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Local and global metrics for the semantics of counterfactual conditionals

Local and global metrics for the semantics of counterfactual conditionals The semantics for counterfactual conditionals employs indexed relations ⁢a between possible worlds, with x >a y read intuitively as «x is closer to a than is y». This paper considers the question how far these different «closeness» relations of a model may be derived from a common source. Despite some well-known negative observations, we show that there is also quite a strong positive answer. Our main result is that for any model equiped with modular relations derived from multiple metrics da via the equation x ⁢a y iff da(a, x) ⁢ da(a, y), there is a model that validates exactly the same formulae of the logic of counterfactuals, and whose relations ⁢a are determined by a common metric d, via the equation x ⁢a y iff da(a, x) ⁢da(a, y). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied Non-Classical Logics Taylor & Francis

Local and global metrics for the semantics of counterfactual conditionals

Local and global metrics for the semantics of counterfactual conditionals

Abstract

The semantics for counterfactual conditionals employs indexed relations ⁢a between possible worlds, with x >a y read intuitively as «x is closer to a than is y». This paper considers the question how far these different «closeness» relations of a model may be derived from a common source. Despite some well-known negative observations, we show that there is also quite a strong positive answer. Our main result is that for any model equiped with modular...
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Publisher
Taylor & Francis
Copyright
Copyright Taylor & Francis Group, LLC
ISSN
1958-5780
eISSN
1166-3081
DOI
10.1080/11663081.1994.10510829
Publisher site
See Article on Publisher Site

Abstract

The semantics for counterfactual conditionals employs indexed relations ⁢a between possible worlds, with x >a y read intuitively as «x is closer to a than is y». This paper considers the question how far these different «closeness» relations of a model may be derived from a common source. Despite some well-known negative observations, we show that there is also quite a strong positive answer. Our main result is that for any model equiped with modular relations derived from multiple metrics da via the equation x ⁢a y iff da(a, x) ⁢ da(a, y), there is a model that validates exactly the same formulae of the logic of counterfactuals, and whose relations ⁢a are determined by a common metric d, via the equation x ⁢a y iff da(a, x) ⁢da(a, y).

Journal

Journal of Applied Non-Classical LogicsTaylor & Francis

Published: Jan 1, 1994

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