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A Gentzen- or Beth-type system, a practical decision procedure and a constructive completeness proof for the counterfactual logics VC and VCS

Published online by Cambridge University Press:  12 March 2014

H. C. M. de Swart
H. C. M. de Swart*
Affiliation:
Catholic University in Tilburg, Tilburg, The Netherlands
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Extract

In [1] and [2] D. Lewis formulates his counterfactual logic VC as follows. The language contains the connectives ∧, ∨, ⊃, ¬ and the binary connective ≤. A ≤ B is read as “A is at least as possible as B”. The following connectives are defined in terms of ≤.

A < B: = ¬(B ≤ A) (it is more possible that A than that B).

◊ A ≔ ¬(⊥ ≤ A) (⊥ is the false formula; A is possible).

□ A ≔ ⊥ ≤ ¬A (A is necessary).

(if A were the case, then B would be the case).

(if A were the case, then B might be the case).

and are two counterfactual conditional operators. (AB) iff ¬(A ¬B).

The following axiom system VC is presented by D. Lewis in [1] and [2]: V: (1) Truthfunctional classical propositional calculus.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 1 , March 1983 , pp. 1 - 20
Copyright
Copyright © Association for Symbolic Logic 1983

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References

REFERENCES

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