Indicative Conditionals: Some Algebraic Considerations

Umberto Rivieccio

doi:10.1007/978-3-031-99536-1_8

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Indicative Conditionals: Some Algebraic Considerations

2026-01-01

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Umberto Rivieccio *

Miguel Muñoz Pérez

DOI：10.1007/978-3-031-99536-1_8

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Abstract

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We consider a family of non-classical three-valued logics that have been proposed to model indicative conditionals - sentences of the if-then type that occur in natural language, and concern what could be true (as opposed to counterfactuals, which concern eventualities that are no longer possible). Among these, we study the systems introduced by B. De Finetti, W.S. Cooper, J. Cantwell and R.J. Farrell, as well as some variants that have not appeared in the literature but seem nevertheless to be natural objects of interest from a formal point of view. We determine which of these logics are algebraizable (in the sense of Blok and Pigozzi), providing for the corresponding algebraic counterparts equational presentations from which finite Hilbert-style calculi can be readily obtained. Even in the non-algebraizable cases we indicate how algebraic techniques may be employed to obtain further semantical insight into the logics and axiomatizations. In the concluding section we point to possible extensions of the present work, such as further analysis of the relevant classes of algebras via twist-structure representations.

Keywords:

Indicative conditionals

Algebraizability

Axiomatization

Algebraic semantics

Connexive logics

Twist-structures