Implicational complexity in intuitionistic arithmetic
نویسندگان
چکیده
منابع مشابه
Proof complexity of intuitionistic implicational formulas
We study implicational formulas in the context of proof complexity of intuitionistic propositional logic (IPC). On the one hand, we give an efficient transformation of tautologies to implicational tautologies that preserves the lengths of intuitionistic extended Frege (EF ) or substitution Frege (SF ) proofs up to a polynomial. On the other hand, EF proofs in the implicational fragment of IPC p...
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We introduce uniform versions of monotone and deep inference proof systems in the setting of bounded arithmetic, relating the size of propositional proofs to forms of proof-theoretic strength in weak fragments of arithmetic. This continues the recent program of studying the complexity of propositional deep inference. In particular this work is inspired by previous work where proofs of the propo...
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We use an alternative graphical representation for formulas in implicational intuitionistic logic in order to obtain and demonstrate results concerning provability. We demonstrate the adequateness of the method in this area, showing that one can easily recognize and prove new results and simplify the proofs of others. As such, we extend a known class of formulas for which uniqueness of -normal ...
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A minimal theorem in a logic L is an L-theorem which is not a nontrivial substitution instance of another L-theorem. Komori (1987) raised the question whether every minimal impli-cational theorem in intuitionistic logic has a unique normal proof in the natural deduction system NJ. The answer has been known to be partially positive and generally negative. It is shown here that a minimal implicat...
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We construct ω-framed Kripke models of i∀1 and iΠ1 non of whose worlds satisfies ∀x∃y(x = 2y∨x = 2y+1) and ∀x, y∃zExp(x, y, z) respectively. This will enable us to show that i∀1 does not prove ¬¬∀x∃y(x = 2y ∨ x = 2y + 1) and iΠ1 does not prove ¬¬∀x, y∃zExp(x, y, z). Therefore, i∀1 0 ¬¬lop and iΠ1 0 ¬¬iΣ1. We also prove that HA 0 lΣ1 and present some remarks about iΠ2. 2000 Mathematics Subject C...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 1981
ISSN: 0022-4812,1943-5886
DOI: 10.2307/2273617