Mark Norris Lance and Philip Kremer
نویسندگان
چکیده
'Entailment' can be said in many ways. In the present paper, we sketch a linguistic theory which motivates taking 'A entails B' to mean 'commitment to A is, in part, commitment to B', and we present four formal systems designed to capture this concept. These four systems turn out (somewhat surprisingly) to be the strict implicational fragments of the modal logics K, T, K4, and $4 (see Hughes and Cresswell 1984), although the motivation is not "modal" in any standard sense. (We note that, though we believe the relevance of A to B cannot be ignored in a final analysis of 'commitment to A is, in part, commitment to B', these systems are not "relevance" systems, in the sense of Anderson and Belnap 1975. We address relevance in "The Logical Structure of Linguistic Commitment II".) We proceed as follows: w 1: We discuss the appropriateness of calling a logical system (or a logic of entailment) the correct logical system (or logic of entailment).
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