Abstract
We present a new semantics for first-order conditional logic, which is a generalization of that of Friedman, Halpern and Koller [7]. We utilize Fitting’s embedding of first-order classical logic in first-order S4 to define our semantics. We explain our semantics by showing how it works on the connective expressing “typically implies”. We argue that it has a number of good properties, in particular, it is more adjustable to special situations than that of [7]. For example, we can make sense of nested conditional implications even when a conditional implication does not necessarily hold on the entire set of possible worlds, but where-ever it is satisfied, the conclusion is typically satisfied.
G. Bana—Part of the work was done while G. Bana was at the University of Luxembourg supported by FNR under the PolLux project VoteVerif (POLLUX-IV/1/2016).
M. Okada was supported by JSPS-AYAME, KAKENKI 17H02265, 17H02263, 19KK0006, and 21H00467.
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Notes
- 1.
This kind of semantics is called “subjective conditionals” in [7], as a hierarchy on the sets of possible worlds indicate what typical is and what atypical is, as opposed to “statistical conditional” where the hierarchy is defined on the domain of interpretation.
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Bana, G., Okada, M. (2021). A Semantics for “Typically” in First-Order Default Reasoning. In: Okazaki, N., Yada, K., Satoh, K., Mineshima, K. (eds) New Frontiers in Artificial Intelligence. JSAI-isAI 2020. Lecture Notes in Computer Science(), vol 12758. Springer, Cham. https://doi.org/10.1007/978-3-030-79942-7_1
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