Notes:

- Learning semantic parsers
- Semantic deep learning
- Word rewriting systems

Wikipedia:

- Calculus of structures
- Classical logic
- Deep inference
- Deep learning
- Minimal logic
- Modal logic
- Propositional calculus

See also:

100 Best WolframAlpha Videos | Deep Inference 2014

**Deep inference** A Guglielmi – 2015 – opus.bath.ac.uk Deep inference could succinctly be described as an extreme form of linear logic [12]. It is a methodology for designing proof formalisms that generalise Gentzen formalisms, ie the sequent calculus and natural deduction [11]. In a sense, deep inference is obtained by Cited by 14 Related articles All 10 versions

**An energy-efficient and scalable deep learning/inference processor with tetra-parallel MIMD architecture for big data applications** SW Park, J Park, K Bong, D Shin, J Lee… – IEEE transactions on …, 2015 – ieeexplore.ieee.org … wearable system. The implemented 2.5 mm mm deep learning/inference processor is fabricated using 65 nm 8-metal CMOS technology for a battery-powered platform with real-time deep inference and deep learning oper- ation. It … Cited by 4 Related articles All 4 versions

**On the relative proof complexity of deep inference via atomic flows** A Das – arXiv preprint arXiv:1502.05860, 2015 – arxiv.org Abstract: We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore Cited by 3 Related articles All 21 versions

**Behavioural analysis of sessions using the calculus of structures** G Ciobanu, R Horne – … Ershov Memorial Conference on Perspectives of …, 2015 – Springer … The approach is made possible by the calculus of structures — a deep inference proof calculus, generalising the sequent calculus, where inference rules are applied in any context. … Application of rules in a context alternating between structures is known as deep inference. … Cited by 5 Related articles All 4 versions

**No complete linear term rewriting system for propositional logic** A Das, L Straßburger – LIPIcs-Leibniz International Proceedings …, 2015 – drops.dagstuhl.de … 1998 ACM Subject Classification F.4 Mathematical Logic and Formal Languages Keywords and phrases Linear rules, Term rewriting, Propositional logic, Proof theory, Deep inference Digital Object Identifier 10.4230/LIPIcs.RTA.2015.127 1 Introduction … Cited by 4 Related articles All 12 versions

**Modal interpolation via nested sequents** M Fitting, R Kuznets – Annals of pure and applied logic, 2015 – Elsevier … Each structural box in the nested sequent corresponds to a child in the tree. Nested sequent calculi are designed to use the mechanism of deep inference, where rules are applied at an arbitrary node of this tree, ie, arbitrarily deep in the nested structure of the sequent. … Cited by 5 Related articles All 10 versions

**Intuitionistic Modal Logic: A 15-year retrospective** C Stewart, V de Paiva, N Alechina – Journal of Logic and …, 2015 – Oxford Univ Press … Galmiche, produce a new version of label-free sequent calculi for intuitionistic modal logics obtained from the combinations of the axioms T, B, 4 and 5. These calculi use multi-contextual sequent structures, called Tree-sequents, based on the ideas of deep inference and the … Cited by 2 Related articles

**On the Power of Substitution in the Calculus of Structures** N Novakovi?, L Straßburger – ACM Transactions on Computational Logic …, 2015 – dl.acm.org … Recently, Bruscoli and Guglielmi [2009] showed that deep inference proof systems, such as the calculus of structures (CoS) [Guglielmi 2007; Br¨unnler and Tiu 2001; Guglielmi and Straßburger 2001], can provide a natural framework for studying ex- tension and substitution. … Cited by 1 Related articles All 11 versions

**Using Linguistic Analysis to Translate Arabic Natural Language Queries to SPARQL** I AlAgha – arXiv preprint arXiv:1508.01447, 2015 – arxiv.org … In contrast, the queries in the Diseases dataset are mostly straightforward and do not require deep inference. 11. … We first aim to enhance the reasoning capabilities so that the approach can handle comparative, superlative modifiers and other queries that need deep inference. … Cited by 1 Related articles All 5 versions

**Some considerations on the complexity of deep inference** P Bruscoli – cs.bath.ac.uk VALIDITY is co-NP-complete: a certificate stating that a formula is not valid can be checked in polynomial time on the size of the formula … Proof = string of symbols; Proof system = algorithms checking proofs in polytime. … 9 super proof system iff NP = co-NP super = with polysize proofs Related articles

**Bounded arithmetic for deep inference and monotone systems** A Das – cs.swansea.ac.uk Bounded arithmetic has been a fruitful way to relate complexity classes with logical theories and propositional proof systems. For example Paris and Wilkie showed that proofs of ?1- sentences in the theory I? 0, Robinson arithmetic with induction on? 0-formulae, translate to Related articles

