Replacement in Logic

被引:5
作者
Humberstone, Lloyd [1 ]
机构
[1] Monash Univ, Dept Philosophy, Clayton, Vic 3800, Australia
关键词
Consequence relations; Classical logic; Intuitionistic logic; Modal logic; Identity; Contexts; Replacement; CONDITIONALS;
D O I
10.1007/s10992-011-9212-4
中图分类号
B81 [逻辑学(论理学)];
学科分类号
010104 ; 010105 ;
摘要
We study a range of issues connected with the idea of replacing one formula by another in a fixed (linguistic) context. The replacement core of a consequence relation aS cent is the relation holding between a set of formulas {A (1), ..., A (m) , ...} and a formula B when for every context C(center dot), we have C(A (1)), ..., C(A (m) ), ... aS cent aEuro parts per thousand C(B). Section 1 looks at some differences between which inferences are lost on passing to the replacement cores of the classical and intuitionistic consequence relations. For example, we find that while the inference from A and B to , sanctioned by both these initial consequence relations, is retained on passage to the replacement core in the classical case, it is lost in the intuitionistic case. Further discussion of these two (and some other) logics occupies Sections 3 and 4. Section 2 looks at the m = 1 case, describing A as replaceable by B according to aS cent when B is a consequence of A by the replacement core of aS cent, and inquiring as to which choices of aS cent render this induced replaceability relation symmetric. Section 5 investigates further conceptual refinements- such as a contrast between horizontal and vertical replaceability-suggested by some work of R. B. Angell and R. Harrop (and a comment on the latter by T. J. Smiley) in the 1950s and 1960s. Appendix 1 examines a related aspect of term-for-term replacement in connection with identity in predicate logic. Appendix 2 is a repository for proofs which would otherwise clutter up Section 3.
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页码:49 / 89
页数:41
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