Abstract
In [1] the modal interpreted language MLv is introduced. It is based on the type system τv that has v individual types and involves all finite levels; and for MLv, quantification and predication are over concepts, i.e. over intensions. In addition, in [1], the modal calculus MCv based on MLv is introduced and developed. By these means, the basic notions of the probability calculus, such as the probability pr(φ,ψ) of the wff(well formed formula) ψ relative to the wff φ, and the ternary relation φ⋺ p ψ(φ implies ψ with the probability p), substantially introduced by Reichenbach in [12], can be dealt with on the basis of MCv, admittedly in a rather indirect way — cf. [3], [5].
This paper has been prepared in the sphere of activity of the C.N.R.(Consiglio Nazionale delle Ricerche) for the academic year 1977–78.
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Bressan, A. (1981). Extensions of the Modal Calculi MCv and MC∞. Comparison of them with Similar Calculi Endowed with Different Semantics. Application to Probability Theory. In: Mönnich, U. (eds) Aspects of Philosophical Logic. Synthese Library, vol 147. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8384-7_2
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