W. Ruitenburg, Basic Logic and Fregean set theory, in Dirk van Dalen Festschrift, Quaestiones Infinitae, 5, edited by H. Barendregt, M. Bezem and J. W. Klop, Utrecht University, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....see that the formula (# A is not provable in VPL, while it is provable in IPL. Visser treated VPL as a preliminary for a study of FPL. VPL, however, was also motivated by a revision of the Brouwer Heyting Kolmogorov (BHK) proof interpretation introduced in Ruitenburg [Rui91] and Ruitenburg [Rui92] (see also Kolmogorov [Kol32] and Heyting [Hey56] Ruitenburg s interpretation for A B is a construction that uses the assumption A to produce a proof of B while the standard BHK interpretation looks like B is a construction that converts proofs of A into proofs of B. Ruitenburg argued ....

W. Ruitenburg, Basic Logic and Fregean set theory, in Dirk van Dalen Festschrift, Quaestiones Infinitae, 5, edited by H. Barendregt, M. Bezem and J. W. Klop, Utrecht University, 1993.

....dispense with the assumption that such states always possibly develop into themselves. There might be information states which in practice simply must be changed, say, in the light of overwhelming and undeniable evidence. In other words, it may make sense not to require reflexivity . Ruitenburg [22], criticizing the BHK interpretation of Int for not explaining the logical connectives in simpler terms, proposed to interpret implication in the following way: ffl a proof of is a construction that uses the assumption to produce a proof of . 1 Using assumption , rather than a proof ....

W. Ruitenburg. Basic logic and Fregean set theory. Technical Report 374, Department of Mathematics, Statistics and Computer Science, Marquette University, 1992.

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