Counterfactual Logic: A Modern Overview
Date
2024-01-26
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Abstract
Lewis (1973) described a family of logics for reasoning about counterfactual statements. These logics also contained additional connectives for reasoning about comparative possibility statements and modalities. Moreover, Lewis described a possible world semantics involving a ``sphere system'' that effectively lets you talk about some worlds being more ``similar'' to a given world than others. The resulting theory is very powerful and flexible in many ways similar to the theory of normal modal logics. Unfortunately, Lewis provided an extremely terse formal description of the theory with many important theorems, definitions, and details omitted or described vaguely. There are no other resources that present a complete formal description of this theory. Without this formal description one is unable to propose new logics in this family and prove soundness and completeness theorems for them. To remedy this, we present a reformulation of Lewis' theory using modern methods and notation. All definitions are described formally and all core results are proven in explicit detail. We include an informal overview of the different kinds of statements associated with each connective. The semantics is reformulated in terms of frames. The syntax includes additional rules and theorems to make it easier to use. Both the soundness and the strong soundness theorems are proven. The completeness theorem uses canonical models and the entire construction is shown explicitly. The first edition of Counterfactuals (Lewis, 1973) had an error exposed by Krabbe (1978) that led to the second edition (Lewis, 2001) having a more complex definition. So we present a reformulation of Krabbe's construction within our modernized setting.
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Keywords
counterfactual logic, counterfactuals, David Lewis, comparative possibility, possible world semantics, modal logic, logic, sphere semantics
Citation
Rios Flores, M. (2024). Counterfactual logic: a modern overview (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.