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Normal bimodal logics of ability and action

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Abstract

The basic bimodal systemK/K can be interpreted as an analysis of the logic of ability developed in [1]. Where in [1] we would express the claimI can bring it about that P using the formula

, with its non-normal operator

, we will now use the formula

. Here

is a normal alethic possibilitation operator.

is a normal necessitation operator, but it is independent of

, and not subject to an alethic interpretation. Rather,

is interpreted to meanI bring it about that P. The result is a simplification and clarification of a combined logic of ability and action like that in [2], but employing only normal operators.

A number of extensions of the basic systemK/K are constructed, first by strengthening the two normal sublogics independently and then by linking the two sublogics via axiom schemata involving both operators. The result is a series of increasingly strong systems which more and more adequately fulfill our expectations for a satisfactory logic of action and ability.

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Authors and Affiliations

  1. Philosophy Department, Syracuse University, 13244, Syracuse, NY, USA

    Mark A. Brown

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  1. Mark A. Brown
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Additional information

I am grateful to Valentin Goranko, David K. Lewis, Marion Sarkis Mircheva, and Solomon Passy for helpful discussions and correspondence on these topics.

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Brown, M.A. Normal bimodal logics of ability and action. Stud Logica 51, 519–532 (1992). https://doi.org/10.1007/BF01028973

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  • DOI: https://doi.org/10.1007/BF01028973

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