预设经典逻辑的形式系统来研究的，该项目进入了一个几乎未开发的领域。在先前工作的基础上，重点将局限于将反事实条件句与语气动词“相信”和“知道”结合起来的结构。

Contemporary intensional semantics rests on model-theoretic foundations. The overall scientific objective of the project is to contribute to the development of proof-theoretic foundations for intensional semantics and to explore the logical, semantic, and philosophical fruitfulness of the contribution. The renewal of this project aims at developing a proof-theoretic semantics for counterfactuals of the form 'If it were the case that A, then it would be the case that B' which are central to ordinary and scientific counterfactual reasoning. The semantics is to be in agreement with an intuitionistic conception of truth as provability. Moreover, it is to be autarkic with respect to its foundations. Specifically, it should not rest on a proof system that is defined on the basis of a model-theoretic semantics. Given the fact that the logic and semantics of counterfactuals is currently almost exclusively studied in terms of formal systems which extend or presuppose classical logic, the project enters an almost unexplored area. Building on previous work, the focus will be confined to constructions which combine counterfactual conditionals with the intensional attitude verbs 'believe' and 'know'.