History The late Grisha Mints asked Scott whether a naive set theory could be consistent in modal logic. Here are two modal forms of comprehension: (∃y)(∀x)(x ∈ y ↔ ϕ) (Comp) (∃y)(∀x)(x ∈ y ↔ ϕ) (Comp) At the time (2009) neither he nor Scott knew the answer. In the most commonly used systems, where the Converse Barcan Formula (∀xϕ → ∀xϕ) is derivable, (Comp) follows from another comprehension p...

The BHK interpretation of logical constants is analyzed in terms of a systematic account given by Prawitz, resulting in a reformulation of the BHK interpretation in which the assertability of atomic propositions is determined by Post systems. It is shown that the reformulated BHK interpretation renders more propositions assertable than are provable in intuitionistic propositional logic. Mints’ ...

C. Gürlich,1 S. Scharinger,1 M. Weides,2,* H. Kohlstedt,3 R. G. Mints,4 E. Goldobin,1 D. Koelle,1 and R. Kleiner1 1Physikalisches Institut–Experimentalphysik II and Center for Collective Quantum Phenomena, Universität Tübingen, Auf der Morgenstelle 14, D-72076, Tübingen, Germany 2Institute of Solid State Research and JARA-Fundamentals of Future Information Technology, Research Center Jülich, D-...

Betrachtet werden zahlentheoretische Systeme erster Stufe mit w-Regel und natOrlichen Schlu~regeln im Sinne von Gentzen. Es wird ein primitiv rekursiver Operator N angegeben, der jede Herleitung in eine Normalform (unter EinschluB permutativer Konversionen) 9berf[hrt. Dieser Operator N bearbeitet Herleitungsb~ume "vonder Wurzel zu den Spitzen" und bestimmt for jeden Knoten a der Normalform expl...

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Hacking applied a method involving the labeling of sequent members to the problem of giving a Gentzen-style system for S 5, called L5, formulated with strict implication and no special modal operator. The method was generalized to a labeling of hypersequents by G. Mints. In this paper, we show how this generalization eliminates an “anti-symmetry” in Hacking’s system and greatly simplifies L5. W...

The presentation will contrast the complexity results for proving assertions in classical and intuitionistic logic. The comparison will be built upon the known results for propositional logic and predicate one. The predicate case will be based upon the Mints hierarchy in intuitionistic logic which will be contrasted with its counterpart i.e. the prenex hierarchy in classical logic. The di erenc...

We show that the one can consider proof of the Gentzen'sLK as the continuation passing style(CPS) programs; and the cut-elimination procedure for LK as computation. To be more precise, we observe that Strongly Normalizable(SN) and Church-Rosser(CR) cut-elimination procedure for (intuitionistic decoration of) LKT and LKQ, as presented in Danos et al.(1993), precisely corresponds to call-by-name(...

M. R. Jackson Bonner states that his narrative of Sasanian political history has been written for a general audience by avoiding academic debates and historiographical digressions. This much needed handbook consists nine chapters in which is assessed within the context all its neighbours; from Iberian territories, to Armenian struggles, Chinese embassies, relationships with nomads Hira, develop...

The transition period from Sasanian to Islamic Iran is a key moment for the upcoming history of both Europe and Asia. It indeed crucial put pieces together draw complex picture this central authority which used intermediaries local functionaries different religions. Among others, there were Christian communities. R. Curiel especially Gyselen studied catalogued Iranian copper coinage 7th 8th cen...