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Journal of Philosophical Logic
Article . 1988 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Article . 1988
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On the logic of ability

Authors: Mark A. Brown;

On the logic of ability

Abstract

It has been argued by philosophers that the `can' expressing a person's ability cannot be considered as a modal operator since it violates the characteristic laws of even the weakest \(\diamond\)-logics, in particular: \(\diamond (AvB)\to (\diamond Av\diamond B)\). (``I am able to draw a card which will have one of the colors red or black, but I cannot draw a red card, and I cannot draw a black card'', p. 2). The author suggests, however, to make the `can' of ability amenable to logical treatment by extending the standard possible worlds-semantics to so-called minimal models in which one has instead of the usual accessability relation, R, a ``relevance relation between a world and a set of possible worlds'' (p. 3). The truth-condition runs as follows: `X can bring it about that A' ``will be true at a given world iff there exists a relevant cluster of worlds, at every world of which A is true'' (p. 5). This semantic analysis reveals that the `can' of ability contains some elements of an ordinary \(\diamond -\) but also some of an ordinary \(\square\)-operator. In the formal part of the paper (pp. 8-22), axiom-systems, corresponding semantic requirements, and completeness-proofs are presented.

Related Organizations
Keywords

ability, minimal models, Philosophical and critical aspects of logic and foundations, Modal logic (including the logic of norms), relevance relation, modal logic

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
68
Top 10%
Top 1%
Top 10%
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