Global Expression for Canonical RulesRohan French (University of California, Davis)
Rohan French (UC Davis) will present "Global Expression for Canonical Rules", at 11 on 24 August in Old Arts 209.
Abstract: Say that a set of valuations V is a global model of a rule if, whenever all the premises of the rule hold on all valuations in V, the conclusion of the rule also holds on every valuation in V. Say that a natural deduction rule globally expresses some property of sets of valuations V just in case the sets of valuations V which have the property in question are precisely those which are global models of that rule. According to James Garson the properties which are globally expressed by natural deduction rules have some claim to capturing the meanings on the connectives they govern. His discussion of the kinds of properties which are globally expressed by natural deduction rules is largely limited to discussion of a few problem cases (notably involving disjunction and negation). Here we give, for a limited class of rules---what Arnon Avron calls `canonical rules'---a uniform procedure for associating with a given rule a condition which it globally expresses, and use the conditions so determined in order to look at the prospects for providing a Garson-style semantic treatment for connectives governed by such rules.
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