{"product_id":"9783032057402","title":"Computer Science Foundations and Applied Logic","description":"\u003ch1\u003eComputer Science Foundations and Applied Logic\u003c\/h1\u003e \u003ch2\u003eLeitsch, Alexander; Cerna, David Michael; Lolic, Anela\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eSchemata are formal tools for describing inductive reasoning. They opened a new area in the analysis of inductive proofs.\u003c\/p\u003e\n\u003cp\u003eThe book introduces schemata for first-order terms, first-order formulas and first-order inference systems. Based on general first-order schemata, the cut-elimination-by-resolution (CERES) method—developed around the year 2000—is extended to schematic proofs. This extension requires the development of schematic methods for resolution and unification which are defined in this book. The added value of proof schemata compared to other inductive approaches consists in the extension of Herbrand’s theorem to inductive proofs (in the form of Herbrand systems, which can be constructed effectively). An application to an analysis of mathematical proof is given.  The work also contains and extends the newest results on schematic unification and corresponding algorithms.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eCore topics covered:\u003c\/strong\u003e\u003c\/p\u003e\n\u003cul\u003e\n\u003cli\u003efirst-order schemata\u003c\/li\u003e\n\u003cli\u003ecut-elimination by resolution\u003c\/li\u003e\n\u003cli\u003epoint transition systems\u003c\/li\u003e\n\u003cli\u003eschematic resolution\u003c\/li\u003e\n\u003cli\u003eHerbrand systems\u003c\/li\u003e\n\u003cli\u003einductive proof analysis\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003cp\u003eThis volume is the first comprehensive work on first-order schemata and their applications. As such, it will be eminently suitable for researchers and PhD students in logic and computer science either working or with an interest in proof theory, inductive reasoning and automated deduction.  Prerequisites are a firm knowledge of first-order logic, basic knowledge of automated deduction and a background in theoretical computer science.\u003c\/p\u003e\n\u003cp\u003e\u003cstrong\u003eAlexander Leitsch\u003c\/strong\u003e and \u003cstrong\u003eAnela Lolic\u003c\/strong\u003e are affiliated with the Institute of Logic and Computation of the Technische Universität Wien, \u003cstrong\u003eDavid M. Cerna \u003c\/strong\u003ewith the Czech Academy of Sciences, Institute of Computer Science (Ústav informatiky AV ČR, v.v.i.).\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2026-01-03\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783032057402\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-032-05741-9\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 246\u003c\/p\u003e ","brand":"Springer Nature Switzerland","offers":[{"title":"Default Title","offer_id":44395093196940,"sku":"9783032057402","price":161.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783032057402.jpg?v=1774536480","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783032057402","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}