Counterfactual Logic: A Modern Overview

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dc.contributor.advisorBauer, Kristine
dc.contributor.advisorZach, Richard
dc.contributor.authorRios Flores, Mohamar
dc.contributor.committeememberCunningham, Clifton
dc.contributor.committeememberPayette, Gillman
dc.date2024-05
dc.date.accessioned2024-01-30T19:23:05Z
dc.date.available2024-01-30T19:23:05Z
dc.date.issued2024-01-26
dc.description.abstractLewis (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.
dc.identifier.citationRios Flores, M. (2024). Counterfactual logic: a modern overview (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.
dc.identifier.urihttps://hdl.handle.net/1880/118138
dc.identifier.urihttps://doi.org/10.11575/PRISM/42982
dc.language.isoen
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgary
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectcounterfactual logic
dc.subjectcounterfactuals
dc.subjectDavid Lewis
dc.subjectcomparative possibility
dc.subjectpossible world semantics
dc.subjectmodal logic
dc.subjectlogic
dc.subjectsphere semantics
dc.subject.classificationMathematics
dc.titleCounterfactual Logic: A Modern Overview
dc.typemaster thesis
thesis.degree.disciplineMathematics & Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.thesis.accesssetbystudentI do not require a thesis withhold – my thesis will have open access and can be viewed and downloaded publicly as soon as possible.
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