Year: 2025
Type: article
Abstract: It is shown that one common formulation of Stalnaker’s semantics for conditionals is incomplete: it has no sound and (strongly) complete proof system. At first, this seems to conflict with well-known completeness results for this semantics (e.g., Stalnaker and Thomason 1967, Stalnaker 1970 and Lewis 1973, ch. 6). As it turns out, it does not: these completeness results rely on another closely-related formulation of the semantics that is provably complete. Specifically, the difference comes down to how the Limit Assumption is stated. I close with some remarks about what this means for the logic of conditionals.
Source: Erkenntnis
Author: Alexander W. Kocurek
Institution: University of California San Diego
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,290
Funder: Australian Research Council
Award: A Unified Theory of 'If's
OpenAlex ID: W4407674182