scholarly journals A Deep Inference System for Differential Linear Logic

2021 ◽  
Vol 353 ◽  
pp. 26-49
Author(s):  
Matteo Acclavio ◽  
Giulio Guerrieri
Keyword(s):  
Linear Logic ◽  
Inference System ◽  
Deep Inference

scholarly journals Deep inference and expansion trees for second-order multiplicative linear logic

2018 ◽  
Vol 29 (8) ◽  
pp. 1030-1060
Author(s):  
LUTZ STRAßBURGER
Keyword(s):  
Original Work ◽  
Linear Logic ◽  
Second Order ◽  
Inference System ◽  
Herbrand’S Theorem ◽  
Deep Inference ◽  
Herbrand's Theorem

In this paper, we introduce the notion of expansion tree for linear logic. As in Miller's original work, we have a shallow reading of an expansion tree that corresponds to the conclusion of the proof, and a deep reading which is a formula that can be proved by propositional rules. We focus our attention to MLL2, and we also present a deep inference system for that logic. This allows us to give a syntactic proof to a version of Herbrand's theorem.

scholarly journals Deep Proof Search in MELL

10.29007/p1fd ◽  
2018 ◽  
Author(s):  
Ozan Kahramanogullari
Keyword(s):  
Classical Logic ◽  
Sequent Calculus ◽  
Linear Logic ◽  
Proof Search ◽  
Proof Construction ◽  
Deep Inference ◽  
Speed Up

The deep inference presentation of multiplicative exponential linear logic (MELL) benefits from a rich combinatoric analysis with many more proofs in comparison to its sequent calculus presentation. In the deep inference setting, all the sequent calculus proofs are preserved. Moreover, many other proofs become available, and some of these proofs are much shorter. However, proof search in deep inference is subject to a greater nondeterminism, and this nondeterminism constitutes a bottleneck for applications. To this end, we address the problem of reducing nondeterminism in MELL by refining and extending our technique that has been previously applied to multiplicative linear logic and classical logic. We show that, besides the nondeterminism in commutative contexts, the nondeterminism in exponential contexts can be reduced in a proof theoretically clean manner. The method conserves the exponential speed-up in proof construction due to deep inference, exemplified by Statman tautologies. We validate the improvement in accessing the shorter proofs by experiments with our implementations.

scholarly journals A Deep Inference System for the Modal Logic S5

Studia Logica ◽  
2007 ◽  
Vol 85 (2) ◽  
pp. 199-214 ◽  
Author(s):  
Phiniki Stouppa
Keyword(s):  
Modal Logic ◽  
Inference System ◽  
Deep Inference

scholarly journals A system of interaction and structure V: the exponentials and splitting

2011 ◽  
Vol 21 (3) ◽  
pp. 563-584 ◽  
Author(s):  
ALESSIO GUGLIELMI ◽  
LUTZ STRAßBURGER
Keyword(s):  
Recent Work ◽  
Process Algebra ◽  
Linear Logic ◽  
Decomposition Theorem ◽  
Quantum Evolution ◽  
Cut Elimination ◽  
Splitting Theorem ◽  
Cut Rule ◽  
Deep Inference ◽  
Turing Complete

System NEL is the mixed commutative/non-commutative linear logic BV augmented with linear logic's exponentials, or, equivalently, it is MELL augmented with the non-commutative self-dual connective seq. NEL is presented in deep inference, because no Gentzen formalism can express it in such a way that the cut rule is admissible. Other recent work shows that system NEL is Turing-complete, and is able to express process algebra sequential composition directly and model causal quantum evolution faithfully. In this paper, we show cut elimination for NEL, based on a technique that we call splitting. The splitting theorem shows how and to what extent we can recover a sequent-like structure in NEL proofs. When combined with a ‘decomposition’ theorem, proved in the previous paper of this series, splitting yields a cut-elimination procedure for NEL.

Aplikasi Peramalan Kebutuhan Beban Listrik Menggunakan Metode Adaptive Neuro Fuzzy Inference System (ANFIS)

2017 ◽  
Vol 3 (1) ◽  
pp. 36-48
Author(s):  
Erwan Ahmad Ardiansyah ◽  
Rina Mardiati ◽  
Afaf Fadhil
Keyword(s):  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Inference System ◽  
Neuro Fuzzy

Prakiraan atau peramalan beban listrik dibutuhkan dalam menentukan jumlah listrik yang dihasilkan. Ini menentukan  agar tidak terjadi beban berlebih yang menyebabkan pemborosan atau kekurangan beban listrik yang mengakibatkan krisis listrik di konsumen. Oleh karena itu di butuhkan prakiraan atau peramalan yang tepat untuk menghasilkan energi listrik. Teknologi softcomputing dapat digunakan  sebagai metode alternatif untuk prediksi beban litrik jangka pendek salah satunya dengan metode  Adaptive Neuro Fuzzy Inference System pada penelitian tugas akhir ini. Data yang di dapat untuk mendukung penelitian ini adalah data dari APD PLN JAWA BARAT yang berisikan laporan data beban puncak bulanan penyulang area gardu induk majalaya dari januari 2011 sampai desember 2014 sebagai data acuan dan data aktual januari-desember 2015. Data kemudian dilatih menggunakan metode ANFIS pada software MATLAB versi b2010. Dari data hasil pelatihan data ANFIS kemudian dilakukan perbandingan dengan data aktual dan data metode regresi meliputi perbandingan anfis-aktual, regresi-aktual dan perbandingan anfis-regresi-aktual. Dari perbandingan disimpulkan bahwa data metode anfis lebih mendekati data aktual dengan rata-rata 1,4%, menunjukan prediksi ANFIS dapat menjadi referensi untuk peramalan beban listrik dimasa depan.

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