**Normalisation and Deep Inference** A Das, A Guglielmi – cs.bath.ac.uk These slides are available at http://cs.bath.ac.uk/ag/t/NDI.pdf Course web page at http://cs.bath .ac.uk/ag/ESSLLI/ Deep inference web site at http://alessio.guglielmi.name/res/cos/ … Introduction Topics and objectives The problem of proof identity … Lecture 1: Open deduction and the Related articles All 4 versions

**Towards an atomic ??-calculus** F He – 2015 – people.bath.ac.uk … We want to study explicit sharing in a calculus with control operators using the concept of atomicity, which comes from deep inference. 1 Introduction and background The methodology of deep inference [6] allows to apply inference rules inside for- mulas, at arbitrary depth. … Related articles All 2 versions

**Multiple Conclusion Linear Logic: Cut Elimination and more** HE III, V de Paiva – vcvpaiva.github.io … level. Clouston et al. give both a deep inference calculus and a display calculus for FILL that admits cut- elimination [6]. Both of these systems are refinements of a larger one called bi-intuitionistic linear logic (BiLL). This logic … Related articles All 5 versions

**Confluent and Natural Cut Elimination in Classical Logic** A Guglielmi, B Ralph – cs.bath.ac.uk … Deep inference is being developed as a modern alter- native to Gentzen systems 4 , and it does offer a solution to the canonicity problem, as we show in this work. Deep inference stipulates that proofs can be composed by the … Related articles All 6 versions

**The Quest for Better Languages** A Guglielmi – 2015 – cs.bath.ac.uk … 11 / 16 Page 12. We improve logic by reducing complexity We control complexity by better composition mechanisms via deep inference [2] t a f … 1382–1393. Available at http://www.ams. org/notices/200811/tx081101382p.pdf. [2] Alessio Guglielmi: Deep Inference. … Related articles

**Implementation and Evaluation of Contextual Natural Deduction for Minimal Logic** BW Paleo – International Andrei Ershov Memorial Conference on …, 2015 – Springer … Contextual inferences have a lot in common with the related idea of deep inference, which has been intensively investigated in the last decade, especially for classical logic (eg [5, 7, 8, 16]) but also for intuitionistic logic [6, 15, 24]. … Related articles All 3 versions

**A note on strictly positive logics and word rewriting systems** LD Beklemishev – arXiv preprint arXiv:1509.00666, 2015 – arxiv.org … As a corollary we obtain examples of undecidable strictly positive normal modal logics. The translation has its counterpart on the level of proofs: we formulate a natural deep inference proof system for strictly positive logics generalizing derivations in word rewriting systems. … Related articles All 5 versions

**Applications of positive and intuitionistic bounded arithmetic to proof complexity** A Das – anupamdas.com … This continues the recent program of studying the complexity of propo- sitional deep inference. In particular this work is inspired by previous work where proofs of the propositional pigeonhole principle in the min- imal deep inference … Related articles All 2 versions

**Phd Confirmation Report** B RALPH – people.bath.ac.uk … Science. Towards a Natural Theory of Quantification for Deep Inference Much of my first year at Bath has been dedicated to immersing myself in what is, to me, largely a new field: the mathematical foundations of computation. … Related articles

**Semantic Deep Learning** H Wang – 2015 – pdfs.semanticscholar.org Page 1. Semantic Deep Learning Hao Wang September 29, 2015 Abstract Artificial intelligence and machine learning research is dedicated to building intelligent ar- tifacts that can imitate or even transcend the cognitive abilities of human beings. … Related articles All 2 versions

**Intuitionistic Modal Logic: A fifteen year retrospective** C Stewart, V de Paiva, N Alechina – 2015 – vcvpaiva.github.io … Galmiche, produce a new version of label-free sequent calculi for intuitionistic modal logics obtained from the combinations of the axioms T, B, 4 and 5. These calculi use multi-contextual sequent structures, called Tree-sequents, based on the ideas of deep inference and the … Related articles All 2 versions

**How Culture Shapes The Reading Of Fairy Tales: A Cross-Cultural Approach** Y Zhang, G Lauer – comparative literature studies, 2015 – JSTOR A large body of research consistently found cultural differences in cognition between Westerners and East Asians. We undertook a study to explore whether cultur… Related articles All 4 versions

**Proof search in nested sequent calculi** B Lellmann, E Pimentel – Logic for Programming, Artificial Intelligence, …, 2015 – Springer … time. This piecewise treatment could be seen as one of the main features of nested sequent calculi and deep inference in general [7]. In particular, it is the key to modularity for nested and linear nested sequent calculi [9, 18]. … Cited by 8 Related articles All 3 versions

