Mercoledì 15 maggio 2024 ore 10.00
Dipartimento di Lettere e Filosofia
via della Pergola 60 - Firenze
Sala Altana
Leonardo Ceragioli (Università di Pisa)
Semantic Pollution for Modal and Classical Logic
Abstract: According to Negri, the old problem of finding good proof-systems for modal logics can be partially solved if labeled sequent calculi are accepted. However, these systems are sometimes considered inferentially unacceptable because polluted by their reference to Kripke’s frames. The status of implicitly polluted systems like Poggiolesi’s tree-hypersequents is another open issue in this debate. I will evaluate both explicit and implicit criteria of semantic pollution, and conclude that we need a different characterization of this notion, one not directly connected with the existence of isomorphisms between proof-systems and semantic structures. I will then make a proposal by comparing different formulations of classical sequent calculi.
Giuliano Rosella (Università di Torino)
New Frontiers in Counterfactuals
Abstract: Counterfactuals, statements like "if A were true, then B would be true," are central to many fields, including artificial intelligence, where they help explain cause-and-effect relationships. Hence, developing a framework for reasoning about counterfactuals is crucial. Traditionally, Lewis and Stalnaker semantics have been seen as competing theories for understanding counterfactuals; they both define a counterfactual "If A were the case then B would be the case" as true if B holds in the closest world to ours where A is true. However, depending on the specification of the similarity measure, Stalnaker's theory validates some logical principles that Lewis' does not.
This work challenges the traditional view and proposes a different perspective, arguing that Lewis and Stalnaker's theories are complementary and can be unified within a more expressive framework. We show that Lewis's similarity-based account can be seen as a special case arising from a deeper Kripke-Stalnaker-style semantics. By interpreting Lewis counterfactuals as a modality of Stalnaker conditionals, we achieve a unified theory. This has significant philosophical implications, suggesting a new interpretation of Lewis counterfactuals and potentially revealing misleading aspects of current conditional logics.
We then explore the ramifications for quantifying uncertainty in counterfactuals and their probability, a major open question in the current literature. We demonstrate that their uncertainty follows a non-standard measure based on Dempster-Shafer theory.
(this works is based on joint papers with Tommaso Flaminio and Stefano Bonzio, and Jan Sprenger)