Abstract
We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the form if not-A, then A, should not hold, since the conditional’s antecedent not-A contradicts its consequent A. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event \({A| \overline{A}}\) is \({p(A| \overline{A})=0}\). In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles: Aristotle’s theses, Aristotle’s Second Thesis, Abelard’s First Principle, and Boethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (like non-symmetry). Both approaches satisfy minimal requirements for a connexive logic. Finally, we compare both approaches conceptually.
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Acknowledgements
Thanks to the anonymous reviewers for their comments and useful suggestions. Niki Pfeifer was supported by the BMBF project 01UL1906X. Giuseppe Sanfilippo is supported by the FFR 2023 project of University of Palermo, Italy and is also affiliated with the INdAM-GNAMPA Research Group, Italy.
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Pfeifer, N., Sanfilippo, G. Connexive Logic, Probabilistic Default Reasoning, and Compound Conditionals. Stud Logica 112, 167–206 (2024). https://doi.org/10.1007/s11225-023-10054-5
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DOI: https://doi.org/10.1007/s11225-023-10054-5