An alternative Gentzenisation of RW+∘

Ilic, Mirjana

doi:10.1002/malq.201400084

Cited by 4 publications

(13 citation statements)

References 10 publications

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“…The rules of cut in

{GRW}_{+}^{\circ}

(cf. [3]) have the following forms:

where Π is non‐empty. They are formulated so as to disallow the inference of the modal fallacy without the help of the truth constant t while enabling the proof of the equivalence between

{GRW}_{+}^{\circ}

and

{RW}_{+}^{\circ}

.…”

Section: Cut Elimination In Grw+∘mentioning

confidence: 99%

“…Bearing in mind that every cut is also an mcut, we want to show that every

{GRW}_{+}^{\circ}

‐proof, where cuts are replaced by mcuts, can be transformed into a proof where no mcut occurs and, consequently, where no cut occurs. We formulate in [3] the following Lemma Let π be a

{GRW}_{+}^{\circ}

‐proof with exactly one application of (mcut) and let it be the last inference rule in π. Then π may be transformed into a multicut‐free

{GRW}_{+}^{\circ}

‐proof of the same endsequent.…”

Section: Cut Elimination In Grw+∘mentioning

confidence: 99%

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A note on an alternative Gentzenization of RW+∘

Ilić

2021

Mathematical Logic Qtrly

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In our paper [3], a sequent system for the contraction‐less positive relevant logic with co‐tenability, , is considered. Its sequent system with the rule of cut, which does not involve the truth constant t, is presented, and the proof that it admits the elimination of cut is given. However, in the proof of the cut‐elimination theorem some forms of proofs, which may cause difficulties for the cut‐elimination argument, are not considered. The purpose of this paper is to present them and to re‐prove that admits the elimination of cut.

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“…The rules of cut in

{GRW}_{+}^{\circ}

(cf. [3]) have the following forms:

where Π is non‐empty. They are formulated so as to disallow the inference of the modal fallacy without the help of the truth constant t while enabling the proof of the equivalence between

{GRW}_{+}^{\circ}

and

{RW}_{+}^{\circ}

.…”

Section: Cut Elimination In Grw+∘mentioning

confidence: 99%

“…Bearing in mind that every cut is also an mcut, we want to show that every

{GRW}_{+}^{\circ}

‐proof, where cuts are replaced by mcuts, can be transformed into a proof where no mcut occurs and, consequently, where no cut occurs. We formulate in [3] the following Lemma Let π be a

{GRW}_{+}^{\circ}

‐proof with exactly one application of (mcut) and let it be the last inference rule in π. Then π may be transformed into a multicut‐free

{GRW}_{+}^{\circ}

‐proof of the same endsequent.…”

Section: Cut Elimination In Grw+∘mentioning

confidence: 99%

A note on an alternative Gentzenization of RW+∘

Ilić

2021

Mathematical Logic Qtrly

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“…This paper is organized as follows. In Section 2, we give the sequent calculus GRW • + (discussed in details in [10]), to which our natural deduction calculus has a simple translational relationship. In Section 3, we present the natural deduction system N RW • + .…”

mentioning

confidence: 99%

“…By the translation defined we have: +proof π of γ. We eliminate cut in π, by the procedure given in [10] and then we transform that proof into the cut-free KE-normal GRW • + proof π . Finally, by the translation defined, we transform π into the normal N RW • + -derivation of γ from the empty multiset of open assumptions.…”

mentioning

confidence: 99%