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Transmission of verification. (English) Zbl 1485.03229

The logical consequence can alternatively be thought of as a matter of truthmaker-transformation, according to N. Tennant [Core logic. Oxford: Oxford University Press (2017; Zbl 1386.03001)]. In this paper, the authors show that there exists a general and uniform method of using a core proof of conclusion \(\varphi\) with premises \(\Delta\) to transform \(M\)-relative truthmakers for the premises in \(\Delta\) into an \(M\)-relative truthmaker for \(\varphi\). One of the consequences is that one can extend the methods of truthmaker-transformation so as to deal with the logical consequences that are established by classical core proofs.

MSC:

03F03 Proof theory in general (including proof-theoretic semantics)
03F05 Cut-elimination and normal-form theorems

Citations:

Zbl 1386.03001
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References:

[1] Tennant, N. (2010). Inferential semantics. In Lear, J., & Oliver, A., editors. The Force of Argument: Essays in Honor of Timothy Smiley. London: Routledge, pp. 223-257.
[2] Tennant, N. (2012). Cut for core logic. Review of Symbolic Logic, 5(3), 450-479. · Zbl 1256.03059
[3] Tennant, N. (2015a). Cut for classical core logic. Review of Symbolic Logic, 8(2), 236-256. · Zbl 1337.03082
[4] Tennant, N. (2015b). The relevance of premises to conclusions of core proofs. Review of Symbolic Logic, 8(4), 743-784. · Zbl 1375.03078
[5] Tennant, N. (2017). Core Logic. Oxford: Oxford University Press. · Zbl 1386.03001
[6] Tennant, N. (2018). A logical theory of truthmakers and falsitymakers. In Glanzberg, M., editor. Handbook on Truth. Oxford: Oxford University Press, pp. 355-393.
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