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"A proof theory for description logics introduces sequent calculi and natural deduction for some DLs (ALC, ALCQ). Cut-elimination and normalization are proved for the calculi. The author argues that such systems can improve the extraction of computational content from DLs proofs for explanation purposes."

"Tugas Akhir ini mengembangkan ontologi semantic web berbasis DescriptionLogic untuk aplikasi pelestarian digital warisan budaya dan sejarah alam Indonesia.Pembuatan ontologi ini penting untuk alasan interoperability dan memudahkankomputer melakukan penalaran pada konsep-konsep budaya. Metode yangdigunakan untuk membangun ontologi ini adalah metode Uschold and King.Pengembangan diawali dengan penentuan tujuan dan ruang lingkup ontologi denganmerancang berbagai competency question terkait domain pelestarian budaya.Selanjutnya, dilakukan pengumpulan kosakata konsep dengan pemetaan daribasis data E-CHNH yang sudah ada menjadi konsep dan property pada ontologi.Pengembangan ontologi E-CHNH dilakukan dengan menggunakan editor ontologiProt´eg´e. Setelah itu, ontologi di-align dengan ontologi level tinggi CIDOC-CRM(Conceptual Reference Model) dan dilakukan skenario perolehan informasi denganSPARQL sesuai dengan masing-masing competency question. Dari hasil verifikasidan pengecekan konsistensi dengan menggunakan Pellet Reasoner, didapatkan199 class, 284 property, dan 29 instance dengan ekspresivitas ALCH I (D) yangmampu memenuhi tujuan perancangan ontologi.

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This Final Project (Tugas Akhir) has developed a Description-Logic-based semantic

web ontology for digital preservation of cultural heritage and natural history

of Indonesia. Ontology is essential for interoperability and enables computer

to perform reasoning on the concepts of cultural domains. The Uschold and

King methodology was utilized to develop this ontology. Development begins by

determining the purpose and scope of the ontology domain corresponding to the

competency questions. Then the concept vocabularies are gathered by a mapping

process from an existing E-CHNH database to the concepts and properties of

the ontology. The ontology was developed using the ontology editor Prot´eg´e.

Furthermore, the ontology is aligned with the upper level ontology CIDOC-CRM

(Conceptual Reference Model). Each competency question is verified by a suitable

SPARQL query. Verification and consistency checking using the Pellet Reasoner

give a positive result with 199 classes, 284 properties, and 29 instances with

expressivity ALCH I (D) that is able to meet the objectives of the ontology

development project."

"Teori graf adalah sebuah bidang studi interdisipliner yang memiliki berbagai aplikasi dalam pemodelan matematika dan ilmu komputer. Penelitian dalam teori graf tidak hanya bergantung pada teorema baru, namun juga pada konjektura baru. Algoritma penyanggah konjektura dapat digunakan untuk menyanggah suatu konjektura dengan cara mencari sebuah counterexample, seringnya dengan cara memaksimumkan suatu fungsi skor pada graf. Penelitian ini mengusulkan sebuah algoritma penyanggah konjektura baru, disebut sebagai algoritma adaptive Monte Carlo search (AMCS), yang diperoleh dari hasil modifikasi algoritma Monte Carlo tree search. Setelah dievaluasikan berdasarkan keberhasilannya dalam menemukan counterexample untuk beberapa konjektura teori graf, ditemukan bahwa AMCS mengungguli algoritma-algoritma penyanggah konjektura yang sudah ada. Algoritma tersebut kemudian digunakan untuk menyanggah enam konjektura terbuka, dua di antaranya merupakan konjektura teori graf kimia yang diformulasikan oleh Liu et al. pada 2021 dan empat di antaranya diformulasikan menggunakan sistem komputer AutoGraphiX pada 2006. Akhirnya, empat dari enam konjektura terbuka tersebut disanggah secara kuat dengan cara memperumum konjektura yang telah diperoleh menggunakan AMCS untuk menghasilkan keluarga graf yang mengandung banyak counterexample. Algoritma ini diharapkan dapat membantu para peneliti menguji konjektura-konjektura yang berkaitan dengan teori graf secara lebih efektif.

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Graph theory is an interdisciplinary field of study that has various applications in mathematical modeling and computer science. Research in graph theory depends on the creation of not only theorems but also conjectures. Conjecture-refuting algorithms attempt to refute conjectures by searching for counterexamples to those conjectures, often by maximizing certain score functions on graphs. This study proposes a novel conjecture-refuting algorithm, referred to as the adaptive Monte Carlo search (AMCS) algorithm, obtained by modifying the Monte Carlo tree search algorithm. Evaluated based on its success in finding counterexamples to several graph theory conjectures, AMCS outperforms existing conjecture-refuting algorithms. The algorithm is further utilized to refute six open conjectures, two of which were chemical graph theory conjectures formulated by Liu et al. in 2021 and four of which were formulated by the AutoGraphiX computer system in 2006. Finally, four of the open conjectures are strongly refuted by generalizing the counterexamples obtained by AMCS to produce a family of counterexamples. It is expected that the algorithm can help researchers test graph-theoretic conjectures more effectively"

"Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important non perturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions."

"Description logics are knowledge representation formalisms that are highly relevant in computer science, knowledge representation and the semantic web. This is the first introductory textbook published on the subject, suitable for self-study by graduate students and as teaching material for university courses"

"This innovative textbook introduces a new pattern-based approach to learning proof methods in the mathematical sciences. Readers will discover techniques that will enable them to learn new proofs across different areas of pure mathematics with ease. The patterns in proofs from diverse fields such as algebra, analysis, topology and number theory are explored. Specific topics examined include game theory, combinatorics, and Euclidean geometry, enabling a broad familiarity.The author, an experienced lecturer and researcher renowned for his innovative view and intuitive style, illuminates a wide range of techniques and examples from duplicating the cube to triangulating polygons to the infinitude of primes to the fundamental theorem of algebra. Intended as a companion for undergraduate students, this text is an essential addition to every aspiring mathematician’s toolkit."