**Herbrand’s Fundamental Theorem-an encyclopedia article** CP Wirth – arXiv preprint arXiv:1503.01412, 2015 – arxiv.org … Rules of Passage: The following six logical equivalences may be used for rewriting from left to right (prenex direction) and from right to left (anti-prenex direction), resulting in twelve deep inference rules (where B is a formula in which the variable x does not occur free): (1) ¬?x … Related articles All 4 versions

**Applications of advanced analytics methods in sas enterprise miner** VS Jotsov, E Iliev – Intelligent Systems’ 2014, 2015 – Springer … The usage of Vi constraints one by one doesn’t always form the necessary closed area. Revealing Vi and other constraints one by one helps represent the resolution process in its dynamics and hence make deep inference to the problem. … Cited by 2 Related articles All 3 versions

**The succinctness of the cover modality** H van Ditmarsch, P Iliev – Journal of Applied Non-Classical Logics, 2015 – Taylor & Francis … of modal logic. However, when studying, for example, interpolation properties for modal systems (Bílková , 2009 Bílková, M. (2009). A note on uniform interpolation proofs in modal deep inference calculi. N. Bezhanishvili, S. Löbner … Related articles All 3 versions

**Minimal type inference for linked data consumers** G Ciobanu, R Horne, V Sassone – … of Logical and Algebraic Methods in …, 2015 – Elsevier We provide an introduction to the Web of Linked Data from the perspective of a Web developer who would like to build an application using Linked Data. We identi. Cited by 6 Related articles All 4 versions

**An Imperative Focus On Semantic Web Principles, Logics And Its Application** NS Kumar, M Dinakaran – academia.edu … longevity. Here are some of the following: 2.1.1Rules and Inference Systems: The alternate perspective of rule specification and deep inference methods were designed and developed for easier conclusion. Rules Interchange … Related articles All 2 versions

**Dependent Communication in Type Theory** N Guenot, D Gustafsson, N Pouillard – nicolaspouillard.fr … From a proof-theoretical viewpoint, this is related to the need to decompose the formulas not only at top level, a question adressed partially using hypersequents [2] and more thoroughly studied in the setting of deep inference [10]. … Related articles

**Proof checking and logic programming** D Miller – International Symposium on Logic-Based Program …, 2015 – Springer … introduce, in part, to support automation of theorem proving. Still more structures can be found that can be accepted as proofs, such as proof nets, matings, deep inference, and winning strategies. In this paper, I will outline a multi … Cited by 1 Related articles All 17 versions

**Bringing Strategic Rewriting into the Mainstream** E Balland, H Cirstea, PE Moreau – 2015 – hal.inria.fr … In this case, clever normalisation strategies allow an efficient representation of the associative- commutative with neutral element operators while strategy constructs allow the management of the high level of non determinism introduced by deep inference. … Related articles All 5 versions

**Unsatisfiability proofs in SAT solving with parity reasoning** A Rebola-Pardo, T Philipp – 2015 – emcl-study.eu Page 1. Unsatisfiability Proofs in SAT Solving with Parity Reasoning Author: Adrián Rebola-Pardo Supervisors: Prof. Dr. habil. Steffen Hölldobler Tobias Philipp (TU Dresden) 22nd November 2015 Page 2. … Cited by 1 Related articles All 3 versions

**The consistency and complexity of multiplicative additive system virtual** R Horne – 2015 – dr.ntu.edu.sg … Keywords: proof theory, deep inference, non-commutative logic. 1 Introduction … Tiu [50] established that a calculus with a self-dual non-commutative operator called BV cannot be expressed without a technique enabled by the calculus of structures, called deep inference. … Cited by 3 Related articles All 4 versions

**Metabolic free energy and biological codes: a ‘Data Rate Theorem’aging model** R Wallace – Bulletin of mathematical biology, 2015 – Springer … That is, \(R(D)\) is always a reverse J-shaped curve. This will prove crucial for the overall argument. Indeed, convexity is an exceedingly powerful mathematical condition and permits deep inference (eg, Rockafellar 1970). Ellis (1985, Ch. … Cited by 5 Related articles All 11 versions

**Language to Code: Learning Semantic Parsers for If-This-Then-That Recipes**. C Quirk, RJ Mooney, M Galley – ACL (1), 2015 – cs.utexas.edu Page 1. Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing, pages 878–888, Beijing, China, July 26-31, 2015. cO2015 Association for Computational Linguistics … Cited by 8 Related articles All 8 versions

**Substructural negations** T Onishi – The Australasian Journal of Logic, 2015 – ojs.victoria.ac.nz … A similar phenomenon is ob- served with Bi-Intuitionistic logic [26]. Several extensions to handle with the difficulty have been proposed such as labelled sequent calculus, nested sequent calculus, and deep inference system [6, 19, 20, 21, 26, 27, 28]. … Cited by 3 Related articles All 2 versions

