Abstract
We present VINTE, a theorem prover for conditional logics for counterfactual reasoning introduced by Lewis in the seventies. VINTE implements some internal calculi recently introduced for the basic system \(\mathbb {V}\) and some of its significant extensions with axioms \(\mathbb {N}\), \(\mathbb {T}\), \(\mathbb {C}\), \(\mathbb {W}\) and \(\mathbb {A}\). VINTE is inspired by the methodology of 
and it is implemented in Prolog. The paper shows some experimental results, witnessing that the performances of VINTE are promising.
Supported by the Project TICAMORE ANR-16-CE91-0002-01, by the EU under Marie Skłodowska-Curie Grant Agreement No. [660047], and by the Project “ExceptionOWL”, Università di Torino and Compagnia di San Paolo, call 2014.
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Notes
- 1.
It is worth noticing that in turn the connective \(\preccurlyeq \) can be defined in terms of
. - 2.
Employing this notation, satisfiability of a \( \preccurlyeq \)-formula in a model becomes the following: \(x \Vdash A\preccurlyeq B \) iff for all
. \( \alpha \Vdash ^{\forall } \lnot B \) or \( \alpha \Vdash ^{\exists } A \). - 3.
It is worth noticing that absoluteness can be equally stated as local absoluteness:
it holds 
. - 4.
It is worth noticing that this translation introduces an exponential blowup.
.
. 
it holds 
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Girlando, M., Lellmann, B., Olivetti, N., Pozzato, G.L., Vitalis, Q. (2017). VINTE: An Implementation of Internal Calculi for Lewis’ Logics of Counterfactual Reasoning. In: Schmidt, R., Nalon, C. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2017. Lecture Notes in Computer Science(), vol 10501. Springer, Cham. https://doi.org/10.1007/978-3-319-66902-1_9
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