The Deduction Theorem for Strong Propositional Proof Systems
نویسندگان
چکیده
منابع مشابه
A semantical proof of the strong normalization theorem for full propositional classical natural deduction
We give in this paper a short semantical proof of the strong normalization for full propositional classical natural deduction. This proof is an adaptation of reducibility candidates introduced by J.-Y. Girard and simplified to the classical case by M. Parigot.
متن کاملPedagogical Natural Deduction Systems: the Propositional Case
This paper introduces the notion of pedagogical natural deduction systems, which are natural deduction systems with the following additional constraint: all hypotheses made in a proof must be motivated by some example. It is established that such systems are negationless. The expressive power of the pedagogical version of some propositional calculi are studied.
متن کاملAlternative forms of propositional calculus for a given deduction theorem
In a propositional calculus based on combinatory logic it is necessary to have a restriction on the deduction theorem for implication as otherwise Curry's paradox results (see [5]). In [1] and [2] we restricted the deduction theorem for implication as follows: where Δ is any sequence of obs and HX stands for "X is a proposition". Motivation for this deduction theorem was given in [2] using the ...
متن کاملStrong Parallel Repetition Theorem for Quantum XOR Proof Systems
We consider a class of two-prover interactive proof systems where each prover returns a single bit to the verifier and the verifier’s verdict is a function of the XOR of the two bits received. Such proof systems, called XOR proof systems, have previously been shown to characterize MIP (= NEXP) in the case of classical provers but to reside in EXP in the case of quantum provers (who are allowed ...
متن کاملA new proof of the compactness theorem for propositional logic
The compactness theorem for propositional logic states that a demumerable set of propositional formulas is satisfiable if every finite subset is satisfiable. Though there are many different proofs, the underlying combinatorial basis of most of them seems to be Kόnig's lemma on infinite trees (see Smullyan [2], Thomson [3]). We base our proof on a different combinatorial lemma due to R. Rado [1]...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theory of Computing Systems
سال: 2008
ISSN: 1432-4350,1433-0490
DOI: 10.1007/s00224-008-9146-6