**Deduction modulo theory** G Dowek – arXiv preprint arXiv:1501.06523, 2015 – pdfs.semanticscholar.org … Propositional logic, linear logic, deep inference, equational logic, explicit substitution calculi, etc. are examples of such systems. From this point of view, Predicate logic appears more as the ultimate goal of the journey, than as its starting point. … Related articles All 14 versions

**Proof nets/Essential nets for MFILL? and MBILL?(Multiplicative Full Intuitionistic and Bi-Intuitionistic Linear Logic without Units)**. G Bellin – 2015 – cs.ioc.ee … nested sequent calculus. ? (Goré et al. 2013) considered the display calculus and deep inference. ? (Crolard 2004) uses a system of annotations on the sequent calculus to ensure constructivity of bi-intuitionistic logic. It provides … Related articles All 3 versions

**Investigations into Linear Logic with Fixed-Point Operators** F Gavazzo – 2015 – illc.uva.nl … Page 4. logical systems. We provide sequent calculi for all the logics investigated, and a deep inference [63] system for the extension of classical linear logic with least and greatest fixed point operators. … 104 4.2 A Deep Inference Calculus . . . . . … Related articles All 3 versions

**On nested sequents for constructive modal logics** A Das, R Arisaka – arXiv preprint arXiv:1505.06896, 2015 – arxiv.org … Proof. By induction on the structure of ?{ }. For showing soundness of the inference rules with one premise, we first have to verify that the deep inference reasoning remains valid in the constructive setting. This is shown in the following three lemmas. Lemma 4.3. … Cited by 2 Related articles All 27 versions

**Wave-style token machines and quantum lambda calculi** UD Lago, M Zorzi – arXiv preprint arXiv:1502.04774, 2015 – arxiv.org Page 1. S. Alves and I. Cervesato (Eds): Third International Workshop on Linearity 2014 (LINEARITY’14) EPTCS 176, 2015, pp. 64–78, doi:10.4204/EPTCS.176.6 c U. Dal Lago & M. Zorzi This work is licensed under the Creative Commons Attribution License. … Cited by 6 Related articles All 9 versions

**Probabilistic reasoning in diagnosing causes of program failures** J Xu, R Chen, Z Du – Software Testing, Verification and …, 2015 – Wiley Online Library … uncertain. So, some deep inference with causality is certainly welcomed. The work focus of this paper is to handle the great uncertainty in software diagnosis decently in the context of single fault and multiple faults. Because … Related articles All 4 versions

**Exponential Lower Bounds for AC 0-Frege Imply Superpolynomial Frege Lower Bounds** Y Filmus, T Pitassi, R Santhanam – ACM Transactions on Computation …, 2015 – dl.acm.org … PROOF. All rules of PK are closed under substitution. The preceding lemma shows that we can lift a proof of a sequent by attaching stuff “below.” The next lemma shows that we can also lift a proof by attachingstuff “above”; this corresponds to deep inference. Definition 4.11. … Cited by 1 Related articles All 13 versions

[BOOK] **An Information Approach to Mitochondrial Dysfunction: Extending Swerdlow’s Hypothesis** R Wallace – 2015 – books.google.com Page 1. || || | 18′ 0. |->| 0107010 World Scientific Series in Information Studies – Wo | . 4 AN INFORMATION APPROACH TO MITOCHONDRIAL DYSFUNCTION Extending SWerdlow’s Hypothesis Rodrick Wallace W9 World Scientific Page 2. … Cited by 5 Related articles All 3 versions

**Tree-sequent calculi and decision procedures for intuitionistic modal logics** D Galmiche, Y Salhi – Journal of Logic and Computation, 2015 – Oxford Univ Press We use cookies to enhance your experience on our website. By continuing to use our website, you are agreeing to our use of cookies. You can change your cookie settings at any time. Find out more. Skip Navigation. … Related articles All 3 versions

**Cut-free proof systems for Geach logics** M Fitting – IfCoLog J. Logics Appl, 2015 – collegepublications.co.uk Page 27. Cut-Free Proof Systems for Geach Logics Melvin Fitting melvinfitting. org melvin. fitting@ gmail. edu Abstract Prefixed tableaus for modal logics have been around since the early 1970s, and are quite familiar by now. … Cited by 2 Related articles All 2 versions

**Guide to the Grigori Mints Papers** D Hartwig – pdf.oac.cdlib.org Page 1. http://oac.cdlib.org/findaid/ark:/13030/c8h1356d No online items Guide to the Grigori Mints Papers SC1225 1 Guide to the Grigori Mints Papers Daniel Hartwig Stanford University. Libraries.Department of Special Collections … All 2 versions