
doi: 10.1007/bf00249673
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.
ability, minimal models, Philosophical and critical aspects of logic and foundations, Modal logic (including the logic of norms), relevance relation, modal logic
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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